lesson 4 homework practice dividing rational numbers

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5.3.4: Dividing Rational Numbers

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Let's divide signed numbers.

Exercise \(\PageIndex{1}\): Tell Me Your Sign

Consider the equation: \(-27x=-35\)

Without computing:

• Is the solution to this equation positive or negative?
• Are either of these two number solutions to the equation?

\(\frac{35}{27}\qquad\qquad -\frac{35}{27}\)

Exercise \(\PageIndex{2}\): Multiplication and Division

• \(-3\cdot 4=?\)
• \(-3\cdot ?=12\)
• \(3\cdot ?=12\)
• \(?\cdot -4=12\)
• \(?\cdot 4=-12\)
• Rewrite the unknown factor problems as division problems.
• The sign of a positive number divided by a positive number is always:
• The sign of a positive number divided by a negative number is always:
• The sign of a negative number divided by a positive number is always:
• The sign of a negative number divided by a negative number is always:
• Where is each person 10 seconds before they meet up?
• When is each person at the position -10 feet from the meeting place?

Are you ready for more?

It is possible to make a new number system using only the numbers 0, 1, 2, and 3. We will write the symbols for multiplying in this system like this: \(1\otimes 2=2\). The table shows some of the products.

• In this system, \(1\otimes 3=3\) and \(2\otimes 3=2\). How can you see that in the table?
• What do you think \(2\otimes 1\) is?
• What about \(3\otimes 3\)?
• What do you think the solution to \(3\otimes n=2\) is?
• What about \(2\otimes n=3\)?

Exercise \(\PageIndex{3}\): Drilling Down

A water well drilling rig has dug to a height of -60 feet after one full day of continuous use.

• Assuming the rig drilled at a constant rate, what was the height of the drill after 15 hours?
• If the rig has been running constantly and is currently at a height of -147.5 feet, for how long has the rig been running?

• Use the coordinate grid to show the drill's progress.
• At this rate, how many hours will it take until the drill reaches -250 feet?

Any division problem is actually a multiplication problem:

• \(6\div 2=3\) because \(2\cdot 3=6\)
• \(6\div -2=-3\) because \(-2\cdot -3=6\)
• \(-6\div 2=-3\) because \(2\cdot -3=-6\)
• \(-6\div 2=3\) because \(-2\cdot 3=-6\)

Because we know how to multiply signed numbers, that means we know how to divide them.

• The sign of a positive number divided by a negative number is always negative.
• The sign of a negative number divided by a positive number is always negative.
• 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 \(x\div -2=5\), the solution is -10, because it is true that \(-10\div -2=5\).

Glossary Entries

Definition: Solution to an Equation

A solution to an equation is a number that can be used in place of the variable to make the equation true.

For example, 7 is the solution to the equation \(m+1=8\), because it is true that \(7+1=8\). The solution to \(m+1=8\) is not 9, because \(9+1\neq 8\).

Exercise \(\PageIndex{4}\)

Find the quotients:

• \(24\div -6\)
• \(-15\div 0.3\)
• \(-4\div -20\)

Exercise \(\PageIndex{5}\)

Find the quotients.

• \(\frac{2}{5}\div\frac{3}{4}\)
• \(\frac{9}{4}\div\frac{-3}{4}\)
• \(\frac{-5}{7}\div\frac{-1}{3}\)
• \(\frac{-5}{3}\div\frac{1}{6}\)

Exercise \(\PageIndex{6}\)

Is the solution positve or negative?

• \(2\cdot x=6\)
• \(-2\cdot x=6.1\)
• \(2.9\cdot x=-6.04\)
• \(-2.473\cdot x=-6.859\)

Exercise \(\PageIndex{7}\)

Find the solution mentally.

