The first step in calculating using the order of operations is to perform operations inside the parentheses. Moving down the list, next perform all exponent operations moving from left to right. Next (left to right once more), perform all multiplications and divisions. Finally, perform the additions and subtractions.
Applying the order of operations with rational numbers.
Correctly apply the rules for the order of operations to accurately compute ( 5 7 − 2 7 ) × 2 3 ( 5 7 − 2 7 ) × 2 3 .
Step 1: To calculate this, perform all calculations within the parentheses before other operations.
( 5 7 − 2 7 ) × 2 3 = ( 3 7 ) × 2 3 ( 5 7 − 2 7 ) × 2 3 = ( 3 7 ) × 2 3
Step 2: Since all parentheses have been cleared, we move left to right, and compute all the exponents next.
( 3 7 ) × 2 3 = ( 3 7 ) × 8 ( 3 7 ) × 2 3 = ( 3 7 ) × 8
Step 3: Now, perform all multiplications and divisions, moving left to right.
( 3 7 ) × 8 = 24 7 ( 3 7 ) × 8 = 24 7
Example \(\pageindex{20}\).
Correctly apply the rules for the order of operations to accurately compute 4 + 2 3 ÷ ( ( 5 9 ) 2 − ( 2 3 + 5 ) ) 2 4 + 2 3 ÷ ( ( 5 9 ) 2 − ( 2 3 + 5 ) ) 2 .
To calculate this, perform all calculations within the parentheses before other operations. Evaluate the innermost parentheses first. We can work separate parentheses expressions at the same time.
Step 1: The innermost parentheses contain 2 3 + 5 2 3 + 5 . Calculate that first, dividing after finding the common denominator.
4 + 2 3 ÷ ( ( 5 9 ) 2 − ( 2 3 + 5 ) ) 2 = 4 + 2 3 ÷ ( ( 5 9 ) 2 − ( 2 3 + 5 1 ) ) 2 = 4 + 2 3 ÷ ( ( 5 9 ) 2 − ( 2 3 + 15 3 ) ) 2 = 4 + 2 3 ÷ ( ( 5 9 ) 2 − ( 17 3 ) ) 2 4 + 2 3 ÷ ( ( 5 9 ) 2 − ( 2 3 + 5 ) ) 2 = 4 + 2 3 ÷ ( ( 5 9 ) 2 − ( 2 3 + 5 1 ) ) 2 = 4 + 2 3 ÷ ( ( 5 9 ) 2 − ( 2 3 + 15 3 ) ) 2 = 4 + 2 3 ÷ ( ( 5 9 ) 2 − ( 17 3 ) ) 2
Step 2: Calculate the exponent in the parentheses, ( 5 9 ) 2 ( 5 9 ) 2 .
4 + 2 3 ÷ ( ( 5 9 ) 2 − ( 17 3 ) ) 2 = 4 + 2 3 ÷ ( ( 25 81 ) − ( 17 3 ) ) 2 4 + 2 3 ÷ ( ( 5 9 ) 2 − ( 17 3 ) ) 2 = 4 + 2 3 ÷ ( ( 25 81 ) − ( 17 3 ) ) 2
Step 3: Subtract inside the parentheses is done, using a common denominator.
4 + 2 3 ÷ ( ( 25 81 ) − ( 17 3 ) ) 2 4 + 2 3 ÷ ( ( 25 81 ) − ( 17 × 27 3 × 27 ) ) 2 4 + 2 3 ÷ ( ( 25 81 ) − ( 459 81 ) ) 2 4 + 2 3 ÷ ( ( − 434 81 ) ) 2 4 + 2 3 ÷ ( ( 25 81 ) − ( 17 3 ) ) 2 4 + 2 3 ÷ ( ( 25 81 ) − ( 17 × 27 3 × 27 ) ) 2 4 + 2 3 ÷ ( ( 25 81 ) − ( 459 81 ) ) 2 4 + 2 3 ÷ ( ( − 434 81 ) ) 2
Step 4: At this point, evaluate the exponent and divide.
4 + 2 3 ÷ ( ( − 434 81 ) ) 2 4 + 2 3 ÷ ( 188,356 6,561 ) = 4 + 2 3 × ( 6,561 188,356 ) = 4 + 2,187 94,178 4 + 2 3 ÷ ( ( − 434 81 ) ) 2 4 + 2 3 ÷ ( 188,356 6,561 ) = 4 + 2 3 × ( 6,561 188,356 ) = 4 + 2,187 94,178
Step 5: Add.
