Dividing a number by a fraction

In this publication, we will consider how a natural number can be divided into an ordinary fraction: proper, improper and mixed. We will also analyze examples of solving problems for a better understanding and consolidation of theoretical material.

Content

Dividing a number by a proper/improper fraction

To divide a natural number n into an ordinary fraction (regular or improper), the latter should be turned over (i.e. change the numerator and denominator in places) and then by this number n.

n :
a/b

 = n

b/a

 = 

n ⋅ b/a

 

Note: if as a result of division a new fraction is obtained, we check whether it is possible.

Dividing a number by a mixed fraction

To find the quotient of a number n into a mixed fraction, the latter must first be represented as . Then we divide the number by the resulting fraction.

n : X
a/b

 = n :

X ⋅ b + a/b

 = n

b/X ⋅ b + a

 = 

n ⋅ b/X ⋅ b + a

Examples of tasks

Task 1

Divide the number 6 by a fraction 
7/12

.

 

Solution

In 6:
7/12

= 6 ⋅

12/7

=

6⋅12/7

=

72/7

= 10

2/7

 

Task 2

Divide the number 3 by the fraction 2
7/11

.

 

Solution

First, we represent the mixed fraction as improper, then we perform the division.

3:2
7/11

= 3 :

2 ⋅ 11 + 7/11

= 3 :

29/11

= 3 ⋅

11/29

=

3⋅11/29

=

33/29

= 1

4/29

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