problem solving decimal operations

Decimal Word Problems (Mixed Operations) Worksheet and Solutions

Decimal Word Problems Worksheets: 1-Step Word Problems, Add, Subtract 2-Step Word Problems, Add, Subtract Decimal Word Problems (Mixed Op) Decimal Word Problems (Mixed Op)

Objective: I can solve word problems involving addition, subtraction, multiplication and division of decimals.

Printable “Decimal Word Problems” Worksheets

Decimal Word Problems Worksheet #1 Decimal Word Problems Worksheet #2 Decimal Word Problems Worksheet #3 Decimal Word Problems Worksheet #4

Online “Decimal Word Problems” Worksheets

Solve the following word problems. Julia cut a string 8.46 m long into 6 equal pieces. What is the length of each piece of string? m The mass of a jar of sweets is 1.4 kg. What is the total mass of 7 such jars of sweets? kg The watermelon bought by Peter is 3 times as heavy as the papaya bought by Paul. If the watermelon bought by Peter has a mass of 4.2 kg, what is the mass of the papaya? kg There is 0.625 kg of powdered milk in each tin. If a carton contains 12 tins, find the total mass of powdered milk in the carton. kg Marcus bought 8.6 kg of sugar. He poured the sugar equally into 5 bottles. There was 0.35 kg of sugar left over. What was the mass of sugar in 1 bottle? kg

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Decimals word problems

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Decimal Word Problem Worksheets

Extensive decimal word problems are presented in these sets of worksheets, which require the learner to perform addition, subtraction, multiplication, and division operations. This batch of printable decimal word problem worksheets is curated for students of grade 3 through grade 7. Free worksheets are included.

Adding Decimals Word Problems

Decimal word problems presented here help the children learn decimal addition based on money, measurement and other real-life units.

• Download the set

Subtracting Decimals Word Problems

These decimal word problem worksheets reinforce the real-life subtraction skills such as tender the exact change, compare the height, the difference between the quantities and more.

Decimals: Addition and Subtraction

It's review time for grade 4 and grade 5 students. Take these printable worksheets that help you reinforce the knowledge in adding and subtracting decimals. There are five word problems in each pdf worksheet.

Multiplying Decimals Whole Numbers

Reduce the chaos and improve clarity in your decimal multiplication skill using this collection of no-prep, printable worksheets. A must-have resource for young learners looking to ace their class!

Decimal Division Whole Numbers

Revive your decimal division skills with a host of interesting lifelike word problems involving whole numbers. Keep up with consistent practice and you’ll fly high in the topic in no time!

Multiplying Decimals Word Problems

Each decimal word problem involves multiplication of a whole number with a decimal number. 5th grade students are expected to find the product and check their answer using the answer key provided in the second page.

Dividing Decimals Word Problems

These division word problems require children to divide the decimals with the whole numbers. Ask the 6th graders to perform the division to find the quotient by applying long division method. Avoid calculator.

Decimals: Multiplication and Division

These decimal worksheets emphasize decimal multiplication and division. The perfect blend of word problems makes the grade 6 and grade 7 children stronger in performing the multiplication and division operation.

Related Worksheets

» Fraction Word Problems

» Ratio Word Problems

» Division Word Problems

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3.2.1: Adding and Subtracting Decimals

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• Page ID 62046

• The NROC Project

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Learning Objectives

• Add two or more decimals.
• Subtract two or more decimals, with and without regrouping.
• Solve application problems that require decimal addition or subtraction.

Introduction

Since dollars and cents are typically written as decimals, you often need to work with decimals. Knowing how to add and subtract decimal numbers is essential when you deposit money to (and withdraw money from) your bank account; perform an incorrect calculation, and you may be costing yourself some cash!

When adding or subtracting decimals, it is essential that you pay attention to the place value of the digits in the numbers you are adding or subtracting. This will be the key idea in the discussion that follows. Let’s begin with an everyday example that illustrates this idea before moving into more general techniques.

