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. $$\color{blue}{\frac{1}{2}-\frac{1}{3}}$$

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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