7th Grade Math

Multiplication and Division Equations

PART A BCD

Multi-Part

Lesson 2

Get ConnectED

GLE 0706.3.8

Use a variety of strategies

to efficiently solve linear

equations and inequalities.

SPI 0706.3.6 Solve linear

equations with rational

coefficients symbolically or

graphically. Also addresses

GLE 0706.1.7, GLE 0706.3.7,

SPI 0706.3.7.

Solve Equations with

Rational Coefficients

HOMEWORK Shawnda spends _^1

2

hour doing homework after

school. Then she spends another _^1

2

hour doing homework before bed.

In all, she spends 2 · _^1

2

or 1 hour doing homework.

1. Copy and complete the table below.

23 × ^23 = ^15 ×^ =^1 ^56 × 56 = 87 × ^87 = (^)
× ^57 = 1 62 × ^62 = _^71 × = 1 × 8 = 1

2. What is true about the products in Exercise 1?

Two numbers with a product of 1 are called multiplicative inverses,

or reciprocals.

Inverse Property of Multiplication

Words The product of a number and its multiplicative inverse is 1.

Examples Numbers Algebra

_ 34 × _^43 = 1 _a

b

· _b

a

= 1, for a, b ≠ 0

Find Multiplicative Inverses

Find the multiplicative inverse of _^2

5

.

Since _^2

5

· _^5

2

= 1, the multiplicative inverse of _^2

5

is _^5

2

, or 2 _^1

2

.

Find the multiplicative inverse of 2 _^1

3

.

2 _^1

3

= _^7

3

Rename the mixed number as an improper fraction.

Since _^7

3

· _^3

7

= 1, the multiplicative inverse of 2 _^1

3

is _^3

7

.

Find the muliplicative inverse of each number.

a. _^5

6

b. 1 _^1

2

c. 8 d. _^4

3

Main Idea

Solve equations with

rational coefficients.

Vocabulary

multiplicative inverse

reciprocal

Lesson 2D Multiplication and Division Equations 221

V

m

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