• \(3\cdot -4=a\)
• \(b=\cdot (-3)=-12\)
• \(-12\cdot c=12\)
• \(d\cdot 24=-12\)

Exercise \(\PageIndex{8}\)

In order to make a specific shade of green paint, a painter mixes \(1\frac{1}{2}\) quarts of blue paint, 2 cups of green paint, and \(\frac{1}{2}\) gallon of white paint. How much of each color is needed to make 100 cups of this shade of green paint?

(From Unit 4.1.2)

Exercise \(\PageIndex{9}\)

Here is a list of the highest and lowest elevation on each continent.

• Which continent has the largest difference in elevation? The smallest?
• Make a display (dot plot, box plot, or histogram) of the data set and explain why you chose that type of display to represent this data set.

(From Unit 5.2.2)

• → Resources
• → 7th Grade
• → Integers & Rational Numbers

Dividing Rational Numbers Lesson Plan

Get the lesson materials.

Dividing Rational Numbers Fractions Decimals Guided Notes Sketch & Doodles

Ever wondered how to teach dividing rational numbers, including fractions, integers, and decimals, in an engaging way to your middle school students?

In this lesson plan, students will learn about dividing rational numbers and their real-life applications. Through artistic and interactive guided notes, check for understanding questions, a color by code activity, and a maze worksheet, students will gain a comprehensive understanding of dividing rational numbers.

The lesson culminates with a real-life example that explores how dividing rational numbers can be applied to splitting a bill at a restaurant.

• Standards : CCSS 7.NS.A.2 , CCSS 7.NS.A.2.a , CCSS 7.NS.A.2.c
• Topics : Integers & Rational Numbers , Fractions , Decimals
• Grade : 7th Grade
• Type : Lesson Plans

Learning Objectives

After this lesson, students will be able to:

Divide rational numbers, including fractions, integers, and decimals

Solve division problems involving positive and negative rational numbers

Apply division of rational numbers to real-life situations

Prerequisites

Before this lesson, students should be familiar with:

Basic operations with rational numbers (adding, subtracting, and multiplying)

Basic understanding of fractions and decimals

Knowledge of how to determine the greatest common factor (GCF) and least common multiple (LCM) of numbers

Colored pencils or markers

Dividing Rational Numbers Fractions Decimals Guided Notes

Key Vocabulary

Rational numbers

Introduction

As a hook, ask students why dividing rational numbers, including fractions, integers, and decimals, is important in real life. Refer to the real-life math application on the last page of the guided notes as well as the FAQs below for ideas.

Use the guided notes to introduce the concept of dividing rational numbers. Walk through the key points of the topic, including the steps and techniques involved in dividing rational numbers. Refer to the FAQ below for a walk through on this, as well as ideas on how to respond to common student questions.

Check for Understanding : Have students walk through the "You Try!" section of the guided notes. Call on students to talk through their answers, potentially on the whiteboard or projector. Based on student responses, reteach concepts that students need extra help with.

Based on student responses, reteach concepts that students need extra help with. If your class has a wide range of proficiency levels, you can pull out students for reteaching, and have more advanced students begin work on the practice exercises.

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. You can assign these activities as homework for the remainder of the class.

Real-Life Application

Bring the class back together, and introduce the concept of rational number division applied to splitting a bill with friends. Refer to the FAQ for more real life applications that you can use for the discussion!

Additional Self-Checking Digital Practice

If you’re looking for digital practice for dividing rational numbers, try my Pixel Art activities in Google Sheets. Every answer is automatically checked, and correct answers unlock parts of a mystery picture. It’s incredibly fun, and a powerful tool for differentiation.

Here's an activity to try:

Multiplying & Dividing Rational Numbers Digital Pixel Art

Additional Print Practice

A fun, no-prep way to practice dividing rational numbers is Doodle Math — they’re a fresh take on color by number or color by code. It includes multiple levels of practice, perfect for a review day or sub plan.

Multiplying & Dividing Rational Numbers | Doodle Math: Twist on Color by Number

What is dividing rational numbers? Open

Dividing rational numbers involves dividing numbers that can be expressed as fractions or decimals. It is the process of finding how many times one number can be evenly divided by another number.

