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Multiplication Facts Worksheets

Welcome to the multiplication facts worksheets page at Math-Drills.com! On this page, you will find Multiplication worksheets for practicing multiplication facts at various levels and in a variety of formats. This is our most popular page due to the wide variety of worksheets for multiplication available. Or it could be that learning multiplication facts and multiplication strategies are essential to many topics in mathematics beyond third grade math.

Learning multiplication facts to the point of quick recall should be a goal for all students and will serve them well in their math studies. Multiplication facts are actually easier to learn than you might think. First of all, it is only essential to learn the facts from 1 to 9. Somewhere along the way students can learn that anything multiplied by zero is zero. Hopefully, that is an easy one. Students also need to learn to multiply by ten as a precursor to learning how to multiply other powers of ten. After those three skills are learned, everything else is long multiplication. Multiplying by 11 is actually two-digit multiplication. Now, learning fact tables of 11 and beyond will do no harm to those students who are keen and able to learn these things quickly, and it might help them figure out how many eggs are in a gross faster than anyone else, but keep it simple for those students who struggle a bit more.

Most Popular Multiplication Facts Worksheets this Week

Multiplication Facts Tables

The multiplication tables with individual questions include a separate box for each number. In each box, the single number is multiplied by every other number with each question on one line. The tables may be used for various purposes such as introducing the multiplication tables, skip counting, as a lookup table, patterning activities, and memorizing.

• Multiplication Facts Tables from 1 to 12 Multiplication Facts Tables in Gray 1 to 12 Multiplication Facts Tables in Gray 1 to 12 (Answers Omitted) Multiplication Facts Tables in Color 1 to 12 Multiplication Facts Tables in Color 1 to 12 (Answers Omitted) Multiplication Facts Tables in Montessori Colors 1 to 12 Multiplication Facts Tables in Montessori Colors 1 to 12 (Answers Omitted)
• Multiplication Facts Tables from 0 to 11 Multiplication Facts Tables in Gray 0 to 11 Multiplication Facts Tables in Gray 0 to 11 (Answers Omitted) Multiplication Facts Tables in Color 0 to 11 Multiplication Facts Tables in Color 0 to 11 (Answers Omitted) Multiplication Facts Tables in Montessori Colors 0 to 11 Multiplication Facts Tables in Montessori Colors 0 to 11 (Answers Omitted)
• Multiplication Facts Tables from 13 to 24 Multiplication Facts Tables in Gray 13 to 24 Multiplication Facts Tables in Gray 13 to 24 (Answers Omitted) Multiplication Facts Tables in Color 13 to 24 Multiplication Facts Tables in Color 13 to 24 (Answers Omitted)

The compact multiplication tables are basically lookup charts. To look up a multiplication fact, find the first factor in the column header and the second factor in the row headers; then use straight edges, your fingers or your eyes to find where the column and row intersect to get the product. These tables are better than the previous tables for finding patterns, but they can be used in similar ways. Each PDF includes a filled out table page and a blank table page. The blank tables can be used for practice or assessment. You might also make a game out of it, such as "Pin the Fact on the Table" (a play on Pin the Tail on the Donkey). Students are given a product (answer) and they pin it on an enlarged version or the table (photocopier enlargement, interactive whiteboard, overhead projector, etc.). Paper-saving versions with multiple tables per page are included. The left-handed versions of the multiplication tables recognize that students who use their left hands might block the row headings on the right-handed versions.

• Compact Multiplication Facts Tables from 1 to 7 Multiplication Table to 49 (1 Filled and 1 Blank) Multiplication Table to 49 (9 Filled and 9 Blank) Left-Handed Multiplication Table to 49 (1 Filled and 1 Blank) Left-Handed Multiplication Table to 49 (9 Filled and 9 Blank)
• Compact Multiplication Facts Tables from 1 to 9 Multiplication Table to 81 (1 Filled and 1 Blank) Multiplication Table to 81 (6 Filled and 6 Blank) Left-Handed Multiplication Table to 81 (1 Filled and 1 Blank) Left-Handed Multiplication Table to 81 (6 Filled and 6 Blank)
• Compact Multiplication Facts Tables from 1 to 10 Multiplication Table to 100 (1 Filled and 1 Blank) Multiplication Table to 100 (6 Filled and 6 Blank) Left-Handed Multiplication Table to 100 (1 Filled and 1 Blank) Left-Handed Multiplication Table to 100 (6 Filled and 6 Blank)
• Compact Multiplication Facts Tables from 1 to 12 Multiplication Table to 144 (1 Filled and 1 Blank) Multiplication Table to 144 (4 Filled and 4 Blank) Left-Handed Multiplication Table to 144 (1 Filled and 1 Blank) Left-Handed Multiplication Table to 144 (4 Filled and 4 Blank)

Five Minute Multiplication Frenzies

Five minute frenzy charts are 10 by 10 grids that are used for multiplication fact practice (up to 12 x 12) and improving recall speed. They are very much like compact multiplication tables, but all the numbers are mixed up, so students are unable to use skip counting to fill them out. In each square, students write the product of the column number and the row number. They try to complete the chart in a set time with an accuracy goal (such as less than five minutes and score 98 percent or better).

It is important to note here that you should NOT have students complete five minute frenzies if they don't already know all of the multiplication facts that appear on them. If you want them to participate with the rest of the class, cross off the rows and columns that they don't know and have them complete a modified version. Remember, these charts are for practice and improving recall, not a teaching tool by itself.

Students who write with their left hands may cover the row headings on the right-handed versions, so the left-handed versions have the row headings on the other side.

• Multiplication Frenzies from 0 to 9 Multiplication Frenzy with Factors from 0 to 9 ( 1 Chart Per Page) Multiplication Frenzy with Factors from 0 to 9 ( 4 Charts Per Page) Left-Handed Multiplication Frenzy with Factors from 0 to 9 ( 1 Chart Per Page) Left-Handed Multiplication Frenzy with Factors from 0 to 9 ( 4 Charts Per Page)
• Multiplication Frenzies from 1 to 10 Multiplication Frenzy with Factors from 1 to 10 ( 1 Chart Per Page) Multiplication Frenzy with Factors from 1 to 10 ( 4 Charts Per Page) Left-Handed Multiplication Frenzy with Factors from 1 to 10 ( 1 Chart Per Page) Left-Handed Multiplication Frenzy with Factors from 1 to 10 ( 4 Charts Per Page)
• Multiplication Frenzies from 2 to 12 Multiplication Frenzy with Factors from 2 to 12 ( 1 Chart Per Page) Multiplication Frenzy with Factors from 2 to 12 ( 4 Charts Per Page) Left-Handed Multiplication Frenzy with Factors from 2 to 12 ( 1 Chart Per Page) Left-Handed Multiplication Frenzy with Factors from 2 to 12 ( 4 Charts Per Page)
• Multiplication Frenzies from 5 to 15 Multiplication Frenzy with Factors from 5 to 15 ( 1 Chart Per Page) Multiplication Frenzy with Factors from 5 to 15 ( 4 Charts Per Page) Left-Handed Multiplication Frenzy with Factors from 5 to 15 ( 1 Chart Per Page) Left-Handed Multiplication Frenzy with Factors from 5 to 15 ( 4 Charts Per Page)

Multiplication Facts up to the 7 Times Table

This section includes math worksheets for practicing multiplication facts to from 0 to 49. There are two worksheets in this section that include all of the possible questions exactly once on each page: the 49 question worksheet with no zeros and the 64 question worksheet with zeros. All others either contain all the possible questions plus some repeats or a unique subset of the possible questions.

• Multiplication Facts up to the 7 Times Table (No Zeros) Multiplication Facts to 49 ( 100 Questions) ( No Zeros ) ✎ Multiplication Facts to 49 ( 50 Questions ) ( No Zeros ) ✎ Multiplication Facts to 49 ( 49 Questions) ( No Zeros ) ✎ Multiplication Facts to 49 ( 25 Questions ) ( No Zeros ) ✎
• Multiplication Facts up to the 7 Times Table (With Zeros) Multiplication Facts to 49 ( 100 Questions) ( With Zeros ) ✎ Multiplication Facts to 49 ( 64 Questions) ( With Zeros ) ✎ Multiplication Facts to 49 ( 50 Questions ) ( With Zeros ) ✎ Multiplication Facts to 49 ( 25 Questions ) ( With Zeros ) ✎
• Horizontally Arranged Multiplication Facts up to the 5 Times Table Horizontally Arranged Multiplication Facts with Products to 25 ( 100 Questions) ✎ Horizontally Arranged Multiplication Facts with Products to 25 ( 50 Questions ) ✎ Horizontally Arranged Multiplication Facts with Products to 25 ( 25 Questions ; Large Print) ✎
• Horizontally Arranged Multiplication Facts up to the 6 Times Table Horizontally Arranged Multiplication Facts with Products to 36 ( 100 Questions) ✎ Horizontally Arranged Multiplication Facts with Products to 36 ( 50 Questions ) ✎ Horizontally Arranged Multiplication Facts with Products to 36 ( 25 Questions ; Large Print) ✎
• Horizontally Arranged Multiplication Facts up to the 7 Times Table Horizontally Arranged Multiplication Facts with Products to 49 ( 100 Questions) ✎ Horizontally Arranged Multiplication Facts with Products to 49 ( 50 Questions ) ✎ Horizontally Arranged Multiplication Facts with Products to 49 ( 25 Questions ; Large Print) ✎

When a student first learns multiplication facts, try not to overwhelm them with the entire multiplication table. The following worksheets include one row of the facts in order with the target digit on the bottom and one row with the target digit on the top. The remaining rows include each of the facts once, but the target digit is randomly placed on the top or the bottom and the facts are randomly mixed on each row.