Adding Decimals

Suppose Celia needs $0.80 to ride the bus from home to her office. She reaches into her purse and pulls out the following coins: 3 quarters, 1 dime and 2 pennies. Does she have enough money to ride the bus?

Take a moment to think about this problem. Does she have enough money? Some people may solve it like this: “I know each quarter is 25¢, so three quarters is 75¢. Adding a dime brings me to 85¢, and then another two pennies is 87¢. So, Celia does have enough money to ride the bus.”

This problem provides a good starting point for our conversation because you can use your knowledge about pocket change to understand the basics about how to add decimals. The coins you use every day can all be represented as whole cent values, as shown above. But they can also be represented as decimal numbers, too, because quarters, dimes, nickels, and pennies are each worth less than one whole dollar.

Celia has 87¢. You can also write this amount in terms of the number of dollars she has: $0.87. The table below shows a step-by-step approach to adding the coins in terms of cents and also as dollars. As you review the table, pay attention to the place values.

When you add whole numbers, as shown in the Value (cents) column above, you line up the numbers so that the digits in the ones place-value column are aligned.

In order to keep the numbers in the proper place-value column when adding decimals, align the decimal points. This will keep the numbers aligned; ones to ones, tenths to tenths, hundredths to hundredths, and so on. Look at the column titled Value (dollars) . You will see that place value is maintained, and that the decimal points align from top to bottom.

To add decimals:

• Align the decimal points, which will allow all the digits to be aligned according to their place values.
• Add just as you would add whole numbers, beginning on the right and progressing to the left.
• Write the decimal point in the sum, aligned with the decimal points in the numbers being added.

Add. 0.23+4.5+20.32

0.23+4.5+20.32=25.05

Add. 4.041+8+510.042

4.041+8+510.042=522.083

Add: 0.08+0.156

• Incorrect. Pay attention to the locations of the decimal points. An answer of 0.956 would have been correct for the problem 0.8+0.156. The correct answer is 0.236.
• Correct. Line up the decimal points and then add. The correct answer is 0.236.
• Incorrect. Pay attention to the locations of the decimal points. An answer of 0.164 would have been correct for the problem 0.008+0.156. You can only add zeros at the end of the number. The correct answer is 0.236.
• Incorrect. Pay attention to the locations of the decimal points. An answer of 0.1568 would have been correct for the problem 0.0008+0.156. You can only add zeros at the end of the number. The correct answer is 0.236.

Subtracting Decimals

Subtracting decimals uses the same setup as adding decimals: line up the decimal points, and then subtract.

In cases where you are subtracting two decimals that extend to different place values, it often makes sense to add extra zeros to make the two numbers line up—this makes the subtraction a bit easier to follow.

To subtract decimals:

• Align the decimal points, which will allow all of the digits to be aligned according to their place values.
• Subtract just as you would subtract whole numbers, beginning on the right and progressing to the left.
• Align the decimal point in the difference directly below the decimal points in the numbers that were subtracted.

Subtract. 39.672-5.431

39.672-5.431=34.241

Subtract. 0.9-0.027

0.9-0.027=0.873

Subtract. 43.21-8.1

• Correct. Line up the two numbers so that the decimal points are aligned, and then subtract. The difference is 35.11.
• Incorrect. Pay attention to the location of the decimal point. An answer of 42.40 would have been correct for the problem 43.21-0.81. The correct answer is 35.11.
• Incorrect. To subtract, you need to align the decimal points first. The correct answer is 35.11.
• Incorrect. Pay attention to the location of the decimal point. An answer of 35.2 would have been correct for the problem 43.21-8.01. The correct answer is 35.11.

Solving Problems

In adding and subtracting decimals, you may have noticed that as long as you line up the decimal points in the numbers you are adding or subtracting, you can operate upon them as you would whole numbers.

Determining whether you need to add or subtract in a given situation is also straightforward. If two quantities are being combined, then add them. If one is being withdrawn from the other, then subtract them.

Javier has a balance of $1,800.50 in his personal checking account. He pays two bills out of this account: a $50.23 electric bill, and a $70.80 cell phone bill.