How do you divide fractions? Open

To divide fractions, you multiply the first fraction by the reciprocal (flipped) form of the second fraction. This can be done by multiplying the numerators together and the denominators together. Simplify the resulting fraction if possible.

How do you divide decimals? Open

Dividing decimals is similar to dividing whole numbers. Use long division to divide the decimal dividend by the decimal divisor. Place the decimal point in the quotient directly above the decimal point in the dividend.

Can you divide positive and negative rational numbers? Open

Yes, you can divide positive and negative rational numbers. The rules for dividing positive and negative numbers are the same as for multiplying them. The result of the division will have a positive quotient if both numbers have the same sign, and a negative quotient if the numbers have different signs.

What is the difference between dividing fractions and dividing decimals? Open

The main difference is in the representation of the numbers. Dividing fractions involves dividing numbers expressed as fractions, while dividing decimals involves dividing numbers expressed as decimal numbers. The processes and calculations are similar, but the final answers may be in different forms.

How can dividing rational numbers be applied in real life? Open

Dividing rational numbers is commonly used in real-life situations such as dividing the bill for a pizza among friends, calculating the cost per unit of a product, or determining the average speed of a moving object. It helps in solving problems that involve sharing, distributing, or comparing quantities.

Are there any tips or tricks for dividing rational numbers? Open

One tip for dividing rational numbers is to always simplify the fraction before dividing. This makes the calculation easier and reduces the chances of errors. Additionally, keeping track of the signs (+/-) and placing the decimal point correctly when dividing decimals will help in obtaining accurate results.

What are some common mistakes to avoid when dividing rational numbers? Open

Common mistakes to avoid when dividing rational numbers include forgetting to simplify the fraction, reversing the order of the fractions when finding the reciprocal, misplacing the decimal point when dividing decimals, and forgetting to consider the signs of the numbers being divided.

Are there any resources available to practice dividing rational numbers? Open

Yes, there are various resources available for practicing dividing rational numbers. This lesson plan includes guided notes, practice worksheets, color by code activities, and a real-life math application.

Want more ideas and freebies?

Get my free resource library with digital & print activities—plus tips over email.

Chapter 4, Lesson 3: Dividing Rational Numbers

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Curriculum  /  Math  /  7th Grade  /  Unit 2: Operations with Rational Numbers  /  Lesson 4

Operations with Rational Numbers

Lesson 4 of 18

Criteria for Success

Tips for teachers, anchor problems, problem set, target task, additional practice.

Model the addition of integers using a number line.

Common Core Standards

Core standards.

The core standards covered in this lesson

The Number System

7.NS.A.1.B — Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.

7.NS.A.1.D — Apply properties of operations as strategies to add and subtract rational numbers.

Foundational Standards

The foundational standards covered in this lesson

6.NS.C.6 — Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.

6.NS.C.7.C — Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. For example, for an account balance of -30 dollars, write |-30| = 30 to describe the size of the debt in dollars.

The essential concepts students need to demonstrate or understand to achieve the lesson objective

• Model addition on a number line using concepts of absolute value and the sign of the number to determine magnitude and direction.
• Determine that the commutative property of addition holds for the addition of integers.
• Represent integer addition problems on a number line.
• Write integer addition problems from models on a number line. 
• Model with mathematics using number lines, equations, and descriptions to show the relationships between the representations (MP.4).

Suggestions for teachers to help them teach this lesson

• In the next three lessons, students begin to operate with signed numbers. In this lesson, they start by building a conceptual understanding of the operation of addition using a number line and familiar contexts. Then in later lessons, students determine efficient ways to add rational numbers without the use of a number line. 
• This lesson only uses integers to allow for students to focus on the concepts and not calculations with fractions or decimals. Other rational numbers will be used in Lessons 5 and 6. 