• Multiplying (1 to 7) by Individual Facts Multiplying (1 to 7) by 1 ✎ Multiplying (1 to 7) by 2 ✎ Multiplying (1 to 7) by 3 ✎ Multiplying (1 to 7) by 4 ✎ Multiplying (1 to 7) by 5 ✎ Multiplying (1 to 7) by 6 ✎ Multiplying (1 to 7) by 7 ✎
• Multiplying (0 to 7) by Individual Facts Multiplying (0 to 7) by 0 ✎ Multiplying (0 to 7) by 1 ✎ Multiplying (0 to 7) by 2 ✎ Multiplying (0 to 7) by 3 ✎ Multiplying (0 to 7) by 4 ✎ Multiplying (0 to 7) by 5 ✎ Multiplying (0 to 7) by 6 ✎ Multiplying (0 to 7) by 7 ✎
• Horizontally Arranged Multiplying (1 to 7) by Individual Facts (100 Questions per page) Horizontally Arranged Multiplying (1 to 7) by 1 ( 100 Questions ) ✎ Horizontally Arranged Multiplying (1 to 7) by 2 ( 100 Questions ) ✎ Horizontally Arranged Multiplying (1 to 7) by 3 ( 100 Questions ) ✎ Horizontally Arranged Multiplying (1 to 7) by 4 ( 100 Questions ) ✎ Horizontally Arranged Multiplying (1 to 7) by 5 ( 100 Questions ) ✎ Horizontally Arranged Multiplying (1 to 7) by 6 ( 100 Questions ) ✎ Horizontally Arranged Multiplying (1 to 7) by 7 ( 100 Questions ) ✎
• Horizontally Arranged Multiplying (1 to 7) by Individual Facts (50 Questions per page) Horizontally Arranged Multiplying (1 to 7) by 1 ( 50 Questions ) ✎ Horizontally Arranged Multiplying (1 to 7) by 2 ( 50 Questions ) ✎ Horizontally Arranged Multiplying (1 to 7) by 3 ( 50 Questions ) ✎ Horizontally Arranged Multiplying (1 to 7) by 4 ( 50 Questions ) ✎ Horizontally Arranged Multiplying (1 to 7) by 5 ( 50 Questions ) ✎ Horizontally Arranged Multiplying (1 to 7) by 6 ( 50 Questions ) ✎ Horizontally Arranged Multiplying (1 to 7) by 7 ( 50 Questions ) ✎
• Horizontally Arranged Multiplying (1 to 7) by Individual Facts (25 Questions per page) Horizontally Arranged Multiplying (1 to 7) by 1 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Multiplying (1 to 7) by 2 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Multiplying (1 to 7) by 3 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Multiplying (1 to 7) by 4 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Multiplying (1 to 7) by 5 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Multiplying (1 to 7) by 6 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Multiplying (1 to 7) by 7 ( 25 Questions ; Large Print) ✎
• Multiplying Doubles Multiplying Doubles up to 7 x 7

Multiplication Facts up to the 9 Times Table

This section includes math worksheets for practicing multiplication facts from 0 to 81. There are three worksheets (marked with *) in this section that include all of the possible questions in the specified range exactly once on each page: the 64 question worksheet with no zeros or ones, the 81 question worksheet with no zeros, and the 100 question worksheet with zeros. All others either contain all the possible questions plus some repeats or a unique subset of the possible questions.

• Multiplication Facts up to the 9 Times Table (No Zeros or Ones) Multiplication Facts to 81 ( 100 Questions) ( No Zeros or Ones ) ✎ Multiplication Facts to 81 ( 81 Questions) ( No Zeros or Ones ) ✎ *Multiplication Facts to 81 ( 64 Questions) ( No Zeros or Ones ) ✎ Multiplication Facts to 81 ( 50 Questions ) ( No Zeros or Ones ) ✎ Multiplication Facts to 81 ( 25 Questions ) ( No Zeros or Ones ) ✎
• Multiplication Facts up to the 9 Times Table (No Zeros) Multiplication Facts to 81 ( 100 Questions) ( No Zeros ) ✎ *Multiplication Facts to 81 ( 81 Questions) ( No Zeros ) ✎ Multiplication Facts to 81 ( 50 Questions ) ( No Zeros ) ✎ Multiplication Facts to 81 ( 25 Questions ) ( No Zeros ) ✎
• Multiplication Facts up to the 9 Times Table (With Zeros) *Multiplication Facts to 81 ( 100 Questions) ( With Zeros ) ✎ Multiplication Facts to 81 ( 81 Questions) ( With Zeros ) ✎ Multiplication Facts to 81 ( 50 Questions ) ( With Zeros ) ✎ Multiplication Facts to 81 ( 25 Questions ) ( With Zeros ) ✎
• Horizontally Arranged Multiplication Facts up to the 8 Times Table Horizontally Arranged Multiplication Facts with Products to 64 ( 100 Questions) ✎ Horizontally Arranged Multiplication Facts with Products to 64 ( 50 Questions ) ✎ Horizontally Arranged Multiplication Facts with Products to 64 ( 25 Questions ; Large Print) ✎
• Horizontally Arranged Multiplication Facts up to the 9 Times Table Horizontally Arranged Multiplication Facts with Products to 81 ( 100 Questions) ✎ Horizontally Arranged Multiplication Facts with Products to 81 ( 50 Questions ) ✎ Horizontally Arranged Multiplication Facts with Products to 81 ( 25 Questions ; Large Print) ✎

When learning multiplication facts, it is useful to have each fact isolated on a set of practice questions to help reinforce the individual fact. The following worksheets isolate each fact. These worksheets can be used as practice sheets, assessment sheets, or in conjunction with another teaching strategy such as manipulative use.

• Multiplying (1 to 9) by Individual Facts (81 Questions per Page) Multiplying (1 to 9) by 0 ( 81 Questions) ✎ Multiplying (1 to 9) by 1 ( 81 Questions) ✎ Multiplying (1 to 9) by 2 ( 81 Questions) ✎ Multiplying (1 to 9) by 3 ( 81 Questions) ✎ Multiplying (1 to 9) by 4 ( 81 Questions) ✎ Multiplying (1 to 9) by 5 ( 81 Questions) ✎ Multiplying (1 to 9) by 6 ( 81 Questions) ✎ Multiplying (1 to 9) by 7 ( 81 Questions) ✎ Multiplying (1 to 9) by 8 ( 81 Questions) ✎ Multiplying (1 to 9) by 9 ( 81 Questions) ✎ Multiplying (1 to 9) by (3 and 4) ( 81 Questions) ✎ Multiplying (1 to 9) by (4 and 5) ( 81 Questions) ✎ Multiplying (1 to 9) by (5 and 6) ( 81 Questions) ✎ Multiplying (1 to 9) by (6 and 7) ( 81 Questions) ✎ Multiplying (1 to 9) by (7 and 8) ( 81 Questions) ✎ Multiplying (1 to 9) by (8 and 9) ( 81 Questions) ✎ Multiplying (1 to 9) by (6 to 8) ( 81 Questions) ✎ Multiplying (1 to 9) by (7 to 9) ( 81 Questions) ✎ Multiplying (1 to 9) by (6 to 9) ( 81 Questions) ✎
• Multiplying (2 to 9) by Individual Facts (100 Questions per Page) Multiplying (2 to 9) by (6 to 8) ( 100 Questions) ✎ Multiplying (2 to 9) by (7 to 9) ( 100 Questions) ✎
• Multiplying (1 to 9) by Individual Facts (36 Questions per Page; Large Print) Multiplying (1 to 9) by 0 ( 36 Questions) ✎ Multiplying (1 to 9) by 1 ( 36 Questions) ✎ Multiplying (1 to 9) by 2 ( 36 Questions) ✎ Multiplying (1 to 9) by 3 ( 36 Questions) ✎ Multiplying (1 to 9) by 4 ( 36 Questions) ✎ Multiplying (1 to 9) by 5 ( 36 Questions) ✎ Multiplying (1 to 9) by 6 ( 36 Questions) ✎ Multiplying (1 to 9) by 7 ( 36 Questions) ✎ Multiplying (1 to 9) by 8 ( 36 Questions) ✎ Multiplying (1 to 9) by 9 ( 36 Questions) ✎ Multiplying (1 to 9) by (6 and 7) ( 36 Questions) ✎ Multiplying (1 to 9) by (7 and 8) ( 36 Questions) ✎ Multiplying (1 to 9) by (8 and 9) ( 36 Questions) ✎ Multiplying (1 to 9) by (6 to 8) ( 36 Questions) ✎ Multiplying (1 to 9) by (7 to 9) ( 36 Questions) ✎ Multiplying (1 to 9) by (6 to 9) ( 36 Questions) ✎
• Horizontally Arranged Multiplying (0 to 9) by Individual Facts (100 Questions per Page) Horizontally Arranged Multiplying ( 0 to 9 ) by 0 ( 100 Questions) ✎ Horizontally Arranged Multiplying ( 0 to 9 ) by 1 ( 100 Questions) ✎ Horizontally Arranged Multiplying ( 0 to 9 ) by 2 ( 100 Questions) ✎ Horizontally Arranged Multiplying ( 0 to 9 ) by 3 ( 100 Questions) ✎ Horizontally Arranged Multiplying ( 0 to 9 ) by 4 ( 100 Questions) ✎ Horizontally Arranged Multiplying ( 0 to 9 ) by 5 ( 100 Questions) ✎ Horizontally Arranged Multiplying ( 0 to 9 ) by 6 ( 100 Questions) ✎ Horizontally Arranged Multiplying ( 0 to 9 ) by 7 ( 100 Questions) ✎ Horizontally Arranged Multiplying ( 0 to 9 ) by 8 ( 100 Questions) ✎ Horizontally Arranged Multiplying ( 0 to 9 ) by 9 ( 100 Questions) ✎
• Horizontally Arranged Multiplying (0 to 9) by Individual Facts (50 Questions per Page) Horizontally Arranged Multiplying ( 0 to 9 ) by 0 ( 50 Questions ) ✎ Horizontally Arranged Multiplying ( 0 to 9 ) by 1 ( 50 Questions ) ✎ Horizontally Arranged Multiplying ( 0 to 9 ) by 2 ( 50 Questions ) ✎ Horizontally Arranged Multiplying ( 0 to 9 ) by 3 ( 50 Questions ) ✎ Horizontally Arranged Multiplying ( 0 to 9 ) by 4 ( 50 Questions ) ✎ Horizontally Arranged Multiplying ( 0 to 9 ) by 5 ( 50 Questions ) ✎ Horizontally Arranged Multiplying ( 0 to 9 ) by 6 ( 50 Questions ) ✎ Horizontally Arranged Multiplying ( 0 to 9 ) by 7 ( 50 Questions ) ✎ Horizontally Arranged Multiplying ( 0 to 9 ) by 8 ( 50 Questions ) ✎ Horizontally Arranged Multiplying ( 0 to 9 ) by 9 ( 50 Questions ) ✎
• Horizontally Arranged Multiplying (0 to 9) by Individual Facts (25 Questions per Page; Large Print) Horizontally Arranged Multiplying ( 0 to 9 ) by 0 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Multiplying ( 0 to 9 ) by 1 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Multiplying ( 0 to 9 ) by 2 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Multiplying ( 0 to 9 ) by 3 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Multiplying ( 0 to 9 ) by 4 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Multiplying ( 0 to 9 ) by 5 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Multiplying ( 0 to 9 ) by 6 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Multiplying ( 0 to 9 ) by 7 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Multiplying ( 0 to 9 ) by 8 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Multiplying ( 0 to 9 ) by 9 ( 25 Questions ; Large Print) ✎
• Multiplying Doubles Multiplying Doubles up to 9 x 9

Some students are a little more motivated when learning is turned into a game. Multiplication bingo encourages students to recall multiplication facts in an environment of competition.

