6th Grade Math Textbook, Progress

Divide Fractions by Fractions

8-6

Eduardo discovered a short way to divide fractions by examining

some division sentences and the related multiplication sentences.

Division Sentence Multiplication Sentence

2


^45 

 110 
 8 
^45 

^110 

^81 
 8

1

reciprocals

2


^35 

 110 
 6 
^35 

^110 

^61 
 6

1

1


 190 

 110 
 9 
 190 

^110 

^91 
 9

1

Eduardo concluded that dividing by a fractiongives the

same result as multiplying by its reciprocal.

To divide a fraction by a fraction:


Multiply by the reciprocal of the divisor.

Simplify using the GCF, where possible.

Then multiply the numerators and the

denominators.

Rename the product as a whole or mixed

number when needed.

Study these examples.

 270 

^15 

 270 

^51 
 
^1114 

^1112 

^1114 

^1121 


1 1 6


 270 

^15 

 270 

^51 

^74 
 1 
^34 
 
^11 
^14 
^1112 

^1114 

^1121 


4 7 1


^1114 

^1112 

^67 

reciprocals

^34 

 116 

^34 

^116 


4


^34 

 116 

^34 

^116 



3

1





4


 1

1

^3

4





1

1

6



^1

1

(^2)
 12
Reciprocal of

1
5

is 5, or

5
1
.
4
5
1
10
whole number
mixed
number
fraction
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