Lesson 9: Dividing
Fractions.
 Reciprocals.
 How to Divide Fractions
 Dividing Simple Fractions.
 Dividing Mixed Fractions.

Practice Game.
RECIPROCALS
When you turn the fraction
upside down you have a RECIPROCAL of the
original fraction.
Turning fraction upside down is
also called inverting.
Examples
A reciprocal of 
3 
is 
4 
= 
1 
1 
4 
3 
3 
A reciprocal of 1 
2 
= 
7 
is 
5 






5 
5 
7 






A reciprocal of 3 
= 
3 
is 
1 


1 
3 


HOW TO DIVIDE FRACTIONS
Do you know how we call the numbers in division?
12 

4 
= 
3 

DIVIDEND 

DIVISOR 

QUOTIENT 

To divide 2 fractions multiply the dividend by the reciprocal of the divisor.
You can do this by following few simple steps:
 Change all mixed
fractions ( if any) to improper fractions.
 Turn the second fraction (divisor) upside down.
 Change the divide sign to multiply sign and multiply the fractions.
DIVIDING SIMPLE FRACTIONS
Example
Find 
1 

2 
2 
5 
Solution:
1 

2 
= 
1 
x 
5 

Change the sign to x. 
2 
5 
2 
2 

Invert (turn upside down) the divisor. 
= 
1 x 5 
= 
5 



Multiply the numerators. 
2 x 2 
4 



Multiply the denominators. 
= 
1 
1 






Change the result to a mixed
fraction. 
4 





Example
Find 
2 

2 
3 
Solution:
2 

2 
= 
2 
x 
3 
Write 2 as 
2 
, invert the divisor and
change the sign to x. 
3 
1 
2 
1 
= 
2 x 3 
= 
6 



Multiply the numerators. 
1 x 2 
2 



Multiply the denominators. 
= 
3 
= 3 
Simplify the result. 

1 


Example
Find 
3 

6 
8 
Solution:
3 

6 
= 
3 

6 
Write 6 as 
6 
. 
8 
8 
1 
1 
= 
3 
x 
1 





Invert the divisor and
change the sign to x. 
8 
6 



= 
3 x 1 
= 
1 x 1 
= 
1 

Multiply the numerators and the
denominators. 
8 x 6 
8 x 2 
16 

Simplify before multiplying (divide 3 and 6
by 3). 
DIVIDING MIXED FRACTIONS
Example
Find 
2 
1 

1 
1 

2 
10 

= 
2 
1 

1 
1 
= 
5 

11 
Convert mixed fractions to 
2 
10 
2 
10 
improper fractions. 
= 
5 
x 
10 





Invert the divisor and
change the sign to x 
2 
11 


= 
5 x 10 
= 
5 x 5 





Simplify before multiplying 
2 x 11 
1 x11 





(divide 10 and 2 by 2) 
= 
25 
= 
2 
3 




Change the result to a mixed
fraction. 
11 
11 