4 + 2,187 94,178 = 378,899 94,178 4 + 2,187 94,178 = 378,899 94,178
Had this been done on a calculator, the decimal form of the answer would be 4.0232 (rounded to four decimal places).
Video \(\pageindex{9}\).
Order of Operations Using Fractions
For any two distinct rational numbers \(a\) and \(b\) where \(a < b\), there exists a rational number \(c\) such that \(a < c < b\). This is called the density property of the rational numbers.
This means that no matter how close two rational numbers are, you can always find another rational number between them. In fact, there are infinitely many rational numbers that are possible between \(a\) and \(b\).
To find one of those numbers:
Step 1: Add the two rational numbers.
Step 2: Divide that result by 2.
The result is always a rational number. This follows what we know about rational numbers. If two fractions are added, then the result is a fraction. Also, when a fraction is divided by a fraction (and 2 is a fraction), then we get another fraction. This two-step process will give a rational number, provided the first two numbers are rational.
Demonstrate the density property of rational numbers by finding a rational number between 4 11 4 11 and 7 12 7 12 .
To find a rational number between 4 11 4 11 and 7 12 7 12 :
Step 1: Add the fractions.
4 11 + 7 12 = 4 × 12 11 × 12 + 7 × 11 12 × 11 = 48 132 + 77 132 = 125 132 4 11 + 7 12 = 4 × 12 11 × 12 + 7 × 11 12 × 11 = 48 132 + 77 132 = 125 132
Step 2: Divide the result by 2. Recall that to divide by 2, you multiply by the reciprocal of 2. The reciprocal of 2 is 1 2 1 2 , as seen below.
125 132 ÷ 2 = 125 132 × 1 2 = 125 264 125 132 ÷ 2 = 125 132 × 1 2 = 125 264
So, one rational number between 4 11 4 11 and 7 12 7 12 is 125 264 125 264 .
We could check that the number we found is between the other two by finding the decimal representation of the numbers. Using a calculator, the decimal representations of the rational numbers are 0.363636…, 0.473484848…, and 0.5833333…. Here it is clear that 125 264 125 264 is between 4 11 4 11 and 7 12 7 12 .
Rational numbers are used in many situations, sometimes to express a portion of a whole, other times as an expression of a ratio between two quantities. For the sciences, converting between units is done using rational numbers, as when converting between gallons and cubic inches. In chemistry, mixing a solution with a given concentration of a chemical per unit volume can be solved with rational numbers. In demographics, rational numbers are used to describe the distribution of the population. In dietetics, rational numbers are used to express the appropriate amount of a given ingredient to include in a recipe. As discussed, the application of rational numbers crosses many disciplines.
Mixing soil for vegetables.
James is mixing soil for a raised garden, in which he plans to grow a variety of vegetables. For the soil to be suitable, he determines that 2 5 2 5 of the soil can be topsoil, but 2 5 2 5 needs to be peat moss and 1 5 1 5 has to be compost. To fill the raised garden bed with 60 cubic feet of soil, how much of each component does James need to use?
In this example, we know the proportion of each component to mix, and we know the total amount of the mix we need. In this kind of situation, we need to determine the appropriate amount of each component to include in the mixture. For each component of the mixture, multiply 60 cubic feet, which is the total volume of the mixture we want, by the fraction required of the component.
Step 1: The required fraction of topsoil is 2 5 2 5 , so James needs 60 × 2 5 60 × 2 5 cubic feet of topsoil. Performing the multiplication, James needs 60 × 2 5 = 120 5 = 24 60 × 2 5 = 120 5 = 24 (found by treating the fraction as division, and 120 divided by 5 is 24) cubic feet of topsoil.
Step 2: The required fraction of peat moss is also 2 5 2 5 , so he also needs 60 × 2 5 60 × 2 5 cubic feet, or 60 × 2 5 = 120 5 = 24 60 × 2 5 = 120 5 = 24 cubic feet of peat moss.
Step 3: The required fraction of compost is 1 5 1 5 . For the compost, he needs 60 × 1 5 = 60 5 = 12 60 × 1 5 = 60 5 = 12 cubic feet.
Example \(\pageindex{23}\), determining the number of specialty pizzas.
At Bella’s Pizza, one-third of the pizzas that are ordered are one of their specialty varieties. If there are 273 pizzas ordered, how many were specialty pizzas?
One-third of the whole are specialty pizzas, so we need one-third of 273, which gives 1 3 × 273 = 273 3 = 91 1 3 × 273 = 273 3 = 91 , found by dividing 273 by 3. So, 91 of the pizzas that were ordered were specialty pizzas.