Lesson Materials

• Laminated number line (1 per student)
• Dry erase marker (1 per student)
• Game piece or token (1 per student)

Unlock features to optimize your prep time, plan engaging lessons, and monitor student progress.

Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding

The number line below represents the road that Joshua lives on, with his home located at point 0. The numbers on the number line represent the number of miles from Joshua’s house, either east or west. Throughout the week, Joshua goes on trips and errands along this road. 

For each day described in the chart, model Joshua’s trip and determine where on the number line he ends up each day. Write an addition equation to represent it.

Guiding Questions

Is $${-7+4}$$ equivalent to $${4+(-7)}$$ ? 

Show the sum for each expression on a number line to justify your answer.

In part (a), model the addition problem on the number line to find the sum. In part (b), write an addition equation to represent what is shown on the number line.

a.       $${5+(-4)+(-3)}$$

A set of suggested resources or problem types that teachers can turn into a problem set

Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.

A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved

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.

Student Response

The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.

• Include problems where students go between addition equations and number line models (e.g., given one, write the other).
• Include error analysis problems where addition equations have been incorrectly written to represent a number line diagram (see notes in Anchor Problem #3).
• Illustrative Mathematics Distances on the Number Line 2
• EngageNY Mathematics Grade 7 Mathematics > Module 2 > Topic A > Lesson 3 — Problem Set #1 only
• EngageNY Mathematics Grade 7 Mathematics > Module 2 > Topic A > Lesson 2 — Examples, Exercises, and Problem Set. (Note, some problems reference the Integer Game. If this game is not being used in class, the problems can be modified to remove the reference.)

Topic A: Adding and Subtracting Rational Numbers

Represent rational numbers on the number line. Define opposites, absolute value, and rational numbers.

Compare and order rational numbers. Write and interpret inequalities to describe the order of rational numbers.

Describe situations in which opposite quantities combine to make zero.

7.NS.A.1.B 7.NS.A.1.D

Determine efficient ways to add rational numbers with and without the number line.

Efficiently add and reason about sums of rational numbers.

Understand subtraction as addition of the opposite value (or additive inverse).

7.NS.A.1.C 7.NS.A.1.D

Find and represent the distance between two rational numbers as the absolute value of their difference.

Subtract rational numbers with and without the number line.

Add and subtract rational numbers efficiently using properties of operations.

Add and subtract rational numbers using a variety of strategies.

7.NS.A.1 7.NS.A.1.A 7.NS.A.1.B 7.NS.A.1.C 7.NS.A.1.D

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Topic B: Multiplying and Dividing Rational Numbers

Determine the rules for multiplying signed numbers.

7.NS.A.2.A 7.NS.A.2.C

Multiply signed rational numbers and interpret products in real-world contexts.

Determine the rules for dividing signed numbers.

7.NS.A.2.B 7.NS.A.2.C

Divide signed rational numbers and interpret quotients in real-world contexts.

Convert rational numbers to decimals using long division and equivalent fractions.

Multiply and divide with rational numbers using properties of operations.

7.NS.A.2 7.NS.A.2.C

Topic C: Using all Four Operations with Rational Numbers

Solve problems with rational numbers and all four operations.

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Into Math Grade 7 Module 5 Lesson 4 Answer Key Multiply and Divide Rational Numbers in Context

We included H MH Into Math Grade 7 Answer Key PDF Module 5 Lesson 4 Multiply and Divide Rational Numbers in Context to make students experts in learning maths.

HMH Into Math Grade 7 Module 5 Lesson 4 Answer Key Multiply and Divide Rational Numbers in Context

I Can multiply and divide rational numbers in context.

Step It Out

Turn and Talk Write and solve your own multiplication problem based on this situation.

B. How do you know that your answer is reasonable? _____________________ _____________________

Turn and Talk What is the scuba diver’s change in elevation in feet per minute during the final ascent? Explain.

