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Converting Mixed Numbers to Decimals

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If you can convert a fraction to a decimal, you can easily convert a mixed number, also called a mixed fraction, to a decimal.

A mixed number is a whole number as well as some parts of a whole as fraction.

For example, 2
62
100
or two and sixty-two hundredths means there are two whole parts and an additional sixty-two out of one hundred parts.

Cmn td1

When you convert a mixed fraction to a decimal, there are two strategies:

  • Change the mixed fraction to an improper fraction and then divide.
  • Convert the fractional part only then add it to the whole number. In other words, just leave the whole number the same and convert the fraction.

Let's take a look at some examples.

Example 1

 
Write 4
2
7
as a decimal.

First change the mixed fraction to an improper fraction.

4
2
7
= 4 +
2
7
=
4
1
+
2
7
=
4 x 7
1 x 7
+
2
7
=
28
7
+
2
7
=
28 + 2
7
=
30
7
 

Now divide 7 into 30.

Since 30 is greater than 7, the quotient will be a whole number and a decimal.

Cmn td2

Round the decimal to the nearest hundredth.

So, 4
2
7
= 4.29
 

Example 2

 
Write 12
3
5
as a decimal.

First change the mixed fraction to an improper fraction.

12
3
5
= 12 +
3
5
=
12
1
+
3
5
=
12 x 5
1 x 5
+
3
5
=
60
5
+
3
5
=
60 + 3
5
=
63
5
 

Now divide 5 into 63.

Cmn td3

So, 12
3
5
= 12.6
 

Example 3

 
Write 3
4
10
as a decimal.
First convert the fractional part
4
10
to decimal 0.4.

Now add 0.4 to 3 .

3
4
10
= 3 + 0.4 = 3.4
So, 3
4
10
= 3.4
 

Example 4

 
Write 6
1
4
as a decimal.

First convert the fractional part by dividing 4 into 1.

Cmn td4

1 ÷ 4 = 0.25

Now add 0.25 to 6.

6
1
4
= 6 +
1
4
= 6 + 0.25 = 6.25
So, 6
1
4
= 6.25
Summary
  • A mixed number is a whole number as well as some parts of a whole as fraction.
  • We can convert a mixed number (or mixed fraction) to a decimal.
  • Strategies to convert mixed fractions to decimals:
    • Change the mixed fraction to an improper fraction and then divide.
    • Convert the fractional part only and then add it to the whole number.

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