Adding fractions – Steps, Examples

The addition of fractions is a little bit different from adding other numbers. Fractions are not easily added like other numbers. This is because a fraction is always written as

\frac{a}{b}\\ 

The top letter “a” is called the numerator and the down letter “b” is called the denominator. The addition of fractions simply means summing two or more fractions.

Steps in Adding Fractions

To add fractions follow the simple steps below

Step1: Check to make sure the denominators of the given fractions are the same.

Step2: when the denominators of the given fractions are the same, add the numerators of the given fractions and take them over the common denominator.

Step3: After adding the numerators and taking them over the common denominator, then simplify the fraction.

How to add like fractions

To add like fractions, since they have the same denominator or common denominator, simply add the numerators and pick a common denominator.

Example: add

\frac{1}{3} + \frac{2}{3}\\

Answer: since they have a common denominator add the numerators and simplify the fraction.

\frac{ 1 + 2 }{3} = \frac{3}{3} = 1

How to add unlike fractions

Since unlike fractions have different denominators, first try to make the given fractions have a common denominator by using the following methods

Firstly: By using LCM. Find the LCM (Lowest Common Multiple) of the given fractions and then proceed to add the fractions. Click here to see how to find Lowest common multiple (LCM)

Example: add

\frac{1}{4} + \frac{2}{3}

Answer: first find the LCM of the denominators, in this case, 4 and 3. The LCM of 4 and 3 is 12. Then follow the steps as shown below

\frac{ 12 × \frac{1}{4} + 12×\frac{2}{3}}{12}= \frac{(3×1) + (4×2)}{12} = \frac{3 +8}{12} = \frac{11}{12}

Secondly: Using Equivalent fractions. Find the equivalent fractions of the given fractions and proceed as follows. Example add 2/5 + 3/4

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Answer:

\frac{2}{5} + \frac{3}{4} = \frac{4 ×2}{4 × 5} + \frac{5 ×3}{5 ×4} = \frac{8}{20} + \frac{15}{20} = \frac{8 +15}{20}=\frac{23}{20} = 1\frac{3}{20}

Adding a Fraction and a Whole number

When adding a fraction and a whole number, first multiply the denominator of the fractions to the whole number and then add the results to the numerator of the fraction all divided by the denominator of the given fractions. Example add 4 + 3/5

Answer:

4 + \frac{3}{5} = \frac{ ( 4 × 5) + 3 }{5} = \frac{20 + 3}{5} = \frac{23}{5} = 4\frac {3} {5}

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