Adding and Subtracting Fractions

Learn to add and subtract fractions with same and different denominators

Same Denominator

When fractions have the same denominator, simply add or subtract the numerators:

$\frac{2}{7} + \frac{3}{7} = \frac{2 + 3}{7} = \frac{5}{7}$

$\frac{5}{9} - \frac{2}{9} = \frac{5 - 2}{9} = \frac{3}{9} = \frac{1}{3}$

Example: $\frac{1}{4} + \frac{1}{6}$

LCM of 4 and 6 is 12: $\frac{1}{4} = \frac{3}{12}, \quad \frac{1}{6} = \frac{2}{12}$

$\frac{3}{12} + \frac{2}{12} = \frac{5}{12}$

Convert to improper fractions first, then add/subtract: $2\frac{1}{3} + 1\frac{1}{2} = \frac{7}{3} + \frac{3}{2}$

Calculate: $\frac{3}{8} + \frac{2}{8}$

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Solution:

Same denominator - add the numerators: $\frac{3}{8} + \frac{2}{8} = \frac{3 + 2}{8} = \frac{5}{8}$

Answer: $\frac{5}{8}$

Calculate: $\frac{2}{3} + \frac{1}{4}$

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Solution:

Find common denominator (LCM of 3 and 4 is 12):

$\frac{2}{3} = \frac{8}{12}$

$\frac{1}{4} = \frac{3}{12}$

Add: $\frac{8}{12} + \frac{3}{12} = \frac{11}{12}$

Answer: $\frac{11}{12}$

Sarah ran $2\frac{3}{4}$ miles on Monday and $1\frac{5}{6}$ miles on Tuesday. How many total miles did she run?

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Solution:

Convert to improper fractions: $2\frac{3}{4} = \frac{11}{4}, \quad 1\frac{5}{6} = \frac{11}{6}$

Find common denominator (LCM of 4 and 6 is 12): $\frac{11}{4} = \frac{33}{12}, \quad \frac{11}{6} = \frac{22}{12}$

Add: $\frac{33}{12} + \frac{22}{12} = \frac{55}{12} = 4\frac{7}{12}$

Answer: $4\frac{7}{12}$ miles

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