• Multiplication Bingo Game Multiplication Bingo Cards for Facts 1 to 9 Multiplication Bingo Facts 1 to 9 Teacher Call Cards

Multiplication Facts up to the 10 Times Table

Multiplying by 10 is often a lesson itself, but here we have included it with the other facts. Students usually learn how to multiply by 10 fairly quickly, so this section really is not a whole lot more difficult than the multiplication facts to 81 section.

• Multiplication Facts up to the 10 Times Table (No Zeros or Ones) Multiplication Facts to 100 ( 100 Questions) ( No Zeros or Ones ) ✎ *Multiplication Facts to 100 ( 81 Questions) ( No Zeros or Ones ) ✎ Multiplication Facts to 100 ( 50 Questions ) ( No Zeros or Ones ) ✎ Multiplication Facts to 100 ( 25 Questions ) ( No Zeros or Ones ) ✎
• Multiplication Facts up to the 10 Times Table (No Zeros) *Multiplication Facts to 100 ( 100 Questions) ( No Zeros ) ✎ Multiplication Facts to 100 ( 50 Questions ) ( No Zeros ) ✎ Multiplication Facts to 100 ( 25 Questions ) ( No Zeros ) ✎
• Multiplication Facts up to the 10 Times Table (With Zeros) Multiplication Facts to 100 ( 100 Questions) ( With Zeros ) ✎ Multiplication Facts to 100 ( 50 Questions ) ( With Zeros ) ✎ Multiplication Facts to 100 ( 25 Questions ) ( With Zeros ) ✎
• Horizontally Arranged Multiplication Facts up to the 10 Times Table Horizontally Arranged Multiplication Facts to 10 × 10 = 100 ( 100 Questions) ✎ Horizontally Arranged Multiplication Facts to 10 × 10 = 100 ( 50 Questions ) ✎

Some students find it easier to focus on one multiplication fact at a time. These multiplication worksheets include some repetition, of course, as there is only one thing to multiply by. Once students practice a few times, these facts will probably get stuck in their heads for life. Some of the later versions include a range of focus numbers. In those cases, each question will randomly have one of the focus numbers in question. For example, if the range is 6 to 8, the question might include a 6, 7 or 8 or more than one depending on which other factor was chosen for the second factor.

• Multiplying (1 to 10) by Individual Facts (100 Questions per Page) Multiplying (1 to 10) by 0 ( 100 Questions) ✎ Multiplying (1 to 10) by 1 ( 100 Questions) ✎ Multiplying (1 to 10) by 2 ( 100 Questions) ✎ Multiplying (1 to 10) by 3 ( 100 Questions) ✎ Multiplying (1 to 10) by 4 ( 100 Questions) ✎ Multiplying (1 to 10) by 5 ( 100 Questions) ✎ Multiplying (1 to 10) by 6 ( 100 Questions) ✎ Multiplying (1 to 10) by 7 ( 100 Questions) ✎ Multiplying (1 to 10) by 8 ( 100 Questions) ✎ Multiplying (1 to 10) by 9 ( 100 Questions) ✎ Multiplying (1 to 10) by 10 ( 100 Questions) ✎
• Multiplying (1 to 10) by Ranges Individual Facts (100 Questions per Page) Multiplying (1 to 10) by (6 and 7) ( 100 Questions) ✎ Multiplying (1 to 10) by (7 and 8) ( 100 Questions) ✎ Multiplying (1 to 10) by (8 and 9) ( 100 Questions) ✎ Multiplying (1 to 10) by (9 and 10) ( 100 Questions) ✎ Multiplying (1 to 10) by (6 to 8) ( 100 Questions) ✎ Multiplying (1 to 10) by (7 to 9) ( 100 Questions) ✎ Multiplying (1 to 10) by (8 to 10) ( 100 Questions) ✎ Multiplying Doubles (aka Squares) from (1 to 10) ( 100 Questions)
• Multiplying (1 to 10) by Individual Facts (50 Questions per Page) Multiplying (1 to 10) by 0 ( 50 Questions ) ✎ Multiplying (1 to 10) by 1 ( 50 Questions ) ✎ Multiplying (1 to 10) by 2 ( 50 Questions ) ✎ Multiplying (1 to 10) by 3 ( 50 Questions ) ✎ Multiplying (1 to 10) by 4 ( 50 Questions ) ✎ Multiplying (1 to 10) by 5 ( 50 Questions ) ✎ Multiplying (1 to 10) by 6 ( 50 Questions ) ✎ Multiplying (1 to 10) by 7 ( 50 Questions ) ✎ Multiplying (1 to 10) by 8 ( 50 Questions ) ✎ Multiplying (1 to 10) by 9 ( 50 Questions ) ✎ Multiplying (1 to 10) by 10 ( 50 Questions ) ✎
• Multiplying (1 to 10) by Ranges of Individual Facts (50 Questions per Page) Multiplying (1 to 10) by (6 and 7) ( 50 Questions ) ✎ Multiplying (1 to 10) by (7 and 8) ( 50 Questions ) ✎ Multiplying (1 to 10) by (8 and 9) ( 50 Questions ) ✎ Multiplying (1 to 10) by (9 and 10) ( 50 Questions ) ✎ Multiplying (1 to 10) by (6 to 8) ( 50 Questions ) ✎ Multiplying (1 to 10) by (7 to 9) ( 50 Questions ) ✎ Multiplying (1 to 10) by (8 to 10) ( 50 Questions ) ✎
• Multiplying (1 to 10) by Individual Facts (36 Questions per Page) Multiplying (1 to 10) by 0 ( 36 Questions) ✎ Multiplying (1 to 10) by 1 ( 36 Questions) ✎ Multiplying (1 to 10) by 2 ( 36 Questions) ✎ Multiplying (1 to 10) by 3 ( 36 Questions) ✎ Multiplying (1 to 10) by 4 ( 36 Questions) ✎ Multiplying (1 to 10) by 5 ( 36 Questions) ✎ Multiplying (1 to 10) by 6 ( 36 Questions) ✎ Multiplying (1 to 10) by 7 ( 36 Questions) ✎ Multiplying (1 to 10) by 8 ( 36 Questions) ✎ Multiplying (1 to 10) by 9 ( 36 Questions) ✎ Multiplying (1 to 10) by 10 ( 36 Questions) ✎
• Multiplying (1 to 10) by Ranges of Individual Facts (42 Questions per Page) Multiplying (1 to 10) by (6 and 7) ( 42 Questions) ✎ Multiplying (1 to 10) by (7 and 8) ( 42 Questions) ✎ Multiplying (1 to 10) by (8 and 9) ( 42 Questions) ✎ Multiplying (1 to 10) by (9 and 10) ( 42 Questions) ✎ Multiplying (1 to 10) by (6 to 8) ( 42 Questions) ✎ Multiplying (1 to 10) by (7 to 9) ( 42 Questions) ✎ Multiplying (1 to 10) by (8 to 10) ( 42 Questions) ✎
• Horizontally Arranged Multiplying (1 to 10) by Individual Facts (100 Questions per Page) Horizontally Arranged Multiplying (1 to 10) by 1 ( 100 Questions ) ✎ Horizontally Arranged Multiplying (1 to 10) by 2 ( 100 Questions ) ✎ Horizontally Arranged Multiplying (1 to 10) by 3 ( 100 Questions ) ✎ Horizontally Arranged Multiplying (1 to 10) by 4 ( 100 Questions ) ✎ Horizontally Arranged Multiplying (1 to 10) by 5 ( 100 Questions ) ✎ Horizontally Arranged Multiplying (1 to 10) by 6 ( 100 Questions ) ✎ Horizontally Arranged Multiplying (1 to 10) by 7 ( 100 Questions ) ✎ Horizontally Arranged Multiplying (1 to 10) by 8 ( 100 Questions ) ✎ Horizontally Arranged Multiplying (1 to 10) by 9 ( 100 Questions ) ✎ Horizontally Arranged Multiplying (1 to 10) by 10 ( 100 Questions ) ✎
• Horizontally Arranged Multiplying (1 to 10) by Individual Facts (50 Questions per Page) Horizontally Arranged Multiplying (1 to 10) by 1 ( 50 Questions ) ✎ Horizontally Arranged Multiplying (1 to 10) by 2 ( 50 Questions ) ✎ Horizontally Arranged Multiplying (1 to 10) by 3 ( 50 Questions ) ✎ Horizontally Arranged Multiplying (1 to 10) by 4 ( 50 Questions ) ✎ Horizontally Arranged Multiplying (1 to 10) by 5 ( 50 Questions ) ✎ Horizontally Arranged Multiplying (1 to 10) by 6 ( 50 Questions ) ✎ Horizontally Arranged Multiplying (1 to 10) by 7 ( 50 Questions ) ✎ Horizontally Arranged Multiplying (1 to 10) by 8 ( 50 Questions ) ✎ Horizontally Arranged Multiplying (1 to 10) by 9 ( 50 Questions ) ✎ Horizontally Arranged Multiplying (1 to 10) by 10 ( 50 Questions ) ✎
• Horizontally Arranged Multiplying (1 to 10) by Individual Facts (25 Questions per Page; Large Print) Horizontally Arranged Multiplying (1 to 10) by 1 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Multiplying (1 to 10) by 2 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Multiplying (1 to 10) by 3 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Multiplying (1 to 10) by 4 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Multiplying (1 to 10) by 5 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Multiplying (1 to 10) by 6 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Multiplying (1 to 10) by 7 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Multiplying (1 to 10) by 8 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Multiplying (1 to 10) by 9 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Multiplying (1 to 10) by 10 ( 25 Questions ; Large Print) ✎

If a student is learning their times tables one at a time, these worksheets will help with practice and assessment along the way. Each one increases the range for the second factor.

