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Adding and subtracting fractions involves combining or finding the difference between parts of a whole. When fractions have different denominators, first find a common denominator and rewrite the fractions as equivalent fractions. Then add or subtract the numerators while keeping the denominator the same. Always simplify your final answer, and convert improper fractions to mixed numbers when appropriate.
Printable PDF and Answer Key 
Practice Problems
\(\textbf{1)}\) \(\hspace{1ex}\displaystyle\frac{1}{3}+\displaystyle\frac{1}{2}\)
The answer is \(\displaystyle\frac{5}{6}\)
\(\,\,\,\,\,\,\frac{1}{3}+\frac{1}{2}\)
\(\,\,\,\,\,\,\frac{2\times1}{2\times3}+\frac{3\times1}{3\times2}\)
\(\,\,\,\,\,\,\frac{2}{6}+\frac{3}{6}\)
\(\,\,\,\,\,\,\frac{2+3}{6}\)
\(\,\,\,\,\,\,\frac{5}{6}\)
\(\,\,\,\,\,\,\frac{1}{3}+\frac{1}{2}\)
\(\,\,\,\,\,\,\frac{2\times1}{2\times3}+\frac{3\times1}{3\times2}\)
\(\,\,\,\,\,\,\frac{2}{6}+\frac{3}{6}\)
\(\,\,\,\,\,\,\frac{2+3}{6}\)
\(\,\,\,\,\,\,\frac{5}{6}\)
\(\textbf{2)}\) \(\hspace{1ex}\displaystyle\frac{4}{5}+\displaystyle\frac{2}{3}\)
The answer is \(\displaystyle\frac{22}{15}=1\frac{7}{15}\)
\(\,\,\,\,\,\,\frac{4}{5}+\frac{2}{3}\)
\(\,\,\,\,\,\,\frac{3\times4}{3\times5}+\frac{5\times2}{5\times3}\)
\(\,\,\,\,\,\,\frac{12}{15}+\frac{10}{15}\)
\(\,\,\,\,\,\,\frac{22}{15}\)
\(\,\,\,\,\,\,1\frac{7}{15}\)
\(\,\,\,\,\,\,\frac{4}{5}+\frac{2}{3}\)
\(\,\,\,\,\,\,\frac{3\times4}{3\times5}+\frac{5\times2}{5\times3}\)
\(\,\,\,\,\,\,\frac{12}{15}+\frac{10}{15}\)
\(\,\,\,\,\,\,\frac{22}{15}\)
\(\,\,\,\,\,\,1\frac{7}{15}\)
\(\textbf{3)}\) \(\hspace{1ex}\displaystyle\frac{2}{3}-\displaystyle\frac{1}{2}\)
The answer is \(\displaystyle\frac{1}{6}\)
\(\,\,\,\,\,\,\frac{2}{3}-\frac{1}{2}\)
\(\,\,\,\,\,\,\frac{4}{6}-\frac{3}{6}\)
\(\,\,\,\,\,\,\frac{4-3}{6}\)
\(\,\,\,\,\,\,\frac{1}{6}\)
\(\,\,\,\,\,\,\frac{2}{3}-\frac{1}{2}\)
\(\,\,\,\,\,\,\frac{4}{6}-\frac{3}{6}\)
\(\,\,\,\,\,\,\frac{4-3}{6}\)
\(\,\,\,\,\,\,\frac{1}{6}\)