Check Understanding

Question 1. If the scuba diver in Task 2 originally swam -12\(\frac{1}{2}\) feet per minute, for 4\(\frac{1}{2}\) minutes, how would this change the situation? Answer: The change in situation is -56.25 feet.

Explanation: Distance travelled per minute = -12\(\frac{1}{2}\) feet Time travelled = 4\(\frac{1}{2}\) minutes Change in elevation = Distance traveled per minute × Time traveled = -12\(\frac{1}{2}\) × 4\(\frac{1}{2}\) Convert them into improper fractions = –\(\frac{25}{2}\) × \(\frac{9}{2}\) = –\(\frac{225}{4}\) = -56.25 feet.

On Your Own

A. Find and interpret the change in temperature for an increase in elevation of 0.2 mile. _____________________ _____________________ Answer: -3.76

Explanation: Temperature change is about -18.8 F per mile an increase in elevation of 0.2 mile -18.8 × 0.2 = -3.76

B. Find and interpret the change in temperature for a decrease in elevation of 0.2 miles. _____________________ _____________________ Answer: 3.76

Explanation: Temperature change is about -18.8 F per mile. Decrease in elevation of 0.2 miles -18.8 × – 0.2 = 3.76

C. How are your answers to Parts A and B related? _____________________ _____________________ Answer: In part A when the elevation increases by 0.2 miles the temperature drops about 3.76° F. In part B when the elevation decreases by 0.2 miles, the temperature rises about 3.76° F.

Question 4. A butterfly is flying 8\(\frac{3}{4}\) feet above the ground. It descends at a steady rate to a spot 6\(\frac{1}{4}\) feet above the ground in 1\(\frac{2}{3}\) minutes. What is the butterfly’s change in elevation in feet per minute? Answer: The required change in elevation of the butterfly is 1.5 ft per min.

Explanation: Given, A butterfly is flying 8\(\frac{3}{4}\) feet above the ground. It descends at a steady rate to a spot 6\(\frac{1}{4}\) feet above the ground in 1\(\frac{2}{3}\) minutes. We have to find the butterfly’s change in elevation in feet per minute Change in elevation = butterfly flying above ground – steady rate to a spot above the ground is 8\(\frac{3}{4}\) – 6\(\frac{1}{4}\) \(\frac{35}{4}\) – \(\frac{25}{4}\) \(\frac{10}{4}\) \(\frac{5}{2}\) 2.5 feet Now change in elevation per minute = 1\(\frac{2}{3}\) =  \(\frac{5}{3}\) Change in elevation 2.5 ÷ \(\frac{5}{3}\) 2.5 × \(\frac{3}{5}\) 1.5 feet per minute.

Question 5. One scuba diver’s elevation changed by -15\(\frac{5}{8}\) feet every minute. This was 1\(\frac{1}{4}\) times the rate of change for a second scuba diver. What was the rate of change in elevation of the second scuba diver in feet per minute? Show your work. Answer: 12.5 or 12\(\frac{1}{2}\)

Explanation: Given, scuba diver’s elevation changed by -15\(\frac{5}{8}\) feet every minute. second scuba diver rate of change is 1\(\frac{1}{4}\) 15\(\frac{5}{8}\) ÷ 1\(\frac{1}{4}\) \(\frac{125}{8}\) ÷ \(\frac{5}{4}\) \(\frac{125}{8}\) × \(\frac{4}{5}\) \(\frac{25}{2}\) 12.5 or 12\(\frac{1}{2}\).

Question 6. Open Ended Write a real-world problem based on one of the contexts in the lesson that can be solved using multiplication or division of negative fractions or decimals. Answer: A store is selling a can of dog food for $0.40. Payal spent $4.80 on cans of dog food. Solve an equation to find how many cans shw bought $0.40. No of cans = $4.80 ÷ $0.40 = 12 cans.

