Adding and Subtracting Fractions

Learn how to add and subtract Fractions in few easy steps.

Step by step guide for Adding and Subtracting Fractions

1. For “like” fractions (fractions with the same denominator), add or subtract the numerators and write the answer over the common denominator.
2. Find equivalent fractions with the same denominator before you can add or subtract fractions with different denominators.
3. Adding and Subtracting with the same denominator:
   \(\frac{a}{\color{blue}{b}} \ + \ \frac{c}{ \color{ blue }{b} } = \frac{a \ + \ c}{ \color{ blue }{b} }\) , \(\frac{a}{ \color{ blue }{b} } \ – \ \frac{c}{ \color{ blue }{b} } =\frac{a \ – \ c}{ \color{ blue }{b} }\)
4. Adding and Subtracting fractions with different denominators:
   \(\frac{a}{ \color{red}{b} } \ + \ \frac{c}{ \color{blue}{d} } = \frac{a \color{blue}{d} \ + \ \color{red}{b} c}{ \color{red}{b} \color{blue}{d} }\) , \(\frac{a}{ \color{red}{b} } \ – \ \frac{c}{ \color{blue}{d} }=\frac{a \color{blue}{d} \ – \ c \color{red}{b} }{ \color{red}{b} \color{blue}{d} }\)

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

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: \(\frac{a}{\color{red}{b}} \ – \ \frac {c}{\color{blue}{d}}=\frac{a \color{blue}{d} \ – \ c \color{red}{b} }{ \color{red}{b} \color{blue}{d} }\)
\(\frac{3}{\color{red}{7}} \ + \ \frac{2}{\color{blue}{3}}=\frac{(3)( \color{blue}{3} ) \ + \ (2)( \color{red}{7} )}{ \color{red}{7} \ \times \ \color{blue}{3} }=\frac{9 \ + \ 14}{21}=\frac{23}{21}\)

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

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

Exercises

Add fractions and Subtract fractions.

• \(\color{blue}{\frac{2}{3}+\frac{1}{2}}\)
• \(\color{blue}{\frac{3}{5}+\frac{1}{3}}\)
• \(\color{blue}{\frac{5}{6}+\frac{1}{2}}\)

• \(\color{blue}{\frac{4}{5}-\frac{2}{5}}\)
• \(\color{blue}{\frac{3}{5}-\frac{2}{7}}\)
• \(\color{blue}{\frac{1}{2}-\frac{1}{3}}\)

Download Adding and Subtracting Fractions Worksheet

Answers

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