Dividing fractions is a mathematical operation that can be done by multiplying by the reciprocal of the second fraction. To divide fractions, keep the first fraction the same, flip the numerator and denominator of the second fraction, and multiply. Then simplify your answer by reducing the fraction to its lowest terms. This method works for proper fractions, improper fractions, whole numbers, and mixed numbers.
Printable PDF and Answer Key 
Notes
“Flip the second fraction and make it a multiply”
\(\displaystyle\frac{a}{b}\div\frac{c}{d} \Rightarrow \frac{a}{b}\times\frac{d}{c}\)
Practice Problems
\(\textbf{1)}\) \(\displaystyle\frac{1}{3}\div\frac{1}{2}\)\(\,\,\,\,\,\)
The answer is \(\displaystyle\frac{2}{3}\)
\(\,\,\,\,\,\,\displaystyle\frac{1}{3}\div\frac{1}{2}\)
\(\,\,\,\,\,\,\displaystyle\frac{1}{3}\times\frac{2}{1}\)
\(\,\,\,\,\,\,\displaystyle\frac{1\times2}{3\times1}\)
\(\,\,\,\,\,\,\displaystyle\frac{2}{3}\)
\(\,\,\,\,\,\,\displaystyle\frac{1}{3}\div\frac{1}{2}\)
\(\,\,\,\,\,\,\displaystyle\frac{1}{3}\times\frac{2}{1}\)
\(\,\,\,\,\,\,\displaystyle\frac{1\times2}{3\times1}\)
\(\,\,\,\,\,\,\displaystyle\frac{2}{3}\)
\(\textbf{2)}\) \(\displaystyle\frac{4}{5}\div2\)\(\,\,\,\,\,\)
The answer is \(\displaystyle\frac{2}{5}\)
\(\,\,\,\,\,\,\displaystyle\frac{4}{5}\div2\)
\(\,\,\,\,\,\,\displaystyle\frac{4}{5}\div\frac{2}{1}\)
\(\,\,\,\,\,\,\displaystyle\frac{4}{5}\times\frac{1}{2}\)
\(\,\,\,\,\,\,\displaystyle\frac{4}{10}\)
\(\,\,\,\,\,\,\displaystyle\frac{4\div2}{10\div2}=\frac{2}{5}\)
\(\,\,\,\,\,\,\displaystyle\frac{4}{5}\div2\)
\(\,\,\,\,\,\,\displaystyle\frac{4}{5}\div\frac{2}{1}\)
\(\,\,\,\,\,\,\displaystyle\frac{4}{5}\times\frac{1}{2}\)
\(\,\,\,\,\,\,\displaystyle\frac{4}{10}\)
\(\,\,\,\,\,\,\displaystyle\frac{4\div2}{10\div2}=\frac{2}{5}\)
\(\textbf{3)}\) \(\displaystyle\frac{3}{8}\div\frac{3}{5}\)
The answer is \(\displaystyle\frac{5}{8}\)
\(\,\,\,\,\,\,\displaystyle\frac{3}{8}\div\frac{3}{5}\)
\(\,\,\,\,\,\,\displaystyle\frac{3}{8}\times\frac{5}{3}\)
\(\,\,\,\,\,\,\displaystyle\frac{15}{24}\)
\(\,\,\,\,\,\,\displaystyle\frac{15\div3}{24\div3}\)
\(\,\,\,\,\,\,\displaystyle\frac{5}{8}\)
\(\,\,\,\,\,\,\displaystyle\frac{3}{8}\div\frac{3}{5}\)
\(\,\,\,\,\,\,\displaystyle\frac{3}{8}\times\frac{5}{3}\)
\(\,\,\,\,\,\,\displaystyle\frac{15}{24}\)
\(\,\,\,\,\,\,\displaystyle\frac{15\div3}{24\div3}\)