Video \(\pageindex{10}\).
Finding a Fraction of a Total
A common application of fractions is called unit conversion , or converting units , which is the process of changing from the units used in making a measurement to different units of measurement.
For instance, 1 inch is (approximately) equal to 2.54 cm. To convert between units, the two equivalent values are made into a fraction. To convert from the first type of unit to the second type, the fraction has the second unit as the numerator, and the first unit as the denominator.
From the inches and centimeters example, to change from inches to centimeters, we use the fraction 2.54 cm 1 in 2.54 cm 1 in . If, on the other hand, we wanted to convert from centimeters to inches, we’d use the fraction 1 in 2.54 cm 1 in 2.54 cm . This fraction is multiplied by the number of units of the type you are converting from , which means the units of the denominator are the same as the units being multiplied.
Converting liters to gallons.
It is known that 1 liter (L) is 0.264172 gallons (gal). Use this to convert 14 liters into gallons.
We know that 1 liter = 0.264172 gal. Since we are converting from liters, when we create the fraction we use, make sure the liter part of the equivalence is in the denominator. So, to convert the 14 liters to gallons, we multiply 14 by 1 gal 0.264172 gal / 1 liter 1 gal 0.264172 gal / 1 liter . Notice the gallon part is in the numerator since we’re converting to gallons, and the liter part is in the denominator since we are converting from liters. Performing this and rounding to three decimal places, we find that 14 liters is 14 liter × 0.264172 gal 1 liter = 3.69841 gal 14 liter × 0.264172 gal 1 liter = 3.69841 gal .
Example \(\pageindex{25}\), converting centimeters to inches.
It is known that 1 inch is 2.54 centimeters. Use this to convert 100 centimeters into inches.
We know that 1 inch = 2.54 cm. Since we are converting from centimeters, when we create the fraction we use, make sure the centimeter part of the equivalence is in the denominator, 1 in 2.54 cm 1 in 2.54 cm . To convert the 100 cm to inches, multiply 100 by 1 in 2.54 cm 1 in 2.54 cm . Notice the inch part is in the numerator since we’re converting to inches, and the centimeter part is in the denominator since we are converting from centimeters. Performing this and rounding to three decimal places, we obtain 100 cm × 1 in 2.54 cm = 39.370 in 100 cm × 1 in 2.54 cm = 39.370 in . This means 100 cm equals 39.370 in.
Video \(\pageindex{11}\).
Converting Units
A percent is a specific rational number and is literally per 100. n n percent, denoted n n %, is the fraction n 100 n 100 .
Rewriting a percentage as a fraction.
Rewrite the following as fractions:
Example \(\pageindex{27}\), rewriting a percentage as a decimal.
Rewrite the following percentages in decimal form:
You should notice that you can simply move the decimal two places to the left without using the fractional definition of percent.
Percent is used to indicate a fraction of a total. If we want to find 30% of 90, we would perform a multiplication, with 30% written in either decimal form or fractional form. The 90 is the total , 30 is the percentage , and 27 (which is 0.30 × 90 0.30 × 90 ) is the percentage of the total .
n % n % of x x items is \(\frac{n}{100} \times x\). The x x is referred to as the total , the n n is referred to as the percent or percentage , and the value obtained from \(\frac{n}{100} \times x\) is the part of the total and is also referred to as the percentage of the total .
Finding a percentage of a total.
In the previous situation, we knew the total and we found the percentage of the total. It may be that we know the percentage of the total, and we know the percent, but we don't know the total. To find the total if we know the percentage the percentage of the total, use the following formula.
If we know that n n % of the total is x x , then the total is \(\frac{100 \times x}{n}\) .
Finding the total when the percentage and percentage of the total are known.
The percentage can be found if the total and the percentage of the total is known. If you know the total, and the percentage of the total, first divide the part by the total. Move the decimal two places to the right and append the symbol %. The percentage may be found using the following formula.
The percentage, n n , of b b that is a a is a b × 100 % a b × 100 % .
Finding the percentage when the total and percentage of the total are known.
Find the percentage in the following:
In the media, in research, and in casual conversation percentages are used frequently to express proportions. Understanding how to use percent is vital to consuming media and understanding numbers. Solving problems using percentages comes down to identifying which of the three components of a percentage you are given, the total, the percentage, or the percentage of the total. If you have two of those components, you can find the third using the methods outlined previously.
Percentage of students who are sleep deprived.