• Multiplying (1 to 10) by Increasing Ranges of Individual Facts (100 Questions per Page) Multiplying (1 to 10) by (1 and 2) ( 100 Questions) ✎ Multiplying (1 to 10) by (1 to 3) ( 100 Questions) ✎ Multiplying (1 to 10) by (1 to 4) ( 100 Questions) ✎ Multiplying (1 to 10) by (1 to 5) ( 100 Questions) ✎ Multiplying (1 to 10) by (1 to 6) ( 100 Questions) ✎ Multiplying (1 to 10) by (1 to 7) ( 100 Questions) ✎ Multiplying (1 to 10) by (1 to 8) ( 100 Questions) ✎ Multiplying (1 to 10) by (1 to 9) ( 100 Questions) ✎
• Multiplying (1 to 10) by Increasing Ranges of Individual Facts (50 Questions per Page) Multiplying (1 to 10) by (1 and 2) ( 50 Questions ) ✎ Multiplying (1 to 10) by (1 to 3) ( 50 Questions ) ✎ Multiplying (1 to 10) by (1 to 4) ( 50 Questions ) ✎ Multiplying (1 to 10) by (1 to 5) ( 50 Questions ) ✎ Multiplying (1 to 10) by (1 to 6) ( 50 Questions ) ✎ Multiplying (1 to 10) by (1 to 7) ( 50 Questions ) ✎ Multiplying (1 to 10) by (1 to 8) ( 50 Questions ) ✎ Multiplying (1 to 10) by (1 to 9) ( 50 Questions ) ✎
• Multiplying Doubles Multiplying Doubles up to 10 x 10

Multiplication Facts up to the 12 Times Table

The Holy Grail of elementary mathematics. Once you learn your twelve times table, it is smooth sailing from now on, right? Well, not exactly, but having a good mental recall of the multiplication facts up to 144 will certainly set you on the right path for future success in your math studies.

• Multiplication Facts up to the 12 Times Table (No Zeros or Ones) Multiplication Facts to 144 ( 100 Questions) ( No Zeros or Ones ) ✎ Multiplication Facts to 144 ( 50 Questions ) ( No Zeros or Ones ) ✎ Multiplication Facts to 144 ( 25 Questions ) ( No Zeros or Ones ) ✎
• Multiplication Facts up to the 12 Times Table (No Zeros) Multiplication Facts to 144 ( 100 Questions) ( No Zeros ) ✎ Multiplication Facts to 144 ( 50 Questions ) ( No Zeros ) ✎ Multiplication Facts to 144 ( 25 Questions ) ( No Zeros ) ✎
• Multiplication Facts up to the 12 Times Table (With Zeros) Multiplication Facts to 144 ( 100 Questions) ( With Zeros ) ✎ Multiplication Facts to 144 ( 50 Questions ) ( With Zeros ) ✎ Multiplication Facts to 144 ( 25 Questions ) ( With Zeros ) ✎
• Horizontally Arranged Multiplication Facts up to the 11 Times Table Horizontally Arranged Multiplication Facts to 11 × 11 = 121 ( 100 Questions) ✎ Horizontally Arranged Multiplication Facts to 11 × 11 = 121 ( 50 Questions ) ✎
• Horizontally Arranged Multiplication Facts up to the 12 Times Table Horizontally Arranged Multiplication Facts to 12 × 12 = 144 ( 100 Questions) ✎ Horizontally Arranged Multiplication Facts to 12 × 12 = 144 ( 50 Questions ) ✎

With one, two or three target numbers at a time, students are able to practice just the multiplication facts they need.

• Multiplying (1 to 12) by Individual Facts (100 Questions per Page) Multiplying (1 to 12) By 0 ( 100 Questions) ✎ Multiplying (1 to 12) By 1 ( 100 Questions) ✎ Multiplying (1 to 12) By 2 ( 100 Questions) ✎ Multiplying (1 to 12) By 3 ( 100 Questions) ✎ Multiplying (1 to 12) By 4 ( 100 Questions) ✎ Multiplying (1 to 12) By 5 ( 100 Questions) ✎ Multiplying (1 to 12) By 6 ( 100 Questions) ✎ Multiplying (1 to 12) By 7 ( 100 Questions) ✎ Multiplying (1 to 12) By 8 ( 100 Questions) ✎ Multiplying (1 to 12) By 9 ( 100 Questions) ✎ Multiplying (1 to 12) By 10 ( 100 Questions) ✎ Multiplying (1 to 12) By 11 ( 100 Questions) ✎ Multiplying (1 to 12) By 12 ( 100 Questions) ✎
• Multiplying (1 to 12) by RAnges of Individual Facts (100 Questions per Page) Multiplying (1 to 12) By (0 and 1) ( 100 Questions) ✎ Multiplying (1 to 12) By (6 and 7) ( 100 Questions) Multiplying (1 to 12) By (7 and 8) ( 100 Questions) ✎ Multiplying (1 to 12) By (8 and 9) ( 100 Questions) ✎ Multiplying (1 to 12) By (9 and 10) ( 100 Questions) ✎ Multiplying (1 to 12) By (10 and 11) ( 100 Questions) ✎ Multiplying (1 to 12) By (11 and 12) ( 100 Questions) ✎ Multiplying (1 to 12) By (6, 7 and 8) ( 100 Questions) ✎ Multiplying (1 to 12) By (7, 8 and 9) ( 100 Questions) ✎ Multiplying (1 to 12) By (8, 9 and 10) ( 100 Questions) ✎ Multiplying (1 to 12) By (9, 10 and 11) ( 100 Questions) ✎ Multiplying (1 to 12) By (10, 11 and 12) ( 100 Questions) ✎
• Multiplying (1 to 12) by Individual Facts (50 Questions per Page) Multiplying (1 to 12) By 0 ( 50 Questions ) ✎ Multiplying (1 to 12) By 1 ( 50 Questions ) ✎ Multiplying (1 to 12) By 2 ( 50 Questions ) ✎ Multiplying (1 to 12) By 3 ( 50 Questions ) ✎ Multiplying (1 to 12) By 4 ( 50 Questions ) ✎ Multiplying (1 to 12) By 5 ( 50 Questions ) ✎ Multiplying (1 to 12) By 6 ( 50 Questions ) ✎ Multiplying (1 to 12) By 7 ( 50 Questions ) ✎ Multiplying (1 to 12) By 8 ( 50 Questions ) ✎ Multiplying (1 to 12) By 9 ( 50 Questions ) ✎ Multiplying (1 to 12) By 10 ( 50 Questions ) ✎ Multiplying (1 to 12) By 11 ( 50 Questions ) ✎ Multiplying (1 to 12) By 12 ( 50 Questions ) ✎
• Multiplying (1 to 12) by Ranges of Individual Facts (50 Questions per Page) Multiplying (1 to 12) By (6 and 7) ( 50 Questions ) ✎ Multiplying (1 to 12) By (7 and 8) ( 50 Questions ) ✎ Multiplying (1 to 12) By (8 and 9) ( 50 Questions ) ✎ Multiplying (1 to 12) By (9 and 10) ( 50 Questions ) ✎ Multiplying (1 to 12) By (10 and 11) ( 50 Questions ) ✎ Multiplying (1 to 12) By (11 and 12) ( 50 Questions ) ✎ Multiplying (1 to 12) By (6, 7 and 8) ( 50 Questions ) ✎ Multiplying (1 to 12) By (7, 8 and 9) ( 50 Questions ) ✎ Multiplying (1 to 12) By (8, 9 and 10) ( 50 Questions ) ✎ Multiplying (1 to 12) By (9, 10 and 11) ( 50 Questions ) ✎ Multiplying (1 to 12) By (10, 11 and 12) ( 50 Questions ) ✎
• Horizontally Arranged Multiplying (0 to 12) by Individual Facts (100 Questions per Page) Horizontally Arranged Multiplying ( 0 to 12 ) by 0 ( 100 Questions) ✎ Horizontally Arranged Multiplying ( 0 to 12 ) by 1 ( 100 Questions) ✎ Horizontally Arranged Multiplying ( 0 to 12 ) by 2 ( 100 Questions) ✎ Horizontally Arranged Multiplying ( 0 to 12 ) by 3 ( 100 Questions) ✎ Horizontally Arranged Multiplying ( 0 to 12 ) by 4 ( 100 Questions) ✎ Horizontally Arranged Multiplying ( 0 to 12 ) by 5 ( 100 Questions) ✎ Horizontally Arranged Multiplying ( 0 to 12 ) by 6 ( 100 Questions) ✎ Horizontally Arranged Multiplying ( 0 to 12 ) by 7 ( 100 Questions) ✎ Horizontally Arranged Multiplying ( 0 to 12 ) by 8 ( 100 Questions) ✎ Horizontally Arranged Multiplying ( 0 to 12 ) by 9 ( 100 Questions) ✎ Horizontally Arranged Multiplying ( 0 to 12 ) by 10 ( 100 Questions) ✎ Horizontally Arranged Multiplying ( 0 to 12 ) by 11 ( 100 Questions) ✎ Horizontally Arranged Multiplying ( 0 to 12 ) by 12 ( 100 Questions) ✎
• Horizontally Arranged Multiplying (0 to 12) by Individual Facts (50 Questions per Page) Horizontally Arranged Multiplying ( 0 to 12 ) by 0 ( 50 Questions ) ✎ Horizontally Arranged Multiplying ( 0 to 12 ) by 1 ( 50 Questions ) ✎ Horizontally Arranged Multiplying ( 0 to 12 ) by 2 ( 50 Questions ) ✎ Horizontally Arranged Multiplying ( 0 to 12 ) by 3 ( 50 Questions ) ✎ Horizontally Arranged Multiplying ( 0 to 12 ) by 4 ( 50 Questions ) ✎ Horizontally Arranged Multiplying ( 0 to 12 ) by 5 ( 50 Questions ) ✎ Horizontally Arranged Multiplying ( 0 to 12 ) by 6 ( 50 Questions ) ✎ Horizontally Arranged Multiplying ( 0 to 12 ) by 7 ( 50 Questions ) ✎ Horizontally Arranged Multiplying ( 0 to 12 ) by 8 ( 50 Questions ) ✎ Horizontally Arranged Multiplying ( 0 to 12 ) by 9 ( 50 Questions ) ✎ Horizontally Arranged Multiplying ( 0 to 12 ) by 10 ( 50 Questions ) ✎ Horizontally Arranged Multiplying ( 0 to 12 ) by 11 ( 50 Questions ) ✎ Horizontally Arranged Multiplying ( 0 to 12 ) by 12 ( 50 Questions ) ✎
• Horizontally Arranged Multiplying (0 to 12) by Individual Facts (25 Questions per Page; Large Print) Horizontally Arranged Multiplying ( 0 to 12 ) by 0 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Multiplying ( 0 to 12 ) by 1 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Multiplying ( 0 to 12 ) by 2 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Multiplying ( 0 to 12 ) by 3 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Multiplying ( 0 to 12 ) by 4 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Multiplying ( 0 to 12 ) by 5 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Multiplying ( 0 to 12 ) by 6 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Multiplying ( 0 to 12 ) by 7 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Multiplying ( 0 to 12 ) by 8 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Multiplying ( 0 to 12 ) by 9 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Multiplying ( 0 to 12 ) by 10 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Multiplying ( 0 to 12 ) by 11 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Multiplying ( 0 to 12 ) by 12 ( 25 Questions ; Large Print) ✎

In the following multiplication worksheets, the facts are grouped into anchor groups.

