How to Add and Subtract Fractions? (+FREE Worksheet!)

• 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: The 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 For education statistics and research

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: \(\frac{4}{6} \ – \ \frac{3}{6}=\frac{4 \ – \ 3}{6}=\frac{1}{6}\)

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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: \(\frac{4}{5}-\frac{3}{5}= \frac{4 \ – \ 3}{5}= \frac{1}{5 }\)

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: \(\frac{a}{ \color{red}{b} } \ – \ \frac{c}{ \color{blue}{d} }=\frac{a \color{blue}{d} \ – \ c \color{red}{b} }{ \color{red}{b} \color{blue}{d} }\)
\(\frac{2}{\color{red}{3}} \ – \ \frac{1}{\color{blue}{2}}=\frac{(2)( \color{blue}{2} ) \ – \ (1)( \color{red}{3} )}{ \color{red}{3} \ \times \ \color{blue}{2} }=\frac{4 \ – \ 3}{6}=\frac{1}{6}\)

Exercises for Adding and Subtracting Fractions

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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