Adding and Subtracting Fractions

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

Step by step guide for Adding and Subtracting Fractions

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

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. \(\color{blue}{\frac{1}{6}}\)