• Multiplying (1 to 12) by Anchor Facts (Commonly Grouped Facts) Multiplying by Anchor Facts 0, 1, 2, 5 and 10 Multiplying by Facts 3, 4 and 6 Multiplying by Facts 7, 8 and 9 Multiplying by Facts 11 and 12 Multiplying by Facts 0 to 5 and 10 Multiplying by Facts 0 to 7 and 10 Multiplying by Facts 0 to 10
• Multiplying (1 to 12) by Increasing Ranges of Individual Facts (100 Questions per Page) Multiplying (1 to 12) by (1 to 5) ( 100 Questions) ✎ Multiplying (1 to 12) by (1 to 6) ( 100 Questions) ✎ Multiplying (1 to 12) by (1 to 7) ( 100 Questions) ✎ Multiplying (1 to 12) by (1 to 8) ( 100 Questions) ✎ Multiplying (1 to 12) by (1 to 9) ( 100 Questions) ✎ Multiplying (1 to 12) by (1 to 10) ( 100 Questions) ✎ Multiplying (1 to 12) by (1 to 11) ( 100 Questions) ✎
• Multiplying (1 to 12) by Increasing Ranges of Individual Facts (50 Questions per Page) Multiplying (1 to 12) by (1 to 5) ( 50 Questions ) ✎ Multiplying (1 to 12) by (1 to 6) ( 50 Questions ) ✎ Multiplying (1 to 12) by (1 to 7) ( 50 Questions ) ✎ Multiplying (1 to 12) by (1 to 8) ( 50 Questions ) ✎ Multiplying (1 to 12) by (1 to 9) ( 50 Questions ) ✎ Multiplying (1 to 12) by (1 to 10) ( 50 Questions ) ✎ Multiplying (1 to 12) by (1 to 11) ( 50 Questions ) ✎

On the following multiplication worksheets, the questions are in order and might be useful for students to remember their times tables or to help them with skip counting.

• Repetitive Multiplying of Individual Facts by (1 to 12) Repetitive Multiplying of 1 by (1 to 12) Repetitive Multiplying of 2 by (1 to 12) Repetitive Multiplying of 3 by (1 to 12) Repetitive Multiplying of 4 by (1 to 12) Repetitive Multiplying of 5 by (1 to 12) Repetitive Multiplying of 6 by (1 to 12) Repetitive Multiplying of 7 by (1 to 12) Repetitive Multiplying of 8 by (1 to 12) Repetitive Multiplying of 9 by (1 to 12) Repetitive Multiplying of 10 by (1 to 12) Repetitive Multiplying of 11 by (1 to 12) Repetitive Multiplying of 12 by (1 to 12)
• Multiplying Doubles Multiplying Doubles up to 12 x 12

Multiplication Facts beyond the 12 Times Table

It is quite likely that there are students who have mastered all of the multiplication facts up to the 12 times tables. In case they want/need an extra challenge, this sections includes multiplication facts worksheets above 12 with the expectation that students will use mental math or recall to calculate the answers.

• Multiplying with Increasing Upper Range Factors from 13 to 20 Multiplying with Factors 2 to 13 (100 Questions) ✎ Multiplying with Factors 2 to 14 (100 Questions) ✎ Multiplying with Factors 2 to 15 (100 Questions) ✎ Multiplying with Factors 5 to 15 (100 Questions) ✎ Multiplying with Factors 5 to 16 (100 Questions) ✎ Multiplying with Factors 5 to 17 (100 Questions) ✎ Multiplying with Factors 5 to 18 (100 Questions) ✎ Multiplying with Factors 5 to 19 (100 Questions) ✎ Multiplying with Factors 5 to 20 (100 Questions) ✎
• Multiplying by Individual Facts from 13 to 25 Multiplying by 13 (49 Questions) ✎ Multiplying by 14 (49 Questions) ✎ Multiplying by 15 (49 Questions) ✎ Multiplying by 16 (49 Questions) ✎ Multiplying by 17 (49 Questions) ✎ Multiplying by 18 (49 Questions) ✎ Multiplying by 19 (49 Questions) ✎ Multiplying by 20 (49 Questions) ✎ Multiplying by 21 (49 Questions) ✎ Multiplying by 22 (49 Questions) ✎ Multiplying by 23 (49 Questions) ✎ Multiplying by 24 (49 Questions) ✎ Multiplying by 25 (49 Questions) ✎

Expand your mental math abilities by learning multiplication facts beyond the twelve times tables with these worksheets. They are horizontally arranged, so you won't be tempted to use an algorithm. Even if you can't recall all these facts yet, you can still figure them out using the distributive property. Let's say you want to multiply 19 by 19, that could be (10 × 19) + (9 × 19). Too hard? How about (10 × 10) + (10 × 9) + (9 × 10) + (9 × 9)! Or just remember that 19 × 19 = 361 :)

• Horizontally Arranged Multiplying with Increasing Upper Range Factors from 13 to 25 Horizontally Arranged Multiplying with Factors 1 to 13 (100 Questions) ✎ Horizontally Arranged Multiplying with Factors 1 to 14 (100 Questions) ✎ Horizontally Arranged Multiplying with Factors 1 to 15 (100 Questions) ✎ Horizontally Arranged Multiplying with Factors 2 to 16 (100 Questions) ✎ Horizontally Arranged Multiplying with Factors 2 to 17 (100 Questions) ✎ Horizontally Arranged Multiplying with Factors 2 to 18 (100 Questions) ✎ Horizontally Arranged Multiplying with Factors 2 to 19 (100 Questions) ✎ Horizontally Arranged Multiplying with Factors 2 to 20 (100 Questions) ✎ Horizontally Arranged Multiplying with Factors 5 to 21 (100 Questions) ✎ Horizontally Arranged Multiplying with Factors 5 to 22 (100 Questions) ✎ Horizontally Arranged Multiplying with Factors 5 to 23 (100 Questions) ✎ Horizontally Arranged Multiplying with Factors 5 to 24 (100 Questions) ✎ Horizontally Arranged Multiplying with Factors 5 to 25 (100 Questions) ✎
• Horizontally Arranged Multiplying by Individual Facts from 13 to 25 Horizontally Arranged Multiplying (1 to 13) by 13 (100 Questions) ✎ Horizontally Arranged Multiplying (1 to 14) by 14 (100 Questions) ✎ Horizontally Arranged Multiplying (1 to 15) by 15 (100 Questions) ✎ Horizontally Arranged Multiplying (1 to 16) by 16 (100 Questions) ✎ Horizontally Arranged Multiplying (1 to 17) by 17 (100 Questions) ✎ Horizontally Arranged Multiplying (1 to 18) by 18 (100 Questions) ✎ Horizontally Arranged Multiplying (1 to 19) by 19 (100 Questions) ✎ Horizontally Arranged Multiplying (1 to 20) by 20 (100 Questions) ✎ Horizontally Arranged Multiplying (1 to 21) by 21 (100 Questions) ✎ Horizontally Arranged Multiplying (1 to 22) by 22 (100 Questions) ✎ Horizontally Arranged Multiplying (1 to 23) by 23 (100 Questions) ✎ Horizontally Arranged Multiplying (1 to 24) by 24 (100 Questions) ✎ Horizontally Arranged Multiplying (1 to 25) by 25 (100 Questions) ✎
• Multiplying Doubles Multiplying Doubles up to 15 x 15 Multiplying Doubles up to 20 x 20

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Grade 6 Math Circles Cryptography

Introduction.

Cryṗtography is the study of h i̇ ddeṅ writing, or reading and writing secret messages or codes. The word cryptograpḣy cȯmes from the Greek word kryptos ( \(\kappa \rho \upsilon \tau \varsigma\) ), meaning "hidden", and graphein ( \(\gamma \rho \alpha \phi \omega\) ), meaning "writing". There are some key words that wi l̇ l come up frequently in today’s lėsson.

Plaintext: The original message or information the sender wants to encode or hide

Encryption: The process of encrypting plaintext such that only authorized parties, such as the sender and intended receiver, can read it

Ciphertext: The plaintext that was encrypted using a cipher (the method of encryption)

Decryption: The process of decoding ciphertext back into its original plaintext

Stop and Think

In our everyday lives, what are some forms of written information that we would want to keep a secret from certain individuals? How often do you use some form of encryption?

The ciphers we will look at in this lesson are substitution ciphers . Substitution ciphers take letters in the alphabet and replace them with other letters in the alphabet, switching them with other letters such that the phrase "Hello!" becomes the gibberish "Svool!" to an eavesdropper.

Atbash Cipher

Originally created using the Hebrew alphabet, the Atbash cipher is created by reversing the alphabet. That is that A becomes Z, B becomes Y, C becomes X, and so on, until Z becomes A.

This is more easily represented below.

• A \(\Leftrightarrow\) Z
• B \(\Leftrightarrow\) Y
• C \(\Leftrightarrow\) X
• D \(\Leftrightarrow\) W
• E \(\Leftrightarrow\) V
• F \(\Leftrightarrow\) U
• G \(\Leftrightarrow\) T
• H \(\Leftrightarrow\) S
• I \(\Leftrightarrow\) R
• J \(\Leftrightarrow\) Q
• K \(\Leftrightarrow\) P
• L \(\Leftrightarrow\) O
• M \(\Leftrightarrow\) N

The plaintext ATBASH CIPHER can be encrypted using the Atbash cipher, giving us the ciphertext ZGYZHS XRKSVI .