How much money is left in Javier’s checking account after he pays these bills?

Javier has $1,679.47 left in his checking account after paying his bills.

Helene ran the 100-meter dash twice on Saturday. The difference between her two times was 0.3 seconds. Which pair of numbers below could have been her individual race times?

• 14.22 and 14.25 seconds
• 14.22 and 17.22 seconds
• 14.22 and 14.58 seconds
• 14.22 and 13.92 seconds
• Incorrect. The difference between these times is 0.03 seconds, not 0.3 seconds. The correct answer is 14.22 and 13.92 seconds.
• Incorrect. The difference between these times is 3 seconds, not 0.3 seconds. The correct answer is 14.22 and 13.92 seconds.
• Incorrect. The difference between these times is 0.36 seconds, not 0.3 seconds. The correct answer is 14.22 and 13.92 seconds.
• Correct. 14.22-13.92=0.3; the difference between Helene’s two race times is 0.3 seconds.

When adding or subtracting decimals, you must always align the decimal points, which will allow the place-value positions to fall in place. Then add or subtract as you do with whole numbers, regrouping as necessary. You can use these operations to solve real-world problems involving decimals, especially those with money.

Math Wheels for Note-taking?

Decimal Operations Math Problem Solving

What’s your favorite type of math activity to have your middle school math students work on?

For me, it’s almost always been math problem solving. This could include word problems that apply specific math concepts, word problems that incorporate a variety of math concepts, logic puzzles, word problems that focus on problem solving  strategies   (create a table,   make an organized list, find a pattern, work backwards, draw a picture, etc). 

I also love using problems that have more than one correct solution, so students can share the thinking that leads to different answers.

Cooperative Groups for Math Problem Solving

When we work on math problem solving activities, I often have students work together, so they can model for each other and share/listen to each others’ thinking and reasoning.

I wrote the “Party Planning” problem shown here to give students practice with:

• decimal operations and 
• solving problems with multiple solutions

To solve the problem, students worked with one or two partners to come up with combinations of foods that Reggie could buy for a party. 

To find their solutions, students needed to:

• add decimals 
• multiply if they were going to include several of one item
• possibly subtract, to revise their answer if their total was over $50

Student Conversation and Feedback

I loved listening to the kids’  conversations as they worked on this problem. I heard comments like

• “No one eats pretzels” 
• “I’d choose candy and chips over pretzels,” and so on.

The students had a few important questions for me, as they were pretty serious about this planning. They asked:

• “Is this a “regular” party or like a sleep-over party, because the kind of food would depend on how long the party is.”
• “How big is the container of ice cream?”
• “How big is the bag of candy?”

In addition to these questions, there were a few other factors that made me realize I needed to revise the problem, and add more details/requirements.

• For example, one student said, “Let’s just get 50 bottles of soda!”
• Another group of students decided that having 5 fruit trays and no other food would be a good plan (even though the problem stated that Reggie wanted a variety of food items).

So, I revised the problem, which you can download below. I hope you can use it!

This problem solving sheet is part of a larger  Decimal Operations resource  that includes several other math problem solving pages, as well as a  Footloose  task card activity.

Do you get to spend much time on math problem solving activities with your students?

If you’d like more math problem solving ideas, check out these posts .

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Solving Problems that Include Fractions and Decimals

Introduction.

There are four important operations that you will encounter when solving problems in mathematics. The figures below indicate some of the actions in a problem that lead to different operations.

Addition and subtraction are related operations. Addition typically means to combine two or more numbers, and subtraction involves the difference , or removal, of one number from another.

Multiplication and division are also related operations. Both operations involve grouping and rates.

You have explored how to tell when to use which operation. Now, you will focus on identifying the operation from a word problem, and then use procedures to actually perform the operation and determine a solution to the problem.

Working with Signed Numbers

Signed numbers include integers and other rational numbers that have either a positive or a negative sign.

