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 0706.2.3 Use rational

numbers and roots of perfect

squares/cubes to solve

contextual problems. Also

addresses GLE 0706.1.2,

SPI 0706.2.1.

168 Rational Numbers

Divide Fractions

Cut two paper

plates into four equal pieces each to

show 2 ÷ _^1

4

.

1. How many _^14 s are in 2 plates?


2. How would you model 3 ÷ _^12?


3. What is true about 3 ÷ _^12 and 3 × 2?

Dividing 2 by _^1

4

is the same as multiplying 2 by the reciprocal of _^1

4

,

which is 4.

same result

reciprocals

÷=÷ ·· =

Is this pattern true for any division expression?

Consider _^7

8

÷ _^3

4

, which can be rewritten as

_^78

_

_^34

.

_^78

_

_^34

=

_ 87 × _^43

_

_ 43 × _^43

Multiply the numerator and denominator by the reciprocal of _^34 , which is _^43.

=

87 _ ×^4 _ 3

_

1

_^34 × _^43 = 1

= _^7

8

× _^4

3

So, _^7

8

÷ _^3

4

= _^7

8

× _^4

3

.

Divide by Fractions

Words To divide by a fraction, multiply by its multiplicative inverse,

or reciprocal.

Examples Numbers Algebra

_ 78 ÷ _ 43 = _ 87 · _ 34 _a

b

÷ _c

d

= _a

b

· d_

c

, where b, c, d ≠ 0

Main Idea

Divide fractions and

mixed numbers.

1

4

1

4

1

4

1

4

1

4

1

4

1

4

1

4

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