Why do we invert and multiply?

or multiply by the reciprocal?

or flip and multiply?

Dividing Fractions

Consider the following division

3/4 ÷ 1/8

What happens when we divide by 1?

Think!

Aha!

So, lets look at ¾ ÷ ⅛ as a complex division

What can we multiply by to make it =1?

Think!

Yes! Multiply by to make it =1?

8

14

3

1

88

1

Remember!

if you multiply the denominator by ,

you must do the same to the numerator

Let’s try another one….

1

8

8

84

24

1

6 6

8

14

3

1

8

1

8

So, lets look at as a complex division

What can we multiply by to make it =1?

Think!

Yes! Multiply by to make it =1?

9

23

2

2

99

2

92

32

Remember!

if you multiply the denominator by ,

you must do the same to the numerator

Now that we understand the “why”, let’s try “multiplying by the reciprocal”.

2

9

18

186

18

1

3 3

9

23

2

2

9

2

9

Lets look at 163

87

multiply by the reciprocal

3

16

8

7

24

112

24

164

3

24

This is why we invert and multiply, or multiply by

the reciprocal, or flip and multiply. It works!

Remember to express your answer as a mixed

fraction and reduce to the lowest terms.