Question 7. Carl has 3\(\frac{1}{2}\) cups of blueberries. He is storing them in containers that each hold \(\frac{2}{3}\) cup. How many containers can he fill? Find the answer and interpret the result. Answer: The total number of containers that can be filled = 5\(\frac{11}{50}\).

Explanation: The blueberries carl has = 3\(\frac{1}{2}\) cups = 3.5 cups The amount of blueberries each container can store = \(\frac{2}{3}\) = 0.67 Total cups = Total amount of blueberries to be stored ÷ Stored in one cup = 3.5 cup ÷ 0.67 = 5.22 = 5\(\frac{11}{50}\).

Question 8. Mrs. Anderson writes a check for $10.50 to each of her four nieces. What will be the total change in Mrs. Anderson’s checking account balance after all four checks are cashed? ____ Answer: -42

Explanation: Given, Mrs. Anderson writes a check for $10.50 to each of her four nieces. $10.50 × 4 42 They are asking how many checks were cashed, the answer will be negative. = -42

Question 9. The denominator of a fraction is \(\frac{-3}{4}\). The numerator is \(\frac{1}{4}\) more than the denominator. Identify the fraction. Then show that it is a rational number. Answer:

Find each quotient.

Expression: Let us solve the given expression \(\frac{7}{10}\) ÷ – \(\frac{1}{5}\) \(\frac{7}{10}\) × – 5 Cancel the common factors –\(\frac{7}{2}\) -3.5

Explanation: Let us solve the given expression –\(\frac{5}{6}\) ÷ – \(\frac{6}{7}\) –\(\frac{5}{6}\) × – \(\frac{7}{6}\) \(\frac{35}{36}\) 0.972

Explanation: Let us solve the given expression \(\frac{252}{4}\) ÷ –\(\frac{3}{8}\) 252 ÷ 4 = 63 63 × –\(\frac{8}{3}\) 21 × -8 -168

Question 13. \(\frac{2.8}{-4}\) _____________________ Answer: –\(\frac{7}{10}\)

Explanation: Let us solve the given expression \(\frac{2.8}{-4}\) –\(\frac{28}{(4 × 10)}\) –\(\frac{7}{10}\)

Question 14. –\(\frac{5.5}{0.5}\) _____________________ Answer: -11

Explanation: Let us solve the given expression –\(\frac{5.5}{0.5}\) Convert the decimal fractions into integers –\(\frac{(55 × 10)}{(5 × 10}\) Cancel all the common factors -11

Question 15. \(\frac{0.72}{-0.9}\) _____________________ Answer: -0.8

Explanation: Let us solve the given expression \(\frac{0.72}{-0.9}\) Convert the decimal fractions into integers \(\frac{(72 × 10)}{(-9 × 100)}\) –\(\frac{8}{10}\) –\(\frac{4}{5}\) -0.8

I’m in a Learning Mindset!

What questions can I ask my teacher to help me understand how to set up a problem that involves division?

Lesson 5.4 More Practice/Homework

Question 1. Math on the Spot Sarah drove her police car at a constant speed down a mountain. Her elevation decreased by 200 feet over a 10-minute period. What was the change in elevation during the first minute? Answer: The change in elevation during the first minute is -20 feet.

Explanation: Elevation decreased by 200 feet over a 10-minute period 200 ÷ 10 20 In her first minute, her elevation decreased by 20 feet.

Question 2. A submarine descends \(\frac{1}{120}\) mile every minute. Write a product of three or more rational numbers to represent the change in the submarine’s elevation after 3 hours. Then find the value of the product, and explain what it represents. Answer: 1.5 mile

Explanation: Submarine descends \(\frac{1}{120}\) mile submarine’s elevation after 3 hours 3 × 60 minutes 3 × 60 × \(\frac{1}{120}\) 3 × \(\frac{1}{2}\) \(\frac{3}{2}\) 1.5 mile.

Question 3. Financial Literacy Tanisha takes a dance class that is priced as shown. The charge appears as negative on her account balance until she makes her monthly payment.