\(\textbf{4)}\) \(\hspace{1ex}\displaystyle\frac{3}{4}+\displaystyle\frac{1}{8}\)
The answer is \(\displaystyle\frac{7}{8}\)
\(\,\,\,\,\,\,\frac{3}{4}+\frac{1}{8}\)
\(\,\,\,\,\,\,\frac{6}{8}+\frac{1}{8}\)
\(\,\,\,\,\,\,\frac{6+1}{8}\)
\(\,\,\,\,\,\,\frac{7}{8}\)
\(\,\,\,\,\,\,\frac{3}{4}+\frac{1}{8}\)
\(\,\,\,\,\,\,\frac{6}{8}+\frac{1}{8}\)
\(\,\,\,\,\,\,\frac{6+1}{8}\)
\(\,\,\,\,\,\,\frac{7}{8}\)
\(\textbf{5)}\) \(\hspace{1ex}\displaystyle\frac{2}{5}-\displaystyle\frac{1}{6}\)
The answer is \(\displaystyle\frac{7}{30}\)
\(\,\,\,\,\,\,\frac{2}{5}-\frac{1}{6}\)
\(\,\,\,\,\,\,\frac{12}{30}-\frac{5}{30}\)
\(\,\,\,\,\,\,\frac{12-5}{30}\)
\(\,\,\,\,\,\,\frac{7}{30}\)
\(\,\,\,\,\,\,\frac{2}{5}-\frac{1}{6}\)
\(\,\,\,\,\,\,\frac{12}{30}-\frac{5}{30}\)
\(\,\,\,\,\,\,\frac{12-5}{30}\)
\(\,\,\,\,\,\,\frac{7}{30}\)
\(\textbf{6)}\) \(\hspace{1ex}\displaystyle\frac{2}{9}+\displaystyle\frac{1}{3}\)
The answer is \(\displaystyle\frac{5}{9}\)
\(\,\,\,\,\,\,\frac{2}{9}+\frac{1}{3}\)
\(\,\,\,\,\,\,\frac{2}{9}+\frac{3}{9}\)
\(\,\,\,\,\,\,\frac{2+3}{9}\)
\(\,\,\,\,\,\,\frac{5}{9}\)
\(\,\,\,\,\,\,\frac{2}{9}+\frac{1}{3}\)
\(\,\,\,\,\,\,\frac{2}{9}+\frac{3}{9}\)
\(\,\,\,\,\,\,\frac{2+3}{9}\)
\(\,\,\,\,\,\,\frac{5}{9}\)
\(\textbf{7)}\) \(\hspace{1ex}\displaystyle\frac{4}{9}+\displaystyle\frac{2}{3}\)
The answer is \(\displaystyle\frac{10}{9}=1\frac{1}{9}\)
\(\,\,\,\,\,\,\frac{4}{9}+\frac{2}{3}\)
\(\,\,\,\,\,\,\frac{4}{9}+\frac{6}{9}\)
\(\,\,\,\,\,\,\frac{10}{9}\)
\(\,\,\,\,\,\,1\frac{1}{9}\)
\(\,\,\,\,\,\,\frac{4}{9}+\frac{2}{3}\)
\(\,\,\,\,\,\,\frac{4}{9}+\frac{6}{9}\)
\(\,\,\,\,\,\,\frac{10}{9}\)
\(\,\,\,\,\,\,1\frac{1}{9}\)
\(\textbf{8)}\) \(\hspace{1ex}\displaystyle\frac{5}{8}-\displaystyle\frac{1}{8}\)
The answer is \(\displaystyle\frac{1}{2}\)
\(\,\,\,\,\,\,\frac{5}{8}-\frac{1}{8}\)
\(\,\,\,\,\,\,\frac{5-1}{8}\)
\(\,\,\,\,\,\,\frac{4}{8}\)
\(\,\,\,\,\,\,\frac{1}{2}\)
\(\,\,\,\,\,\,\frac{5}{8}-\frac{1}{8}\)
\(\,\,\,\,\,\,\frac{5-1}{8}\)
\(\,\,\,\,\,\,\frac{4}{8}\)
\(\,\,\,\,\,\,\frac{1}{2}\)
