Dividing a decimal by a common fraction and vice versa

In this publication, we will look at how division is performed, which involves ordinary (simple) and decimal fractions. We will also analyze examples to consolidate the material presented.

Content

Division Rule

To divide a decimal fraction into an ordinary one (or vice versa – an ordinary fraction into a decimal one), one of the fractions must be reduced to the form of another. After that, you can perform division of the same type of fractions.

Notes:

1. Infinite decimals are first necessary before the final ones.

2. Mixed simple fractions must first be converted to .

Examples

Example 1

Let’s find the result of dividing the number 3,5 by a fraction
1/4

.

 

Solution 1

Let’s turn:

1/4

=

1⋅25/4⋅25

=

25/100

= 0,25

 

Now let’s do the division:

3,5: 0,25 = 14

Solution 2

Let’s transform .

= 3,5 3
5/10

=

3 ⋅ 10 + 5/10

=

35/10

=

7/2

 

Now we can find the quotient of :

7/2

:

1/4

=

7/2

4/1

=

7⋅4/2⋅1

=

28/2

= 14

 

Example 2

Divide the number 8,14 by the fraction 4
2/9

.

 

Solution

First, let’s turn the mixed fraction into an improper one:

4
2/9

=

4 ⋅ 9 + 2/9

=

38/9

 

We can then go two ways: convert the fraction to decimal or the decimal to fraction. As an example, let’s focus on the second option.

= 8,14 8
14/100

=

8 ⋅ 100 + 14/100

=

814/100

=

407/50

 

It remains only to perform the division:

407/50

:

38/9

=

407/50

9/38

=

407⋅9/50⋅38

=

3663/1900

= 1

1763/1900

Leave a Reply