A study revealed that 70% of students suffer from sleep deprivation, defined to be sleeping less than 8 hours per night. If the survey had 400 participants, how many of those participants had less than 8 hours of sleep per night?
The percentage of interest is 70%. The total number of students is 400. With that, we can find how many were in the percentage of the total, or, how many were sleep deprived. Applying the formula from above, the number who were sleep deprived was 0.70 × 400 = 280 0.70 × 400 = 280 ; 280 students on the study were sleep deprived.
Example \(\pageindex{32}\), amazon prime subscribers.
There are 126 million users who are U.S. Amazon Prime subscribers. If there are 328.2 million residents in the United States, what percentage of U.S. residents are Amazon Prime subscribers?
We are asked to find the percentage. To do so, we divide the percentage of the total, which is 126 million, by the total, which is 328.2 million. Performing this division and rounding to three decimal places yields 126 328.2 = 0.384 126 328.2 = 0.384 . The decimal is moved to the right by two places, and a % sign is appended to the end. Doing this shows us that 38.4% of U.S. residents are Amazon Prime subscribers.
Example \(\pageindex{33}\).
Evander plays on the basketball team at their university and 73% of the athletes at their university receive some sort of scholarship for attending. If they know 219 of the student-athletes receive some sort of scholarship, how many student-athletes are at the university?
We need to find the total number of student-athletes at Evander’s university.
Step 1: Identify what we know. We know the percentage of students who receive some sort of scholarship, 73%. We also know the number of athletes that form the part of the whole, or 219 student-athletes.
Step 2: To find the total number of student-athletes, use \(\frac{100 \times x}{n}\), with \(x = 219\) and \(n = 73\). Calculating with those values yields 100 × 219 73 = 300 100 × 219 73 = 300 .
So, there are 300 total student-athletes at Evander’s university
Check your understanding.
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Adding and subtracting rational numbers to solve problems.
Students will compute and solve problems using rational numbers. They will:
60–90 minutes
The possible inclusion of commercial websites below is not an implied endorsement of their products, which are not free, and are not required for this lesson plan.
IXL’s Grade 7 Add and Subtract Rational Numbers will give students additional practice with addition and subtraction of rational numbers.
IXL’s Grade 8 Add and Subtract Rational Numbers: Word Problems will give students additional practice with solving word problems that involve rational numbers.
: | Students will learn to compute with rational numbers and use these skills to solve real-world problems. |
: | Hook students into the lesson by asking them to model a problem involving the addition of two rational numbers using a number line. |
: | The focus of the lesson is on computing sums and differences of rational numbers. Once students are adept at computing with rational numbers, the lesson will proceed to problem solving with rational numbers. After you walk students through several example problems, students will participate in the final class activity, which culminates in a class PowerPoint file. |
: | Opportunities for discussion occur with each computation and real-world example, leading students to rethink and revise their understanding throughout the lesson. The PowerPoint activity gives students an opportunity to review their understanding, prior to completing the exit ticket. |
: | Evaluate students’ level of understanding and comprehension by giving students the exit ticket. |
: | Using suggestions in the Extension section, the lesson can be modified to meet the needs of students. The Small-Group Practice worksheet offers more practice for students. The Expansion Worksheet includes more difficult numeric expressions and additional word problems for students who are ready for a challenge. |
: | The lesson is scaffolded so that students first model an addition problem with manipulatives before attempting to compute a few sums and differences. Next, students discuss the computation process for all examples. The second part of the lesson involves problem solving with rational numbers. Students provide the solution process with the teacher serving as a facilitator. This lesson is meant as a refresher for adding and subtracting rational numbers and as an introduction to problem solving with rational numbers. The next lesson in the unit will present multiplication and division with rational numbers and problem solving using these operations on rational numbers. |
As students come into class, have them evaluate the following expressions using a number line.
Walk around the classroom as students are working through the example problems. Briefly discuss the answers and make sure students are comfortable modeling addition and subtraction of rational numbers on a number line before moving on.
“In Lesson 1 of this unit, we learned how to model addition and subtraction of rational numbers on a number line. Today, we are going to focus on performing these computations without the use of a number line. We will then use these skills to solve some real-life problems.”
Computations: Adding and Subtracting Rational Numbers
Before presenting some real-world problems, give students the opportunity to practice adding and subtracting rational numbers without the help of a number line. If necessary, go over the following examples together as a class.
the other is not. Often, when computing with fractions, it is best to write all numbers in fraction form.”
common denominator. The lowest common denominator in this case would be 5.”
numerators as indicated. The denominator will stay as is.”
it is, but we may want to rewrite the fraction as a mixed number to get a better idea of the value.”