\(\textbf{9)}\) \(\hspace{1ex}\displaystyle\frac{2}{3}+\displaystyle\frac{4}{3}\)
The answer is \(2\)
\(\,\,\,\,\,\,\frac{2}{3}+\frac{4}{3}\)
\(\,\,\,\,\,\,\frac{2+4}{3}\)
\(\,\,\,\,\,\,\frac{6}{3}\)
\(\,\,\,\,\,\,2\)
\(\,\,\,\,\,\,\frac{2}{3}+\frac{4}{3}\)
\(\,\,\,\,\,\,\frac{2+4}{3}\)
\(\,\,\,\,\,\,\frac{6}{3}\)
\(\,\,\,\,\,\,2\)
\(\textbf{10)}\) \(\hspace{1ex}5\displaystyle\frac{1}{3}+6\displaystyle\frac{1}{2}\)
The answer is \(11\frac{5}{6}\)
\(\,\,\,\,\,\,5\frac{1}{3}+6\frac{1}{2}\)
\(\,\,\,\,\,\,\frac{16}{3}+\frac{13}{2}\)
\(\,\,\,\,\,\,\frac{32}{6}+\frac{39}{6}\)
\(\,\,\,\,\,\,\frac{71}{6}\)
\(\,\,\,\,\,\,11\frac{5}{6}\)
\(\,\,\,\,\,\,5\frac{1}{3}+6\frac{1}{2}\)
\(\,\,\,\,\,\,\frac{16}{3}+\frac{13}{2}\)
\(\,\,\,\,\,\,\frac{32}{6}+\frac{39}{6}\)
\(\,\,\,\,\,\,\frac{71}{6}\)
\(\,\,\,\,\,\,11\frac{5}{6}\)
\(\textbf{11)}\) \(\hspace{1ex}\displaystyle\frac{3}{8}-\displaystyle\frac{1}{9}\)
The answer is \(\displaystyle\frac{19}{72}\)
\(\,\,\,\,\,\,\frac{3}{8}-\frac{1}{9}\)
\(\,\,\,\,\,\,\frac{27}{72}-\frac{8}{72}\)
\(\,\,\,\,\,\,\frac{27-8}{72}\)
\(\,\,\,\,\,\,\frac{19}{72}\)
\(\,\,\,\,\,\,\frac{3}{8}-\frac{1}{9}\)
\(\,\,\,\,\,\,\frac{27}{72}-\frac{8}{72}\)
\(\,\,\,\,\,\,\frac{27-8}{72}\)
\(\,\,\,\,\,\,\frac{19}{72}\)
\(\textbf{12)}\) \(\hspace{1ex}\displaystyle\frac{2}{5}-\displaystyle\frac{1}{4}\)
The answer is \(\displaystyle\frac{3}{20}\)
\(\,\,\,\,\,\,\frac{2}{5}-\frac{1}{4}\)
\(\,\,\,\,\,\,\frac{8}{20}-\frac{5}{20}\)
\(\,\,\,\,\,\,\frac{8-5}{20}\)
\(\,\,\,\,\,\,\frac{3}{20}\)
\(\,\,\,\,\,\,\frac{2}{5}-\frac{1}{4}\)
\(\,\,\,\,\,\,\frac{8}{20}-\frac{5}{20}\)
\(\,\,\,\,\,\,\frac{8-5}{20}\)
\(\,\,\,\,\,\,\frac{3}{20}\)
\(\textbf{13)}\) \(\hspace{1ex}\displaystyle\frac{4}{5}+\displaystyle\frac{1}{6}\)
The answer is \(\displaystyle\frac{29}{30}\)
\(\,\,\,\,\,\,\frac{4}{5}+\frac{1}{6}\)
\(\,\,\,\,\,\,\frac{24}{30}+\frac{5}{30}\)
\(\,\,\,\,\,\,\frac{24+5}{30}\)
\(\,\,\,\,\,\,\frac{29}{30}\)
\(\,\,\,\,\,\,\frac{4}{5}+\frac{1}{6}\)
\(\,\,\,\,\,\,\frac{24}{30}+\frac{5}{30}\)
