How to Add and Subtract Fractions

How to Add and Subtract Fractions

The fraction is a part of a whole or, more generally, any number of equal components. In everyday conversation, fractions are used to describe how many components there are with certain values.

Each fraction consists of a numerator that is placed above the line and a non-zero denominator that is placed below that line.

In this post, you can learn how to add and subtract fractions in few easy steps.

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Step by step guide for Adding and Subtracting Fractions

Addition and subtraction of fractions are of two types:

1- Addition and subtraction of “like” fractions with the same denominator:

  • For “like” fractions, if the denominator of all fractions is the same, the numerators of all fractions are added together. In this case, the denominator does not change and you can write the answer over the common denominator.

2- Addition and subtraction of “unlike” fractions with different denominators:

  • Step 1: Find equivalent fractions with the same denominator before you add or subtract fractions with different denominators. Adding and Subtracting with the same denominator:
    \(\frac{a}{\color{blue}{b}} \ + \ \frac{c}{ \color{ blue }{b} } = \frac{a \ + \ c}{ \color{ blue }{b} }\) , \(\frac{a}{ \color{ blue }{b} } \ – \ \frac{c}{ \color{ blue }{b} } =\frac{a \ – \ c}{ \color{ blue }{b} }\)
  • Step 2: Multiply two denominators (or as many as there are) to get a common denominator.
  • Step 3:  If one of the denominators was divisible by the other denominators, select the greater denominator as the common denominator.
  • Step 4: numerators are enlarged to fit the common denominator. In this case, the numerators of fractions are added together.
    \(\frac{a}{ \color{red}{b} } \ + \ \frac{c}{ \color{blue}{d} } = \frac{a \color{blue}{d} \ + \ \color{red}{b} c}{ \color{red}{b} \color{blue}{d} }\) , \(\frac{a}{ \color{red}{b} } \ – \ \frac{c}{ \color{blue}{d} }=\frac{a \color{blue}{d} \ – \ c \color{red}{b} }{ \color{red}{b} \color{blue}{d} }\)

Adding and Subtracting Fractions – Example 1:

Subtract fractions. \( \frac{4}{6} \ – \ \frac{3}{6} = \)

Solution:

For “like” fractions, subtract the numerators and write the answer over the common denominator. then: \(\frac{4}{6} \ – \ \frac{3}{6}=\frac{4 \ – \ 3}{6}=\frac{1}{6}\)

Adding and Subtracting Fractions – Example 2:

Add fractions. \(\frac{3}{7} \ + \ \frac{2}{3}=\)

Solution:

For “unlike” fractions, find equivalent fractions with the same denominator before you can add or subtract fractions with different denominators. Use this formula: \(\frac{a}{\color{red}{b}} \ + \ \frac {c}{\color{blue}{d}}=\frac{a \color{blue}{d} \ + \ c \color{red}{b} }{ \color{red}{b} \color{blue}{d} }\)
\(\frac{3}{\color{red}{7}} \ + \ \frac{2}{\color{blue}{3}}=\frac{(3)( \color{blue}{3} ) \ + \ (2)( \color{red}{7} )}{ \color{red}{7} \ \times \ \color{blue}{3} }=\frac{9 \ + \ 14}{21}=\frac{23}{21}\)

Adding and Subtracting Fractions – Example 3:

Subtract fractions. \(\frac{4}{5} \ – \ \frac{3}{5}=\)

Solution:

For “like” fractions, subtract the numerators and write the answer over the common denominator. then: \(\frac{4}{5}-\frac{3}{5}=\frac{1}{5 }\)

Adding and Subtracting Fractions – Example 4:

Subtract fractions. \(\frac{2}{3} \ – \ \frac{1}{2}=\)

Solution:

For “unlike” fractions, find equivalent fractions with the same denominator before you can add or subtract fractions with different denominators. Use this formula: \( \frac{a \color{blue}{d} \ – \ c \color{red}{b} }{ \color{red}{b} \color{blue}{d} }\)
\(\frac{2}{\color{red}{3}} \ – \ \frac{1}{\color{blue}{2}}=\frac{(2)( \color{blue}{2} ) \ – \ (1)( \color{red}{3} )}{ \color{red}{3} \ \times \ \color{blue}{2} }=\frac{4 \ – \ 3}{6}=\frac{1}{6}\)

Exercises for Adding and Subtracting Fractions

Add fractions and Subtract fractions.

  1. \(\color{blue}{\frac{2}{3}+\frac{1}{2}}\)
  2. \(\color{blue}{\frac{3}{5}+\frac{1}{3}}\)
  3. \(\color{blue}{\frac{5}{6}+\frac{1}{2}}\)
  4. \(\color{blue}{\frac{4}{5}-\frac{2}{5}}\)
  5. \(\color{blue}{\frac{3}{5}-\frac{2}{7}}\)
  6. \(\color{blue}{\frac{1}{2}-\frac{1}{3}}\)

Download Adding and Subtracting Fractions Worksheet

  1. \(\color{blue}{\frac{7}{6}}\)
  2. \(\color{blue}{\frac{14}{15}}\)
  3. \(\color{blue}{\frac{4}{3}}\)
  4. \(\color{blue}{\frac{2}{5}}\)
  5. \(\color{blue}{\frac{11}{35}}\)
  6. \(\color{blue}{\frac{1}{6}}\)

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