A. Show how to find the balance of Tanisha’s account for dance classes during a 4-week period in which she attends 3 classes per week. Answer:

Explanation: Amount per class is $12.50 Now we need to find out Tanisha’s account for 3 classes per week. one class per week = $12.50 3 classes per week = $12.50 × 3 = $37.5

B. Reason Suppose the balance on Tanisha’s account for a 2-week period is -$100. If Tanisha attended at least 1 dance class per week, how many classes could she have attended each week? Explain your reasoning. Answer: Tanisha attended 2 dance classes. Given, the balance on Tanisha’s account for a 2-week period is -$100 For 1 week it is – 100 ÷ 2 = -$50 Tanisha attended at least 1 dance class per week, 1 week = 1 dance class Therefore Tanisha attended 2 dance classes for the balance on Tanisha’s account for a 2-week period is -$100.

C. Evaluate the expression -112.50 ÷ (-12.50) and interpret what it could mean in this context. Answer: 9

Explanation: Given, the expression -112.50 ÷ (-12.50) We need to evaluate the expression Now cancel the minus symbol from both sides 112.50 ÷ 12.50 9

Explanation: Let us solve the given expression \(\frac{-5}{8}\) ÷ \(\frac{15}{16}\) \(\frac{-5}{8}\) × \(\frac{16}{15}\) Cancel the common factors –\(\frac{2}{3}\)

Explanation: Let us solve the given expression \(\frac{-2}{3}\) ÷ –\(\frac{4}{9}\) Cancel the minus symbol from both sides \(\frac{2}{3}\) × \(\frac{9}{4}\) \(\frac{3}{2}\) 1.5

Explanation: Let us solve the given expression \(\frac{24}{7}\) ÷ \(\frac{-6}{35}\) \(\frac{24}{7}\) × –\(\frac{35}{6}\) Cancel the common factors 4 × -5 -20

Question 7. Salton Sea Beach in California has an elevation of about – 230 feet. This is about 11.5 times the elevation of Indio, California. What is the elevation of Indio, California? about ___ feet Answer: -20

Explanation: California has an elevation of about – 230 feet. 11.5 times the elevation of Indio, California -230 ÷ 11.5 = -20

Question 8. During a winter cold spell, the temperature change was – 1.2 °F per hour for a period of 4.5 hours. Which expressions can be used to find the overall change in temperature during that time period? A. 4.5 ÷ (-1.2) degrees Fahrenheit B. 4.5 × (- 1.2) degrees Fahrenheit C. 4.5 – (- 1.2) degrees Fahrenheit D. (-1.2) + (-1.2) + (-1.2) + (-1.2) degrees Fahrenheit E. 4(- 1.2) + (0.5)(-1.2) degrees Fahrenheit Answer: B. 4.5 × (- 1.2) degrees Fahrenheit

Explanation: The expressions can be used to find the overall change in temperature during that time period is 4.5 × (- 1.2) degrees Fahrenheit.

Spiral Review

Question 10. What is the difference when – 2 is subtracted from 2? Answer: 4

Explanation: The difference when – 2 is subtracted from 2 is 4. 2 – (-2) = 4

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Chapter 3, Lesson 4: Dividing Rational Numbers

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• Grade 7 McGraw Hill Glencoe - Answer Keys

Explanation:

• \(-\frac{5}{6}+(-\frac{4}{9})=-\)
• \((\frac{7}{8}+\frac{3}{11})+\frac{1}{8}=\)
• \(\frac{4}{5}-\frac{3}{10}=\)
• \(\frac{3}{8}-(-\frac{1}{4})=\)
• \(\frac{3}{4}-\frac{1}{3}=\)

Cassandra cuts \(\frac{5}{16}\) inch off the top of a photo and \(\frac{3}{8}\) inch off the bottom. How much shorter is the total height of the photo now? Explain.

Building on the Essential Question Compare adding unlike fractions and adding like fractions.

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