Source: Badwater Elevation Sign, Complex01 and Elevation Benchmark, Jeff Kramer, Wikimedia Commons

Use the diagram below to review standard procedures for adding, subtracting, multiplying, and dividing integers.

Adding and Subtracting Decimals

You have applied the rules of integers to solve word problems. Now, you will review ways to add and subtract decimals, and then use what you learn to solve problems relating to addition and subtraction of positive and negative decimals.

Click on the image below to open a base-ten model interactive in a new web browser tab or window. The interactive represents the two addends in an addition problem, or the minuend  and subtrahend in a subtraction problem. Use the manipulative to work through at least 3 problems.

• Click on a block and drag it on top of its opposite block to remove zero pairs.
• Click on a block and drag it to the next column to regroup.
• Click “Next Problem” to move to the next problem when you are ready.

Need additional help for addition?

Need additional help for subtraction?

Use what you noticed in the interactive to answer the following questions.

In the original problem, 4.3 – 1.5, when you dragged a ones rod into the tenths column, it split into 10 tenths. How does that relate to the regrouping that was recorded symbolically in the image shown below?

In an addition problem, such as 6.4 + 4.8, when you regroup 10 tenths into 1 one and drag the ones rod into the ones place, how did that action appear in the regrouping that was recorded symbolically such as the regrouping shown in the image below?

Pause and Reflect

1. Why is it important to line up the decimal point when adding or subtracting decimal numbers?

2. When regrouping 1 one and 3 tenths into 13 tenths, why do you cross out the original 3 in the tenths place and replace it with 13? 

Adding and Subtracting Fractions

You have used models and algorithms to add and subtract decimals, paying special attention to the regrouping that was necessary to perform the computations. Now, you will extend the idea of regrouping to models and procedures used to add and subtract fractions, including mixed numbers.

Consider the following problem.

The example below shows how Marley used fraction strips to solve this problem.

Click the image below to view additional examples, including a video with a worked-out example for you to follow.

1. How is regrouping when subtracting mixed numbers similar to regrouping when subtracting decimals?

2. When adding decimals, you regroup when the sum of the two digits in a place value that is greater than 10. When would you need to regroup as you add mixed numbers?

Multiplying and Dividing Decimals

Now that you’ve investigated addition and subtraction with decimals and fractions, let’s take a closer look at multiplication and division. You will start in this section with decimals, and then use a similar model to multiply and divide fractions and mixed numbers in the next section.

• Write an expression that you can use to determine the amount of oil that Rachel started with.
• How would you represent 2.2 and 2.5 as improper fractions with denominators of 10?

The interactive below uses blocks to multiply decimals. When the blocks are combined, they will form a rectangle; the area of the rectangle is the product of the two decimals or the answer to Rachel’s problem.

• In the first activity, the first decimal is the length of the rectangle, and the second decimal is the width. Represent each decimal by dragging the appropriate blocks and moving them to the area for each decimal.
• In the second activity, use the information from the decimals and drag the blocks to the open area to create a rectangle. You will use the green blocks to fill in the missing pieces of the rectangle.
• Is the answer the same as what we found earlier in Anu's solution?
• Adjust the numerators to create and represent two more multiplication problems. Record those problems on a piece of paper.

Based on what you saw in the interactive, why do you think that the product has the same number of digits to the right of the decimal as the total number of digits to the right of the decimal in the two factors ?

Multiplying and Dividing Fractions

In this section, you will look at models to represent multiplying and dividing fractions.

Multiplying Fractions

Use the interactive below to represent the problem and graphically illustrate the product. Use the Numerator and Denominator sliders to create each fraction or mixed number. You may also need to use the Zoom in/out sliders to see the entire model.

Need additional directions?

Use the interactive to answer the following questions:

• What are the dimensions of the shaded rectangle in the solution? Check Your Answer
• The solid lines represent the boundaries of a rectangle with an area of 1 square unit. The dashed lines represent the boundaries of a number of equal-sized regions within this area. What fraction of 1 does each smaller rectangle represent? Check Your Answer

• What mixed number does this rearranged figure represent? How does this compare with the product of 3 4 and 6 1 2 ? Check Your Answer

Dividing Fractions

To solve this problem, Barbara used a fraction strip generator, which gave her the following diagram.

