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Mixed numbers. Changing mixed numbers into improper fraction using a quick method.

Updated on March 14, 2013

Mixed Numbers To Improper Fraction Video


A mixed number is a number that is made up of a whole number and fractional part. It may also be referred to a mixed fraction. 3 ¼ is an example of a mixed number.

An improper fraction is a fraction where the numerator is larger than the denominator. For example, 5/2 is an improper fraction.

In certain circumstances, such as, adding and taking fractions, it may be useful to convert the mixed number into an improper fraction. This can be done by multiplying the denominator by the whole number and adding on the numerator of the mixed number. Put this answer on the numerator of the improper fraction and keep the denominator the same as the denominator of the mixed number.

Example 1

Change 3 ½ to an improper fraction.

First, multiply the denominator by the whole number and add on the numerator of the mixed number.

3 × 2 + 1 = 7

This 7 goes on the numerator of the improper fraction. Also since 2 is the denominator of the mixed number then 2 will also be the denominator of the improper fraction.

3 ½ = 7/2

Example 2

Change 5 ¼ to an improper fraction.

First, multiply the denominator by the whole number and add on the numerator of the mixed number.

5 × 4 + 1 = 21

So, put 21 on the numerator of the improper fraction. Also, since 4 is the denominator of the mixed number, then 4 will also be the denominator of the improper fraction.

Therefore 5 ¼ = 21/4

Example 3

Change 6 2/5 to an improper fraction.

First, multiply the denominator by the whole number and add on the numerator of the mixed number.

6 × 5 + 2 = 32

So, put 32 on the numerator of the improper fraction. Also, since 5 is the denominator of the mixed number, then 5 will also be the denominator of the improper fraction.

Therefore 6 2/5 = 32/5

Example 4

Change 7 5/8 to an improper fraction.

First, multiply the denominator by the whole number and add on the numerator of the mixed number.

7 × 8 + 5 = 61

So, put 61 on the numerator of the improper fraction. Also, since 8 is the denominator of the mixed number, then 8 will also be the denominator of the improper fraction.

Therefore, 7 5/8 = 61/8

Example 5

Work out 2 1/8 – 1 1/2

Let’s subtract these fractions by converting them to improper fractions:

2 1/8 = 17/8 and 1 ½ = 3/2

So:

2 1/8 – 1 ½ = 17/8 – 3/2

All you need to do now is change 3/2 into 12/8 (multiply by 4) so that 8 is the common denominator of both fractions that you are taking away.

17/8 – 3/2

= 17/8 – 12/8

= 5/8

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