7th Grade Math

Multiply and Divide Fractions

PART A BCD

Multi-Part

Lesson 3

Get ConnectED

GLE 0706.2.2

Understand and work with

the properties of and

operations on the system of

rational numbers.

SPI 0706.2.1 Simplify

numerical expressions

involving rational numbers.

Also addresses GLE 0706.1.3,

GLE 0706.1.8.

158 Rational Numbers

Main Idea

Model multiplication

of fractions and mixed

numbers.

Multiply Fractions with Models

Just as the product 3 × 4 is the number of square units in a rectangle,

the product of two fractions can be shown using area models.

Find _^3

4

× _^2

3

using a geoboard.

The first factor is 3 fourths and the second factor is 2 thirds.

Use one geoband to show fourths and another to show

thirds on the geoboard.

Use geobands to form a rectangle. Place one geoband

on the peg to show 3 fourths and another on the peg

to show 2 thirds.

Connect the geobands to show a small rectangle.

5

4

3

2

1

12345

1 3 1 3 1 3 1 4

1

4

1

4

1

4

5

4

3

2

1

12345

2

3

3

4

The area of the small rectangle is 6 square units. The area of the

large rectangle is 12 square units. So, _^3

4

× _^2

3

= _^6

12

or _^1

2

.

Find 2 × _^1

4

using an area model.

Draw two squares

1

4

2

side by side. Shade a

rectangle that is 2 units

long and _^14 unit wide.

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