• Barbara knew this was a division problem, not a multiplication problem. How did she know that? Check Your Answer
• Use the diagram to explain why the quotient of 6 1 2 ÷ 1 2 is 13. Check Your Answer

Use the same fraction strip generator that Barbara used to solve the problem below.

Click the image below to open the fraction strip generator in a new web browser tab or window. Enter the key information from the problem, including the dividend and the divisor , and then use the results to answer the questions that follow.

In the fraction diagrams, both 5 3 4 and 3 8 are marked off into eighths. Why do you think that is the case? Check Your Answer

To divide 5 3 4 by 3 8 , the number sentence beneath the diagrams shows multiplication of 5 3 4 by 8 3 , which is the reciprocal of 3 8 . Multiplying by 8 3 is the same as multiplying by 8 , and then dividing by 3 . Why do you need to multiply 5 3 4 by 8 , which is the numerator of the reciprocal? Check Your Answer

The next step in the number sentence divides the product of 5 3 4 and 8 by 3 (multiplies 5 3 4 by the fraction 8 3 ) . Why do you need to divide by 3 at this point? Check Your Answer

See the completed fraction diagram for Patrice's ornament problem.

Completed fraction diagram

1. How does the multiplication algorithm connect to the area model that you used in the first interactive?

2. How does the division algorithm connect to the fraction strip model that you used in the interactive?

You studied models that represent operations on rational numbers (fractions and decimals). You also connected those models to the standard algorithms for performing the operations.

The graphic below summarizes procedures to add, subtract, multiply, and divide decimals.

The graphic below summarizes procedures to add, subtract, multiply, or divide fractions, including mixed numbers.

Copy and paste the link code above.

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Unit 3: Fractions, decimals, & percentages

About this unit.

In these tutorials, we'll explore the number system. We'll convert fractions to decimals, operate on numbers in different forms, meet complex fractions, and identify types of numbers. We'll also solve interesting word problems involving percentages (discounts, taxes, and tip calculations).

Converting fractions to decimals

• Rewriting decimals as fractions: 2.75 (Opens a modal)
• Worked example: Converting a fraction (7/8) to a decimal (Opens a modal)
• Fraction to decimal: 11/25 (Opens a modal)
• Fraction to decimal with rounding (Opens a modal)
• Rewriting decimals as fractions challenge Get 5 of 7 questions to level up!
• Converting fractions to decimals Get 3 of 4 questions to level up!

Adding & subtracting rational numbers

• Comparing rational numbers (Opens a modal)
• Adding & subtracting rational numbers: 79% - 79.1 - 58 1/10 (Opens a modal)
• Adding & subtracting rational numbers: 0.79 - 4/3 - 1/2 + 150% (Opens a modal)
• Order rational numbers Get 3 of 4 questions to level up!
• Adding & subtracting rational numbers Get 3 of 4 questions to level up!

Percent word problems

• Solving percent problems (Opens a modal)
• Percent word problem: magic club (Opens a modal)
• Percent word problems: tax and discount (Opens a modal)
• Percent word problem: guavas (Opens a modal)
• Equivalent expressions with percent problems Get 3 of 4 questions to level up!
• Percent problems Get 3 of 4 questions to level up!
• Tax and tip word problems Get 3 of 4 questions to level up!
• Discount, markup, and commission word problems Get 3 of 4 questions to level up!

Rational number word problems

• Rational number word problem: school report (Opens a modal)
• Rational number word problem: cosmetics (Opens a modal)
• Rational number word problem: cab (Opens a modal)
• Rational number word problem: ice (Opens a modal)
• Rational number word problem: computers (Opens a modal)
• Rational number word problem: stock (Opens a modal)
• Rational number word problem: checking account (Opens a modal)
• Rational number word problems Get 3 of 4 questions to level up!