Adding and Subtracting Fractions: Practice

The denominators already match, so keep the denominator $7$ and add the numerators.

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

Adding the denominators too would give $\frac{5}{14}$, which is wrong: the pieces stay sevenths.

The denominators match, so keep the denominator $9$ and subtract the numerators.

$\frac{5}{9} - \frac{1}{9} = \frac{5 - 1}{9} = \frac{4}{9}$

Since $4$ and $9$ share no factor above $1$, $\frac{4}{9}$ is already in lowest terms.

Keep the denominator $5$ and add the numerators.

$\frac{1}{5} + \frac{3}{5} = \frac{1 + 3}{5} = \frac{4}{5}$

Adding the denominators too would give $\frac{4}{10}$, which is wrong.

Keep the denominator $10$ and add the numerators.

$\frac{3}{10} + \frac{4}{10} = \frac{3 + 4}{10} = \frac{7}{10}$

Since $7$ and $10$ share no factor above $1$, $\frac{7}{10}$ is in lowest terms.

Keep the denominator $6$ and add the numerators.

$\frac{1}{6} + \frac{1}{6} = \frac{1 + 1}{6} = \frac{2}{6}$

Now write it in lowest terms by dividing the top and bottom by $2$.

$\frac{2}{6} = \frac{1}{3}$

Adding the denominators to get $\frac{2}{12}$ is wrong: each piece stays a sixth.

Keep the denominator $11$ and subtract the numerators.

$\frac{9}{11} - \frac{4}{11} = \frac{9 - 4}{11} = \frac{5}{11}$

Since $5$ and $11$ share no factor above $1$, $\frac{5}{11}$ is in lowest terms.

Keep the denominator $7$ and subtract the numerators.

$\frac{6}{7} - \frac{2}{7} = \frac{6 - 2}{7} = \frac{4}{7}$

Since $4$ and $7$ share no factor above $1$, $\frac{4}{7}$ is in lowest terms.

Keep the denominator $12$ and subtract the numerators.

$\frac{11}{12} - \frac{5}{12} = \frac{11 - 5}{12} = \frac{6}{12}$

Now simplify by dividing the top and bottom by their greatest common factor $6$.

$\frac{6}{12} = \frac{6 \div 6}{12 \div 6} = \frac{1}{2}$

Keep the denominator $5$ and add the numerators.

$\frac{3}{5} + \frac{1}{5} = \frac{3 + 1}{5} = \frac{4}{5}$

Since $4$ and $5$ share no factor above $1$, $\frac{4}{5}$ is in lowest terms.

Keep the denominator $10$ and subtract the numerators.

$\frac{7}{10} - \frac{3}{10} = \frac{7 - 3}{10} = \frac{4}{10}$

Now simplify by dividing the top and bottom by their greatest common factor $2$.

$\frac{4}{10} = \frac{4 \div 2}{10 \div 2} = \frac{2}{5}$

Keep the denominator $15$ and add the numerators.

$\frac{2}{15} + \frac{6}{15} = \frac{2 + 6}{15} = \frac{8}{15}$

Since $8$ and $15$ share no factor above $1$, $\frac{8}{15}$ is in lowest terms.

Keep the denominator $8$ and add the numerators.

$\frac{1}{8} + \frac{5}{8} = \frac{1 + 5}{8} = \frac{6}{8}$

Now simplify by dividing the top and bottom by their greatest common factor $2$.

$\frac{6}{8} = \frac{6 \div 2}{8 \div 2} = \frac{3}{4}$