Example 2: − 4.64 + 9.85
you suspect our final answer here will be positive or negative?” (Positive, the absolute value of 9.85 is larger than the absolute value of −4.64.)
Distribute the Lesson 2 Computations Worksheet ( M-7-5-2_Computations and KEY.docx ). Instruct students to complete the worksheet individually. Walk around the room as students work to be sure they are on task and performing the computations accurately. Following the worksheet, provide time for students to discuss any problems they encountered, questions they have, or revelations they discovered. First, ask students to describe the computation process used to find each sum or difference. Then confirm their understanding by restating the correct process.
Problem Solving with Rational Numbers
Now it is time for students to apply their understanding of computation to solving real-world problems. Discuss the following examples together as a class.
Distribute Lesson 2 Word-Problem Examples ( M-7-5-2_Word Problem Examples and KEY.docx ). Have students discuss the solution process for each example problem in a manner similar to the process demonstrated above. Confirm the correct ideas students express. Then say: “Look through the problems you just received. Think of how the example word problems can be solved. Do you need to add or subtract the rational numbers? How will you go about doing this for fractions with unlike denominators, or for mixed numbers?”
Activity 1: Write-Pair-Share
Ask the whole class to think of some real-world contexts that involve the addition or subtraction of rational numbers. Students should make a list of at least five real-world contexts and provide one word problem. Ask students to share their ideas with a partner. Give students about 5 minutes to share contexts and word problems. During this time, each partner may ask questions of the other partner. Then, the whole class can reconvene. One member from each partner group will share the list of real-world contexts and word problems with the class. The teacher may wish to post the real-world contexts and word problems in a file on the class Web page or use them as a classroom display. These student examples would then serve as a reference tool.
Have students complete Lesson 2 Exit Ticket ( M-7-5-2_Exit Ticket and KEY.docx ) at the close of the lesson to evaluate students’ level of understanding.
Use the suggestions in the Routine section to review lesson concepts throughout the school year. Use the small-group suggestions for any students who might benefit from additional instruction. Use the Expansion section to challenge students who are ready to move beyond the requirements of the standard.
Insert template, information.
IMAGES
COMMENTS
Dividing Rational Numbers Practice and Problem Solving: A/B Find each quotient. 1. 1 2 y 3 2. 6 y 3 4 §·¨¸ ©¹ 3. 5 6 y 10 BBBBBBBBBBBBBBBBB BBBBBBBBBBBBBBBBB BBBBBBBBBBBBBBBBB 4. 5.25 15 5. 24 y 3.2 6. 0.125 y 0.5 BBBBBBBBBBBBBBBBB BBBBBBBBBBBBBBBBB BBBBBBBBBBBBBBBBB 7. 13 714 y 8. 3 2 9 8 9. 11 13 23 y
Choose and complete a graphic organizer to help you study the concept. 1. dividing integers. 2. writing fractions or mixed numbers as decimals. 3. writing decimals as fractions or mixed numbers. 4. multiplying rational numbers. 5. dividing rational numbers. "I finished my Information Frame about rainforests.
Practice. Have students practice dividing rational numbers including fractions, integers, and decimals using the color by code activity included in the resource. Walk around the classroom to answer any student questions and provide assistance as needed. Fast finishers can work on the maze activity for extra practice.
The short solution is as follows: Example 2. Find the value of the expression. This is a multiplication of rational numbers with different signs. Multiply the modules of these numbers and put minus in front of the answer: The solution for this example can be written in a shorter form: Example 3.
Lesson Plan I. Topic: Dividing Rational Numbers II. Goals and Objectives: ... Problem-solving skills (explore, plan, solve, verify.) 3. PA.3.3 ... Independent Practice: Dividing Rational Numbers Worksheet A. Class work: #2 - 44 Even B. Homework: #1 - 45 odds C. Due in two days. Allow for the day in between the date assigned and the date due for
Sam remembers that to divide rational numbers, he can actually turn this problem into a multiplication problem by flipping the second rational number. So 7/8 becomes 8/7 and the division symbol ...
The sign of a negative number divided by a negative number is always positive. A number that can be used in place of the variable that makes the equation true is called a solution to the equation. For example, for the equation x ÷ − 2 = 5, the solution is -10, because it is true that − 10 ÷ − 2 = 5.
