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ADDING FRACTIONS

When you have finished this page, try the Adding Fractions Quiz.

Adding or the addition of fractions has several important rules. First of all, it is necessary that the fractions that are being added have like or same denominators. Then one simply adds the numerators and keeps the denominator the same throughout. The numerators are indicated in red and the denominators in blue. Also notice that the fraction is reduced or simplified in the last step. Visit the Equal Fractions page if you don't remember what this means or how to do it.

The example below shows how and why:

2
10

Two tenths plus
 

3
10

Three tenths
 


Five tenths which can be reduced by dividing the numerator and denominator by five to

 

1
2

One half

What happens if one wants to add two fractions with unlike denominators. It is then necessary to change the fractions to equivalent fractions with like or same denominators. The example below shows how this looks:

One Fifth equals two tenths animation

1
5

One fifth must be converted to tenths to add it to

3
10

Three tenths which equals

5
10 1
2

Five tenths which when reduced by dividing both the numerator and denominator by five equals

 

One half

It is important when adding fractions to change any numbers that are improper fractions to mixed numbers.

When adding mixed numbers, and an improper fraction is part of the anwer, the whole number that is part of the conversion is added to the whole number in the mixed number.

 

1

1
2

3
6

To add one and one half to one and two thirds, the fractions must be converted to equal fractions with common denominators. For one half it is three sixths

1

2
3

4
6

The converted fraction for two thirds is four sixths.

2

 

7
6

One adds the fractions and the whole numbers. The fraction is an improper fraction which must be converted to a mixed number, one and one sixth.

3

 

1
6

The one and one sixth from the converted improper fraction is added to the whole number to get the final answer of three and one sixth.

 

 

 

 

 

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