Encrypt and decrypt the respective plaintext and ciphertext using the Atbash cipher.

SLICE OF PI

HRTNZ HFNNZGRLM

Exercise 1 Solution

SLICE OF PI = HORXV LU KR

HRTNZ HFNNZGRLM = SIGMA SUMMATION

Caesar Cipher

This is one of the most well-known substitution ciphers. It is named after Julius Caesar who would encrypt communication intended for his army. Caesar encrypted his messages by shifting over every letter of the alphabet by 3 units. The cipher is as follows:

Suppose Caesar wanted to send the following message:

BEWARE THE IDES OF MARCH

Using the cipher above, we take the plaintext letters and rewrite their corresponding ciphertext letters to get:

EHZDUH WKH LGHV RI PDUFK

When Caesar’s best friend Brutus receives this message, he can refer to the same cipher, but decrypt by comparing the ciphertext letters with the corresponding plaintext letters.

The idea of the Caesar shift can be improved by using shift numbers other than 3.

Encrypt or decrypt the following messages using the shift number given in parentheses.

MY SALAD NEEDS DRESSING (8)

GUR YRGGHPR UNF R PBYV (13)

Exercise 2 Solution

Encrypting the plaintext gives UG AITIL VMMLA LZMAAQVO .

The decrypted ciphertext gives THE LETTUCE HAS E COLI .

The last Exercise shouldn’t be too difficult since the shift number was provided. This is why the shift number, or key , is usually not sent along with the ciphertext itself, but agreed on before hand by both sender and receiver.

When talking about the effectiveness of ciphers, we also ask about the security of the cipher. A cipher is secure when it is very difficult to decrypt a given ciphertext without the shift number, key, or context of the message.

Breaking Ciphers

So far we have looked at certain ciphers and how to encrypt or decrypt their messages as intended. But a major component of cryptography is how ciphers are to be broken . To break a cipher means to decrypt the ciphertext using brute force or clever guesses.

Cryptography has its historical roots in warfare as we saw in the case of the Caesar cipher. If our communications to our allies are not encrypted when sent, enemies who intercept our messages gain unwanted access to our secret plans. By encrypting communications however, enemies may never understand our plans, or at the very least, we slow them down as they need to take some time to decipher them.

Notably World War II took place during a time where ciphers were becoming more and more complex. Emerging technologies were invented to encode, decode, and break ciphers much quicker. The Enigma Machine is a notable and well-known example of a cipher machine used by the Germans. Alan Turing , the "Father of Computer Science" was on the team of cryptographers who broke Enigma. This breakthrough not only contributed to the war ending sooner, but it was a major feat in computing and mathematics at the time.

Suppose we intercepted the following Caesar ciphertext but do not know the shift number.

WZXLIV FLK NYRK ZK JRPJ

What are some things we could do to decode this message and figure out what it says?

Solution: There are a couple of different approaches. One way that will always work is to test all 26 unique shift numbers and apply them to the cipher text.

XAYMJW GML OZSL AL KSQK

YBZNKX HNM PATM BM LTRL

ZCAOLY ION QBUN CN MUSM

ADBPMZ JPO RCVO DO NVTN

BECQNA KQP SDWP EP OWUO

CFDROB LRQ TEXQ FQ PXVP

DGESPC MSR UFYR GR QYWQ

EHFTQD NTS VGZS HS RZXR

FIGURE OUT WHAT IT SAYS

GJHVSF PVU XIBU JU TBZT

HKIWTG QWV YJCV KV UCAU

ILJXUH RXW ZKDW LW VDBV

JMKYVI SYX ALEX MX WECW

KNLZWJ TZY BMFY NY XFDX

LOMAXK UAZ CNGZ OZ YGEY

MPNBYL VBA DOHA PA ZHFZ

NQOCZM WCB EPIB QB AIGA

ORPDAN XDC FQJC RC BJHB

PSQEBO YED GRKD SD CKIC

QTRFCP ZFE HSLE TE DLJD

RUSGDQ AGF ITMF UF EMKE

SVTHER BHG JUNG VG FNLF

TWUIFS CIH KVOH WH GOMG

UXVJGT DJI LWPI XI HPNH

VYWKHU EKJ MXQJ YJ IQOI

What was the shift used?

Applying the remaining 25 shifts to a Caesar ciphertext might have been a long and tedious process in the times of Caesar, it is very accessible to break Caesar ciphers with the use of modern technology. For example, I ran the ciphertext through a website that brute-forced all possible shifts in a couple of seconds.

The security of the Caesar cipher, or the Atbash cipher for that matter, can be easily challenged by a computer program or very determined codebreaker. This doesn’t mean that all substitution ciphers can be broken as easily.

Consider this random substitution cipher I created just now with no pattern and no shift number in mind.

• A \(\Leftrightarrow\) U
• B \(\Leftrightarrow\) Q
• C \(\Leftrightarrow\) Z
• D \(\Leftrightarrow\) V
• E \(\Leftrightarrow\) P
• F \(\Leftrightarrow\) X
• G \(\Leftrightarrow\) O
• H \(\Leftrightarrow\) W
• J \(\Leftrightarrow\) Y
• K \(\Leftrightarrow\) S
• L \(\Leftrightarrow\) N
• M \(\Leftrightarrow\) T

If I send out the message HWUM MRTP RK NALZW? without the cipher attached, anyone who intercepts the cipher may try to break it using the Caesar or Atbash ciphers without success. They will have to resort to other means of decoding it. This means that the security of substitution ciphers is not weak at all. You can easily upgrade my shift by not having the same letters map to each other (e.g. A encodes to U , but U encodes to G , G encodes to W , etc.).

Even if you are a computer programmer, there are \(26! = 403291461126605635584000000\) possible arrangements of the English alphabet, meaning there are far too many possible substitution ciphers to brute force. This implies that we will need to be more clever with the ways that we narrow down the best approaches to breaking a cipher.

Frequency Analysis

One method of breaking an encryption is known as frequency analysis . Since we are dealing with letters, frequency is the number of times a letter occurs. This is particularly useful for substitution ciphers. By noting the most frequent letters in a ciphertext, we can begin to deduce what letters they might correspond to in the plaintext.

Below is the frequency graph that shows the average frequency of each letter in the English alphabet.

The most commonly used letter of the English alphabet is the letter E. Following E, we have the letters T, A, O, I, N, etc.

In knowing the most frequent letters of a message, we can begin to take guesses at possible substitutions of its letters. If the message is long enough, we might even observe common groups of letters being used multiple times, indicating frequently used words of the language.

Consider the ciphertext

RXHX GX WF UWUYK

What is the most common letter in the ciphertext? Assuming that the plaintext is in English, what letter in the ciphertext likely corresponds to the plaintext letter E ?

Note that you do not have to decode this cipher.

Exercise 3 Solution

If we assume that the most frequent letter in the plaintext is E , then the most frequent letter in the ciphertext, X , is probably E . This is not certain, as messages can contain letters that have lower frequencies of the letter E .

Vigenère Cipher

Let us look at one more substitution cipher that can be considered more secure than ciphers we have seen before. The Vigenère cipher was invented in by Giovan Battista Bellaso in 1553 despite being named after Blaise de Vigenère.

Vigenère encryption uses a keyword . Using this keyword, we will apply several Caesar ciphers at a time. We will also need to translate the alphabet into numbers:

Suppose we use the keyword CODE and we want to encrypt the following plaintext:

TIME FOR COOKIE

To begin, write out the plaintext and keyword on a table, repeating the keyword until the end of the plaintext.

We then translate each letter in our keywords into numbers and write them underneath in the shift number row. These correspond to the shift numbers you will use to apply a Caesar shift to each plaintext letter.

Starting on the left column, our plaintext letter is T and our shift number is 2 (from our keyword letter C). Thus to get our ciphertext we apply a Caesar shift of 2 on T .

With a Caesar Shift of 2:

We get V for our ciphertext letter as shown above. (Note we could also just count 2 letters to the right from T in the alphabet to find our ciphertext letter V .) Our original chart now looks like this

The next column of the chart we have the letter I and a shift number of 14. So we apply a Caesar shift of 14 to the letter I .

With a Caesar Shift of 14:

We get W for our ciphertext letter. We update the chart as follows.

As you can see, each letter in the ciphertext is determined by the shift number and the plaintext letter. For each plaintext letter, we apply a Caesar cipher using the corresponding shift number.

The Vigenère Cipher is much harder to break compared to the ciphers from before. In the last example, the two O ’s in COOKIE will be shifted by 2 and 14 respectively, leading to them not sharing the same ciphertext letter despite being the same plaintext letter. In the Problem Set, we will work on decrypting Vigenère ciphertexts and explore how frequency analysis can be used to break it.

Complete the Vigenère encryption from Example 5. Note, the final ciphertext will have spaces at the same locations as the plaintext:

The following Caesar shift tables will be helpful.

Exercise 4 Solution

The ciphertext that we get is

VWPH HCU FQCNLG

Fraction Word Problems Worksheets

The fraction word problems worksheet helps the students uncover fraction concepts and their usage in real-life situations. Fractions mean a part of the whole and they find their place everywhere making it an important topic to learn.

Benefits of Fraction Word Problems Worksheets

These worksheets are thoughtfully curated for the students to put their knowledge of fractions into use. The benefit of fraction word problem worksheets is that the young minds get to explore the vastness of usage of fractions in mathematics and real life.

The students will learn a lot using their basic knowledge of addition subtraction multiplication and division in dealing with word problems including fractions, mixed fractions, and ratios.

Download Fraction Word Problems Worksheet PDFs

These math worksheets are free to download and easy to proceed with, as the questions are arranged in increasing order of difficulty. The interactive and engaging question problems help the students explore a wide range of fraction usage and their applicability in real life scenarios.

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Fraction Word Problem Worksheets

Featured here is a vast collection of fraction word problems, which require learners to simplify fractions, add like and unlike fractions; subtract like and unlike fractions; multiply and divide fractions. The fraction word problems include proper fraction, improper fraction, and mixed numbers. Solve each word problem and scroll down each printable worksheet to verify your solutions using the answer key provided. Thumb through some of these word problem worksheets for free!

Represent and Simplify the Fractions: Type 1

Presented here are the fraction pdf worksheets based on real-life scenarios. Read the basic fraction word problems, write the correct fraction and reduce your answer to the simplest form.