The focus of the lesson is on computing products and quotients of rational numbers. Students will then solve problems involving rational numbers. In the final class activity, students will be given an opportunity to write an original word problem that involves the multiplication or division of rational numbers, and also to show the solution ...
Lesson 5: Rational numbers. Intro to rational & irrational numbers. ... Adding & subtracting rational numbers: 79% - 79.1 - 58 1/10. Adding & subtracting rational numbers: 0.79 - 4/3 - 1/2 + 150%. Adding & subtracting rational numbers. Multiplying positive and negative fractions. ... One way to find the reciprocal of a number is to divide 1 ...
Video Transcript. In this lesson, what we'll be looking at is dividing rational numbers. And this will include fractions and decimals. So by the end of the lesson, what we should be able to do is divide a rational decimal by a rational decimal, divide a fraction by a fraction, divide rational numbers in various different forms, and, finally ...
So, ( 1)( 1) 1. Work with a partner. a. Graph each number below on three different number lines. Then multiply each number by 1 and graph the product on the appropriate number line. In this lesson, you will multiply and divide rational numbers. solve real-life problems. Learning Standards. b.
5-10 minutes. Represent each addition problem in parts A through C on a number line and find each sum. a. − 9 + 5. b. 8 + ( − 7) c. − 3 + ( − 6) d. Choose one problem from A through C and write a real-world situation that could be modeled by the problem.
Problem. Answer two questions about the following rational division. 1. What is the quotient in lowest terms? 2. What values of x must we exclude from the domains of the expressions? Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more.
The steps to be followed to divide two rational numbers are given below: Step 1: Take the reciprocal of the divisor (the second rational number). 2x/9 = 9/2x. Step 2: Multiply it to the dividend. −4x/3 × 9/2x. Step 3: The product of these two numbers will be the solution. (−4x × 9) / (3 × 2x) = −6.
Problem-Solving Strategy Updates Scavenger Hunt Recording Sheet ... Data Updates Problem of the Week Cards TAKS Test Practice Lesson Resources Extra Examples Parent and Student Study Guide Self-Check Quizzes. ... First Edition Chapter 4, Lesson 3: Dividing Rational Numbers. Extra Examples; Parent and Student Study Guide; Self-Check Quizzes; Log ...
Problem Solving With Rational Numbers. Digging into 7th-grade standard 7.NS.A.3. By: ... This is not the time or place to start back at square one teaching students to add, subtract, multiply, and divide whole numbers, fractions, and decimals. ... Let's take a look at a problem from this 7th-grade lesson in the Illustrative Mathematics ...
Standardized Test Practice Problem of the Week Math in the Workplace Lesson Resources Extra Examples Self-Check Quizzes Data Updates Parent Student Study Guide. Mathematics. Home > Chapter 4 > Lesson 3. ron algebra C and A. First Edition Chapter 4, Lesson 3: Dividing Rational Numbers. Extra Examples; Self-Check Quizzes ; Data Updates; Parent ...
Learning to multiply and divide rational numbers? Follow these 3 steps! See examples with negative fractions and decimals in this interactive math lesson.
Student Facing Goals I can represent situations with expressions that include rational numbers. I can solve problems using the four operations with rational numbers. Lesson Narrative In this lesson students put together what they have learned about rational number arithmetic and the interpretation of negative quantities, such as negative time or negative rates of change.
Math in Motion Reading in the Content Area ... Standardized Test Practice Vocabulary Review Lesson Resources Extra Examples Personal Tutor Self-Check Quizzes. Common Core State Standards Supplement, SE ... Study to Go Online Calculators. Mathematics. Home > Chapter 3 > Lesson 4. Pre-Algebra. Chapter 3, Lesson 4: Dividing Rational Numbers. Extra ...
A rational number is any number that can be made by dividing two integers. Learn all about rational numbers in this free math lesson. Start learning now!
Forms of Rational Numbers. Fraction Form: A rational number can be written as a fraction, where the numerator and denominator are integers and the denominator is not zero. Example: \(\frac{6}{11}\), \(-\frac{5}{7}\), \(\frac{2}{1}\) Decimal Form: A rational number can be expressed as decimals, which can either terminate or repeat. Terminating Decimal: A decimal that ends after a finite number ...
Cite this lesson. The steps of multiplying or dividing rational polynomial expressions are to factor, flip (when dividing), slash or cancel, and multiply. Put these steps for multiplying and ...
The second part of the lesson involves problem solving with rational numbers. Students provide the solution process with the teacher serving as a facilitator. This lesson is meant as a refresher for adding and subtracting rational numbers and as an introduction to problem solving with rational numbers.