Adding Fractions

Before adding two fractions, we need to find their common denominator. After finding the equivalent fractions and common denominators, we are able to add the fractions.

Adding Fractions

Here are the steps to follow to add fractions:

Rule

  1. We look for a common denominator.

  2. For each fraction, find an equivalent fraction.

  3. We only add the numerators.

When one of the denominators is a multiple of the other

23+1623+16

  1. We look for a common denominator.

    Here, the common multiple for both 33 and 66 is 6.6. Thus, the common denominator is 6.6. ?6+?6?6+?6

  2. For each fraction, find an equivalent fraction.

    To convert the fractions into equivalent fractions, multiply the numerator and the denominator by the same factor. 23=2×23×2=4616=1×16×1=16

  3. We only add the numerators. 46+16=4+16=56

When one of the denominators is not a multiple of the other

78+23

  1. We look for a common denominator.

    Here, the common multiple for both 8 and 3 is 24. Thus, the common denominator is 24. ?24+?24

  2. For each fraction, find an equivalent fraction.

    To convert the fractions into equivalent fractions, multiply the numerator and the denominator by the same factor.

    78=7×38×3=2124

    23=2×83×8=1624

  3. We only add the numerators.

    2124+1624=21+1624=3724


 

Adding Mixed Numbers

If an equation contains mixed numbers, there are two ways to solve the addition.

  • Perform the operation on the integers first, then on the fractions.
     


213+313

First, focus on the integers: 2+3=5. 

Then the fractions, thus 13+13=23. 

The result is 213+313=523. 
 

513+225=163+125=8015+3615=80+3615=11615=71115

Adding Mixed Numbers on a Number Line

A number line can be used to illustrate a fraction.

Separate each whole on the number line into as many parts as the value of the denominator.
 

For example, using the fraction 34, the 4th line marks the whole, or the fraction 44.

Image

The steps for adding fractions are as follows:

Rule

  1. We look for the common denominator of the fractions.

  2. For each fraction, we create an equivalent fraction.

  3. We segment each whole on the number line into as many parts as the value of the common denominator.

  4. We place the 1st fraction on the number line according to its numerator.

  5. We add the 2nd fraction to the 1st.

We want to add 38+14.

  1. We look for the common denominator of the fractions.

    Here, the common denominator of 4 and 8 is 8.

  2. For each fraction, we create an equivalent fraction.

    To convert the fractions into equivalent fractions, we multiply the numerator and the denominator by the same factor. 38=3×18×1=3814=1×24×2=28

  3. We segment each whole on the number line in as many parts as the value of the common denominator.

Image

  1. We place the 1st fraction on the number line according to its numerator.

Image

  1. We add the 2nd fraction to the 1st.

Image

Therefore, 38+14=38+28=58.