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Represent and Simplify the Fractions: Type 2

Before representing in fraction, children should perform addition or subtraction to solve these fraction word problems. Write your answer in the simplest form.

Adding Fractions Word Problems Worksheets

Conjure up a picture of how adding fractions plays a significant role in our day-to-day lives with the help of the real-life scenarios and circumstances presented as word problems here.

(15 Worksheets)

Subtracting Fractions Word Problems Worksheets

Crank up your skills with this set of printable worksheets on subtracting fractions word problems presenting real-world situations that involve fraction subtraction!

Multiplying Fractions Word Problems Worksheets

This set of printables is for the ardently active children! Explore the application of fraction multiplication and mixed-number multiplication in the real world with this exhilarating practice set.

Fraction Division Word Problems Worksheets

Gift children a broad view of the real-life application of dividing fractions! Let them divide fractions by whole numbers, divide 2 fractions, divide mixed numbers, and solve the word problems here.

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Grade 6 Fraction Worksheets

Free grade 6 fraction worksheets to help your students improve their knowledge and skills in mathematics. Fractions in grade 6 start to get quite challenging! Students will need to draw on their ability to multiply and divide large numbers when working with fraction equations. Just like all maths, repetition is the key. Give your students time each day to work on problems that involve fractions, whether it’s adding fractions, subtracting fractions, finding fractions of numbers, adding and subtracting mixed numbers, multiplying fractions or dividing fractions to name a few! Use these free worksheets to save your time! Click on the images below to download.

Adding Fractions

Equivalent fractions, mixed numbers, multiplying fractions, dividing fractions.

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Grade 5 Fraction Worksheets

If the grade 6 fraction worksheets are a bit challenging, give your students grade 5 fraction worksheets. These cover a range of concepts and are a good place to start.

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Free Printable Fractions Worksheets for 6th Grade

Math Fractions: Discover a vast collection of free printable worksheets for Grade 6 students, designed to enhance their understanding and mastery of fractions. Explore, learn, and excel with Quizizz!

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Fractions worksheets for Grade 6 are essential tools for teachers to help their students master the concepts of fractions, decimals, and percentages in mathematics. These worksheets provide a variety of exercises, ranging from simple addition and subtraction of fractions to more complex operations like multiplication and division. With a wide range of topics covered, Grade 6 math teachers can easily find worksheets that cater to the specific needs of their students. By incorporating these resources into their lesson plans, educators can ensure that their students have a solid foundation in fractions, setting them up for success in higher-level math courses.

Quizizz offers an excellent platform for teachers to access not only fractions worksheets for Grade 6 but also a plethora of other math resources. This interactive platform allows educators to create engaging quizzes and games that can be used in conjunction with worksheets to reinforce learning and assess students' understanding of the material. Quizizz also provides teachers with valuable insights into their students' progress, enabling them to tailor their instruction to meet the individual needs of each learner. With its vast library of resources, including worksheets, quizzes, and games, Quizizz is an invaluable tool for Grade 6 math teachers looking to enhance their students' learning experience and ensure their success in mastering fractions and other mathematical concepts.

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Grade 6 Fractions Worksheets

Grade 6 maths fractions multiple choice questions (mcqs).

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6th Grade Fraction Worksheets

Updated on June 6, 2023

The use of the fraction worksheets 6th grade is a seamless way to make your sixth graders master the concepts of fractions. These worksheets comprise questions on various forms of fractions, fraction conversion, and fraction word problems. The worksheets have lots of benefits for students, tutors, and parents.

Simplifying Fractions Worksheet 6th Grade

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Brighterly’s fraction word problems worksheets 6th grade

By learning with the fractions worksheets, students will master mathematical concepts like ratios, proportions, percentages, etc. Top experts with years of experience tutoring kids in mathematics design worksheets. Thus, the sheets are tailored to meet the demands of kids and make learning seamless for them.

Brighterly’s 6th grade fraction to decimal worksheet is suitable for all grade six students, irrespective of their learning capability. The worksheets are deliberately designed to make learning an enjoyable and interactive experience.

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Furthermore, the questions on the worksheets are arranged according to varying difficulty levels. That is, kids proceed from less complicated to more challenging tasks.

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Mathematical worksheets have many uses as they can be utilized in assessment, drill, and instruction. During school vacations, parents can work with their kids on additional practice, teach them a new arithmetic skill, or keep a child’s abilities sharp. This paper covers the benefits of multi digit division worksheets and the reasons Brighterly’s tutors use […]

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6th Grade Fraction Worksheets

The number of equal parts that are taken into account out of all the equal parts is how we can visualize a fraction. By presenting more concepts associated with fractions, these sixth grade fraction worksheets assist students in deepening their comprehension of the concept of fractions. ...Read More Read Less

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Choose math worksheets by topic, 6th grade fraction worksheets explained:.

A fraction is a part of a whole. It consists of two natural numbers,say a and b, written in an ‘ a b ’ form where the number a represents the number of equal parts that are being counted, and number b represents the number of equal parts that are in a whole. These fraction worksheets for grade 6 consist of different varieties of questions related to fractions such as equivalent fractions, conversion of fractions and decimals, conversion of improper fractions to mixed numbers and mixed numbers to improper fractions. These fraction worksheets for grade 6 help students to recall and examine the terms and concepts related to fractions in a comprehensive manner.

The sixth grade fraction worksheets consist of questions based on the following topics:

• Simplifying fractions: The numerators and denominators of fractions may have common factors. Dividing the numerator and denominator with their common factors until no common factor except 1 exists is called ‘simplification’ of fractions. Students simplify fractions to make calculation easier.
• Finding equivalent fractions: Worksheets on fractions for sixth grade include calculations of equivalent fractions as well as comparisons of two fractions using the method of converting fractions into equivalent fractions. These activities help students to improve their math skills.
• Converting fractions into decimals: Sixth grade interactive worksheets contain questions in which the conversion of decimals to fractions is tested, and this conversion is done without simplifying the fraction.
• Converting fractions into mixed numbers: Mixed numbers can be used to represent improper fractions. On the other hand, improper fractions can also be used to represent mixed numbers. The grade 6 fraction worksheets have questions that aid students in understanding how to convert fractions.

If you feel the need to refresh your understanding of fractions as a concept, click on the following links:

• Introduction of fractions
• https://byjus.com/us/math/introduction-to-fractions/
• Equivalent fractions and their comparison
• https://byjus.com/us/math/equivalent-fractions-and-their-comparison/
• https://byjus.com/us/math/addition-and-subtraction-of-fractions/
• Find the sum of fractions by decomposing the fractions
• https://byjus.com/us/math/find-the-sum-of-fractions-by-decomposing-the-fractions/
• Understand multiples of fractions using unit fractions
• https://byjus.com/us/math/understand-multiples-of-fractions-using-unit-fractions/
• Concept of multiplication in whole numbers and fractions
• https://byjus.com/us/math/concept-of-multiplication-in-whole-numbers-and-fractions/
• Fractions, decimals and Percents
• https://byjus.com/us/math/fractions-decimals-and-percentages/
• Addition and subtraction of fractions
• https://byjus.com/us/math/addition-and-subtraction-of-fractions-2/
• Ordering and comparing Percents, decimals and fractions
• https://byjus.com/us/math/ordering-and-comparing-percents,-decimals-and-fractions /
• Percents and Fractions
• https://byjus.com/us/math/percents-and-fractions/
• Operations on fraction using division of mixed fractions
• https://byjus.com/us/math/operations-on-fractions-using-division-of-mixed-fractions/
• Problem solving using fractions
• https://byjus.com/us/math/problem-solving-using-fractions/

Benefits of 6th Grade Fraction Worksheets:

• Fraction problems (Easy): These fraction worksheets for sixth grade are beneficial in assisting the student to remember how to investigate and approach problems with fractions. At the initial stages students begin to solve worksheets by working on fundamental operations like identifying equivalent fractions, converting decimals to fractions and changing improper fractions into mixed numbers.     
• Fraction problems (Medium): Printable fraction worksheets for grade 6 enable students to relate to real life situations in which fractions are commonly observed. It also helps students to strengthen their ability to quickly solve problems on fractions.
• Fraction problems (Hard): Online and printable free fraction worksheets for sixth grade encourage students in understanding particular types of problems where two or more steps are required to solve the issue. As a result, students are better equipped to write solutions for more complex problems. These worksheets also assist students in developing their problem-solving abilities for upcoming grades.    

Printable PDFs and Online Worksheets:

Free printable fraction worksheets for 6th grade act as an excellent resource to boost skills related to solving problems on fractions, and to prepare students for school tests and other aptitude exams. The 6th grade fraction worksheets assist students to comprehensively understand methods of solving problems, as the questions are descriptive and are supported with visuals in most cases. An important impact is the application of this understanding of fractions to real life situations. Attempting challenging questions that appear in higher grades is an added advantage. These math fraction worksheets for grade 6 cover addition and subtraction operations and the application of different types of methods to solve problems related to fractions. Interactive sixth grade fraction worksheets are supported by visuals, making learning interesting, in which students can test their knowledge on fractions by applying the most appropriate method to solve problems. Timed worksheets also help the student to enhance  time management skills, especially while solving particular types of questions. The student can also compare the scores and time taken for a worksheet with friends and challenge them as well.

What are the methods to convert fractions into decimals?

The following are two methods for converting a fraction to a decimal:

• Long division method
• By changing the denominator of fraction to a power of 10.

How are 6th grade fraction worksheets advantageous to students?

When students solve worksheets on their own, it promotes active learning as they feel a sense of accomplishment. It raises the curiosity level about fractions, especially in relation to specific topics within this chapter, and in turn, enables them to take up more challenging questions. In the fraction worksheets for grade 6 by BYJU’S Math, students also learn the method of applying step-wise solutions that further strengthens their understanding of operations related to fractions.

How can a student simplify fractions

The numerator and denominator of a fraction may have common factors. Dividing the numerator and denominator with their common factors until no common factor except 1 exists, is called simplification of fractions.

Why are these interactive worksheets necessary for students?

These free online interactive grade 6 fraction worksheets link learning multiple concepts with a fun element. These worksheets follow the common core math structure and assist the student to be completely familiar with the methods and terms used in 6th grade.

How to convert mixed numbers into improper fractions?

A mixed number consists of two parts, one is a whole number and the other is a fraction. Multiplying the denominator of a fraction to the whole number and adding the product to the numerator of the fraction gives the numerator of an improper fraction. The denominator of an improper fraction remains the same as the denominator of the fraction part of a mixed number.