\(\,\,\,\,\,\,\frac{24+5}{30}\)
\(\,\,\,\,\,\,\frac{29}{30}\)
\(\textbf{14)}\) \(\hspace{1ex}\displaystyle\frac{7}{8}-\displaystyle\frac{3}{4}\)
The answer is \(\displaystyle\frac{1}{8}\)
\(\,\,\,\,\,\,\frac{7}{8}-\frac{3}{4}\)
\(\,\,\,\,\,\,\frac{7}{8}-\frac{6}{8}\)
\(\,\,\,\,\,\,\frac{7-6}{8}\)
\(\,\,\,\,\,\,\frac{1}{8}\)
\(\,\,\,\,\,\,\frac{7}{8}-\frac{3}{4}\)
\(\,\,\,\,\,\,\frac{7}{8}-\frac{6}{8}\)
\(\,\,\,\,\,\,\frac{7-6}{8}\)
\(\,\,\,\,\,\,\frac{1}{8}\)
\(\textbf{15)}\) \(\hspace{1ex}\displaystyle\frac{2}{3}+\displaystyle\frac{3}{5}\)
The answer is \(\displaystyle\frac{19}{15}=1\frac{4}{15}\)
\(\,\,\,\,\,\,\frac{2}{3}+\frac{3}{5}\)
\(\,\,\,\,\,\,\frac{10}{15}+\frac{9}{15}\)
\(\,\,\,\,\,\,\frac{10+9}{15}\)
\(\,\,\,\,\,\,\frac{19}{15}\)
\(\,\,\,\,\,\,1\frac{4}{15}\)
\(\,\,\,\,\,\,\frac{2}{3}+\frac{3}{5}\)
\(\,\,\,\,\,\,\frac{10}{15}+\frac{9}{15}\)
\(\,\,\,\,\,\,\frac{10+9}{15}\)
\(\,\,\,\,\,\,\frac{19}{15}\)
\(\,\,\,\,\,\,1\frac{4}{15}\)
\(\textbf{16)}\) \(\hspace{1ex}\displaystyle\frac{5}{6}+\displaystyle\frac{3}{8}\)
The answer is \(1\frac{5}{24}\)
\(\,\,\,\,\,\,\frac{5}{6}+\frac{3}{8}\)
\(\,\,\,\,\,\,\frac{20}{24}+\frac{9}{24}\)
\(\,\,\,\,\,\,\frac{29}{24}\)
\(\,\,\,\,\,\,1\frac{5}{24}\)
\(\,\,\,\,\,\,\frac{5}{6}+\frac{3}{8}\)
\(\,\,\,\,\,\,\frac{20}{24}+\frac{9}{24}\)
\(\,\,\,\,\,\,\frac{29}{24}\)
\(\,\,\,\,\,\,1\frac{5}{24}\)
\(\textbf{17)}\) \(\hspace{1ex}\displaystyle\frac{7}{10}-\displaystyle\frac{2}{5}\)
The answer is \(\displaystyle\frac{3}{10}\)
\(\,\,\,\,\,\,\frac{7}{10}-\frac{2}{5}\)
\(\,\,\,\,\,\,\frac{7}{10}-\frac{4}{10}\)
\(\,\,\,\,\,\,\frac{7-4}{10}\)
\(\,\,\,\,\,\,\frac{3}{10}\)
\(\,\,\,\,\,\,\frac{7}{10}-\frac{2}{5}\)
\(\,\,\,\,\,\,\frac{7}{10}-\frac{4}{10}\)
\(\,\,\,\,\,\,\frac{7-4}{10}\)
\(\,\,\,\,\,\,\frac{3}{10}\)
\(\textbf{18)}\) \(\hspace{1ex}\displaystyle\frac{1}{4}+\displaystyle\frac{2}{3}+\displaystyle\frac{1}{6}\)
The answer is \(1\frac{1}{12}\)
\(\,\,\,\,\,\,\frac{1}{4}+\frac{2}{3}+\frac{1}{6}\)
\(\,\,\,\,\,\,\frac{3}{12}+\frac{8}{12}+\frac{2}{12}\)
