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Multiplication and Division of Rational Numbers

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Common Core For Grade 7

Examples, videos, and solutions to help Grade 7 students learn how to multiply and divide rational numbers.

New York State Common Core Math Grade 7, Module 2, Lesson 15

Download worksheets for Grade 7, Module 2, Lesson 15

Lesson 15 Student Outcomes

Students recognize that the rules for multiplying and dividing integers apply to rational numbers.
Students interpret products and quotients of rational numbers by describing real-world contexts.

Lesson 15 Summary

The rules that apply for multiplying and dividing integers apply to rational numbers.
We can use the products and quotients of rational numbers to describe real-world situations.

Exercise 2

a. In one year, Melinda’s parents spend $2,640.90 on cable and internet service. If they spend the same amount each month, what is the resulting monthly change in the family’s income?
b. The Rules for Dividing Rational Numbers are the same as the Rules for Dividing Integers:
1. Divide the absolute values of the two rational numbers.
2. If the two numbers (dividend and divisor) have the same sign, their quotient is positive.
3. If the two numbers (dividend and divisor) have opposite signs, their quotient is negative.

Exercise 3

Use the fundraiser chart to help answer the questions that follow.
Jeremy is selling plants for the school’s fundraiser, and listed above is a chart from his fundraiser order form. Use the information in the chart to answer the following questions. Show your work and represent the answer as a rational number; then, explain your answer in the context of the situation.
a. If Tamara Jones writes a check to pay for the plants, what is the resulting change in her checking account balance?
b. Mr. Clark wants to pay for his order with a $20 bill, but Jeremy does not have change. Jeremy tells Mr. Clark he will give him the change later. How will this affect the total amount of money Jeremy collects? Explain. What rational number represents the change that must be made to the money Jeremy collects?
c. Jeremy’s sister, Susie, borrowed the money from their mom to pay for her order. Their mother has agreed to deduct an equal amount of money from Susie’s allowance each week for the next five weeks to repay the loan. What is the weekly change in Susie’s allowance?
d. Jeremy’s grandparents want to change their order. They want to order three daisies and one geranium, instead of four daisies. How does this change affect the amount of their order? Explain how you arrived at your answer.
e. Jeremy approaches three people who do not want to buy any plants; however, they wish to donate some money for the fundraiser when Jeremy delivers the plants one week later. If the people promise to donate a total of $14.40 , what will be the average cash donation?
f. Jeremy spends one week collecting orders. If 22 people purchase plants totaling $270, what is the average amount of Jeremy’s sale?

Lesson 15 Problem Set

1. At lunch time, Benjamin often borrows money from his friends to buy snacks in the school cafeteria. Benjamin borrowed $0.75 from his friend Clyde five days last week to buy ice cream bars. Represent the amount Benjamin borrowed as the product of two rational numbers; then, determine how much Benjamin owed his friend last week.

2. Monica regularly records her favorite television show. Each episode of the show requires 3.5% of the total capacity of her video recorder. Her recorder currently has 62% of its total memory free. If Monica records all five episodes this week, how much space will be left on her video recorder?

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