How to form an equivalent fraction for any fraction?

An equivalent fraction is calculated by multiplying a specific number with both the numerator and the denominator of a given fraction. An infinite number of equivalent fractions of a fraction can be calculated. 6th Grade worksheets on fractions also contain multiple problems on equivalent fractions.

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Mixed division practice

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Fractions worksheets: Mixed division practice

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• 6th Grade Math
• Solving word problems

Grade 6 Math Word Problems: Tips, Tricks, and Answers

Do you want to stimulate your 6 th grader’s creative thinking skills? Then, enjoy this brilliant math article. In this comprehensive guide, we will provide you with a treasure trove of fun solving strategies, tips, tricks, and answers to tackle those tricky grade 6 math word problems that have been confusing your students for some time now.

In this page, you will discover why math word problems are important for 6th-graders and simple methods of breaking down complex word problems into manageable steps.

Nevertheless, we will introduce you to Mathskills4kids.com , an outstanding website with thousands of common types of grade 6 math word problems and a step-by-step approach to solving them. Interestingly, we will illustrate how to use diagrams and models to solve math word problems efficiently.

Learn to love Grade 6 Math word problems with these worksheets and answers

Hello and welcome to Grade 6 Math word problems worksheets and answers , where your 6 th Grade students will learn to love and solve math problems and activities at all times.

We understand that word problems can often frustrate students, as they require a solid understanding of mathematical concepts and the ability to interpret and apply them to real-life situations. That's why we have compiled a collection of proven strategies and techniques to empower your students to approach word problems confidently and accurately.

From understanding problem-solving strategies to breaking down complex questions into manageable steps, this guide will equip you with the knowledge and resources to make math word problems a breeze. So, let's dive in and unlock the secrets to conquering grade 6 math word problems together!

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• Operations with integers
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Start practice on Sixth Grade here

Why are math word problems important for 6th-graders.

Math word problems are about more than just doing calculations. They are also about applying your math knowledge to real-world situations. Math word problems are important for 6 th graders because they help them to:

• Learn how to use different math concepts and skills in various contexts
• Develop their logical thinking and reasoning abilities
• Enhance their communication and literacy skills
• Prepare them for standardized tests and future math courses

Math word problems also make math more exciting and relevant. They show us how math can solve everyday problems and challenges. They also expose us to different topics and scenarios we may not encounter in our regular math lessons.

Strategies for solving Grade 6 math word problems

Solving Grade 6 math word problems can be intimidating, especially involving multiple steps or operations. But don't worry. Some general strategies will help your students confidently approach any word problem. Here are some of them:

• Please encourage them to read the problem carefully and identify the given information, the unknowns, and the question.
• They should rewrite the problem in their own words or summarize it in a sentence.
• Let them choose a suitable method or strategy to solve the problem. Some standard methods are guessing and checking, making a table or chart, drawing a picture or diagram, using a formula or equation, working backward, or using logical reasoning.
• They must show their work and explain each step clearly. Use appropriate units, labels, symbols, and terms.
• Lastly, tell them to check their answer by plugging it back into the problem or using a different method. Ensure their answer makes sense and answers the question.

Breaking down complex word problems into manageable steps

Some word problems may seem too complex or confusing at first glance. They may have too much information, too many steps, or too many operations. In such cases, breaking down the problem into smaller and simpler parts is helpful. Here are some tips on how to do that:

Words like "difference," "subtract," "take away," or "minus" indicate s ubtraction .

Words like "product," "multiply," "times," or "of" indicate multiplication .

Words like "quotient," "divide," "per," or "out of" indicate division .

Words like "ratio," "fraction," "percent," or "part" indicate fractions or decimals .

Words like "equal," "same as," or "is" indicate equations .

Words like "more than,” “less than," "greater than," or "smaller than" indicate inequalities .

Words like "average," "mean," or "median" indicate statistics .

Words like "area," "perimeter," "volume," or "surface area" indicate geometry , etc.

• Use parentheses, brackets, or other symbols to group the parts of the problem that belong together . For example, if the problem says:

You can rewrite it as:

• (John has 12 apples) + (Mary has 8 apples) = (total number of apples) / (4 people) = (number of apples per person)

This way, you can see the structure of the problem more clearly and focus on one part at a time.

• Solve each part of the problem separately and write down the intermediate results . For example, using the previous problem:
• (John has 12 apples) + (Mary has 8 apples) = (total number of apples)
• 12 + 8 = 20
• (total number of apples) / (4 people) = (number of apples per person)

This way, you can keep track of your work and avoid making mistakes.

• Combine the intermediate results to get the final answer. For example, using the previous problem :

This way, you can answer the question and check your answer.

Common types of grade 6 math word problems

There are many types of word problems that you may encounter in grade 6 math . Some of the most common ones found on Mathskills4kids.com are:

• Ratio and proportion problems : These problems involve finding the relationship between two quantities with the same unit or measure. For example, if 12 pencils cost $3, how much do 20 pencils cost?
• Percent problems : These problems involve finding the part, whole, or percent of a quantity. For example, if 30% of a class is boys, and there are 24 students, how many boys are there?
• Fraction problems : These problems involve adding, subtracting, multiplying, or dividing fractions. For example, how much pizza do you have left if you have 2/3 of a pizza and eat 1/4?
• Decimal problems : These problems involve adding, subtracting, multiplying, or dividing decimals. For example, if you buy a shirt for $12.50 and a pair of jeans for $24.75, how much change do you get from $50?
• Measurement problems : These problems involve converting between different units of measurement or finding the perimeter, area, or volume of shapes. For example, if a rectangle has a length of 15 cm and a width of 10 cm, what is its area in square meters?
• Algebra problems : These problems involve finding the value of an unknown variable or expression. For example, if x + 5 = 13, what is the value of x?

A step-by-step approach to solving different types of word problems

No matter what type of word problem your 6 th graders are faced with, they can use the following steps to solve it:

• They should read the problem carefully and identify the given information and the question.
• They must choose a variable to represent the unknown quantity and write an equation or expression that relates the given information and the question.
• They can now solve the equation or expression and find the variable's value.
• They can check their answer by plugging it back into the equation or expression to see if it makes sense.
• They can now write their answer in complete sentences and include the appropriate units.

Using diagrams and models to solve math word problems

Sometimes, it can be helpful to use diagrams and models to visualize the problem and make it easier to solve. Some examples of diagrams and models for solving math word problems are:

• Tape diagrams : These are horizontal or vertical bars showing the relationship between two quantities. For example, you can use a tape diagram to show how much money each person gets when $60 is shared equally among 4 people.
• Number lines : These horizontal lines show numbers and their relative positions. For example, you can use a number line to show how to add or subtract fractions with different denominators.
• Tables : These are grids that show data in rows and columns. For example, you can use a table to show how to find equivalent ratios or fractions.
• Charts : These are graphical representations of data using bars, circles, lines, or other shapes. For example, you can use a chart to show how to find the percent of a quantity or compare different quantities.
• Drawings : These are sketches or illustrations that show shapes or objects. For example, you can use a drawing to show how to find a shape's perimeter, area, or volume.

Providing answers and explanations to sample Mathskills4kids’ Grade 6 math word problems

Here are some sample Grade 6 math word problems with answers and explanations available at Mathskills4kids.com :

Answer : 6 cups of flour

Explanation : This is a ratio problem. We can use a tape diagram to show the relationship between flour and sugar.

Flour →|<---2 cups--->|<---2 cups--->|<---2 cups---> = 6

Sugar→|<---3 cups--->|<---3 cups--->|<---3 cups---> = 9

We can see that for every 3 cups of sugar, we need 2 cups of flour. So, for 9 cups of sugar, we need 6 cups of flour.

Answer : $15

Explanation : This is a percent problem. We can use a formula to find the sale price of the shirt.

Sale price = Original price - Discount

Discount = Percent off x Original price

We know the percent off is 40%, and the original price is $25. So, we can plug these values into the formula and solve for the sale price.

Discount = 40% x $25

Discount = 0.4 x $25

Discount = $10

Sale price = $25 - $10

Sale price = $15

Tips for improving problem-solving skills in Grade 6 math

Here are some tips that can help students improve their problem-solving skills in grade 6 math :

• Please encourage them to practice regularly and try different types of word problems.
• They should review the concepts and skills they have learned and apply them to new situations.
• They can use different strategies and methods to solve word problems and compare their results.
• Let them ask for help from the teacher, parents, or peers if they get stuck or confused.
• They should learn from their mistakes and try to avoid them in the future.

Bonus: additional resources to reinforce Grade 6 math problem skills

If you want to enhance your student's Grade 6 math word problem skills , or if you need some extra help, here are some additional and useful web links that you can check out:

• Math Playground : This website has a lot of fun and interactive games that let 6 th graders practice different types of math word problems, such as fractions, decimals, ratios, proportions, and more. They can also watch videos explaining how to solve some problems. https://www.mathplayground.com/wordproblems.html .
• Khan Academy : This website has many videos and exercises covering various topics in Grade 6 math, including word problems. Students can learn at their own pace and track their progress. https://www.khanacademy.org/math/cc-sixth-grade-math .
• IXL : This website has many practice questions aligned with the Common Core standards for Grade 6 math. Students can choose from different categories of word problems, such as expressions and equations, geometry, statistics, and more. They can also get instant feedback and explanations for their answers. https://www.ixl.com/math/grade-6 .
• Math Goodies : This website has a lot of worksheets and lessons that teach 6 th graders how to solve different types of word problems, such as percent, ratio, proportion, and more. They can also find tips and tricks for solving word problems faster and easier. https://www.mathgoodies.com/math-mammoth/worksheets/pdf/grade_6_word_problems.pdf .

Thank you for sharing the links of MathSkills4Kids.com with your loved ones. Your choice is greatly appreciated.

Math word problems can be challenging for many 6th-graders, but they are also important for developing their mathematical thinking and reasoning skills.

Using the strategies and steps we discussed in this article, your student's ability to solve different types of word problems in Grade 6 math can be improved.

You can also use the diagrams and models we have shown you to help your students visualize the problem and find the solution. Encourage them to practice as much as possible, and they must not be afraid to ask for help if needed.

You can also use the web links that we have provided to reinforce your student’s learning and have fun with math. We hope this article has helped your 6th-grade students feel more confident and prepared for tackling Grade 6 math word problems.

Happy problem-solving!

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