\(\,\,\,\,\,\,\frac{3+8+2}{12}\)
\(\,\,\,\,\,\,\frac{13}{12}\)
\(\,\,\,\,\,\,1\frac{1}{12}\)
\(\,\,\,\,\,\,\frac{1}{4}+\frac{2}{3}+\frac{1}{6}\)
\(\,\,\,\,\,\,\frac{3}{12}+\frac{8}{12}+\frac{2}{12}\)
\(\,\,\,\,\,\,\frac{3+8+2}{12}\)
\(\,\,\,\,\,\,\frac{13}{12}\)
\(\,\,\,\,\,\,1\frac{1}{12}\)
\(\textbf{19)}\) \(\hspace{1ex}2\frac{1}{4}-\frac{5}{6}\)
The answer is \(1\frac{5}{12}\)
\(\,\,\,\,\,\,2\frac{1}{4}-\frac{5}{6}\)
\(\,\,\,\,\,\,\frac{9}{4}-\frac{5}{6}\)
\(\,\,\,\,\,\,\frac{27}{12}-\frac{10}{12}\)
\(\,\,\,\,\,\,\frac{17}{12}\)
\(\,\,\,\,\,\,1\frac{5}{12}\)
\(\,\,\,\,\,\,2\frac{1}{4}-\frac{5}{6}\)
\(\,\,\,\,\,\,\frac{9}{4}-\frac{5}{6}\)
\(\,\,\,\,\,\,\frac{27}{12}-\frac{10}{12}\)
\(\,\,\,\,\,\,\frac{17}{12}\)
\(\,\,\,\,\,\,1\frac{5}{12}\)
\(\textbf{20)}\) \(\hspace{1ex}\displaystyle\frac{3}{4}+\displaystyle\frac{5}{6}-\displaystyle\frac{1}{3}\)
The answer is \(1\frac{1}{4}\)
\(\,\,\,\,\,\,\frac{3}{4}+\frac{5}{6}-\frac{1}{3}\)
\(\,\,\,\,\,\,\frac{9}{12}+\frac{10}{12}-\frac{4}{12}\)
\(\,\,\,\,\,\,\frac{9+10-4}{12}\)
\(\,\,\,\,\,\,\frac{15}{12}\)
\(\,\,\,\,\,\,\frac{5}{4}\)
\(\,\,\,\,\,\,1\frac{1}{4}\)
\(\,\,\,\,\,\,\frac{3}{4}+\frac{5}{6}-\frac{1}{3}\)
\(\,\,\,\,\,\,\frac{9}{12}+\frac{10}{12}-\frac{4}{12}\)
\(\,\,\,\,\,\,\frac{9+10-4}{12}\)
\(\,\,\,\,\,\,\frac{15}{12}\)
\(\,\,\,\,\,\,\frac{5}{4}\)
\(\,\,\,\,\,\,1\frac{1}{4}\)
See Related Pages\(\)
\(\bullet\text{ Reducing Fractions}\)
\(\,\,\,\,\,\,\,\,\frac{9}{15}=\frac{3}{5}…\)
\(\bullet\text{ Comparing Fractions}\)
\(\,\,\,\,\,\,\,\,\frac{3}{4} \bigcirc \frac{4}{5}…\)
\(\bullet\text{ Adding and Subtracting Fractions}\)
\(\,\,\,\,\,\,\,\,\frac{4}{5}+\frac{2}{3}…\)
\(\bullet\text{ Multiplying Fractions}\)
\(\,\,\,\,\,\,\,\,\frac{2}{5}\times\frac{5}{8}…\)
\(\bullet\text{ Dividing Fractions}\)
\(\,\,\,\,\,\,\,\,\frac{2}{7}\div\frac{1}{5}…\)
\(\bullet\text{ Improper Fractions and Mixed Numbers}\)
\(\,\,\,\,\,\,\,\,\frac{35}{4}=8\frac{3}{4}…\)
\(\bullet\text{ Dividing Mixed Numbers}\)
\(\,\,\,\,\,\,\,\,3 \frac{2}{3}÷1 \frac{1}{5}…\)