\(\,\,\,\,\,\,\displaystyle\frac{5}{8}\)
\(\textbf{4)}\) \(4\div\displaystyle\frac{1}{10}\)
The answer is \(40\)
\(\,\,\,\,\,\,\displaystyle4\div\frac{1}{10}\)
\(\,\,\,\,\,\,\displaystyle\frac{4}{1}\div\frac{1}{10}\)
\(\,\,\,\,\,\,\displaystyle\frac{4}{1}\times\frac{10}{1}\)
\(\,\,\,\,\,\,\displaystyle\frac{40}{1}=40\)
\(\,\,\,\,\,\,\displaystyle4\div\frac{1}{10}\)
\(\,\,\,\,\,\,\displaystyle\frac{4}{1}\div\frac{1}{10}\)
\(\,\,\,\,\,\,\displaystyle\frac{4}{1}\times\frac{10}{1}\)
\(\,\,\,\,\,\,\displaystyle\frac{40}{1}=40\)
\(\textbf{5)}\) \(6\div\displaystyle\frac{3}{10}\)\(\,\,\,\,\,\)
The answer is \(20\)
\(\,\,\,\,\,\,\displaystyle6\div\frac{3}{10}\)
\(\,\,\,\,\,\,\displaystyle\frac{6}{1}\times\frac{10}{3}\)
\(\,\,\,\,\,\,\displaystyle\frac{60}{3}\)
\(\,\,\,\,\,\,20\)
\(\,\,\,\,\,\,\displaystyle6\div\frac{3}{10}\)
\(\,\,\,\,\,\,\displaystyle\frac{6}{1}\times\frac{10}{3}\)
\(\,\,\,\,\,\,\displaystyle\frac{60}{3}\)
\(\,\,\,\,\,\,20\)
\(\textbf{6)}\) \(\displaystyle\frac{5}{9}\div\frac{1}{3}\)
The answer is \(\displaystyle\frac{5}{3}=1\frac{2}{3}\)
\(\,\,\,\,\,\,\displaystyle\frac{5}{9}\div\frac{1}{3}\)
\(\,\,\,\,\,\,\displaystyle\frac{5}{9}\times\frac{3}{1}\)
\(\,\,\,\,\,\,\displaystyle\frac{15}{9}\)
\(\,\,\,\,\,\,\displaystyle\frac{15\div3}{9\div3}=\frac{5}{3}\)
\(\,\,\,\,\,\,\displaystyle1\frac{2}{3}\)
\(\,\,\,\,\,\,\displaystyle\frac{5}{9}\div\frac{1}{3}\)
\(\,\,\,\,\,\,\displaystyle\frac{5}{9}\times\frac{3}{1}\)
\(\,\,\,\,\,\,\displaystyle\frac{15}{9}\)
\(\,\,\,\,\,\,\displaystyle\frac{15\div3}{9\div3}=\frac{5}{3}\)
\(\,\,\,\,\,\,\displaystyle1\frac{2}{3}\)
\(\textbf{7)}\) \(6\div\displaystyle\frac{1}{3}\)
The answer is \(18\)
\(\,\,\,\,\,\,\displaystyle6\div\frac{1}{3}\)
\(\,\,\,\,\,\,\displaystyle\frac{6}{1}\times\frac{3}{1}\)
\(\,\,\,\,\,\,\displaystyle\frac{18}{1}\)
\(\,\,\,\,\,\,18\)
\(\,\,\,\,\,\,\displaystyle6\div\frac{1}{3}\)
\(\,\,\,\,\,\,\displaystyle\frac{6}{1}\times\frac{3}{1}\)
\(\,\,\,\,\,\,\displaystyle\frac{18}{1}\)
\(\,\,\,\,\,\,18\)
\(\textbf{8)}\) \(\displaystyle\frac{2}{5}\div6\)
The answer is \(\displaystyle\frac{1}{15}\)
\(\,\,\,\,\,\,\displaystyle\frac{2}{5}\div6\)
\(\,\,\,\,\,\,\displaystyle\frac{2}{5}\div\frac{6}{1}\)
\(\,\,\,\,\,\,\displaystyle\frac{2}{5}\times\frac{1}{6}\)
\(\,\,\,\,\,\,\displaystyle\frac{2}{30}\)
\(\,\,\,\,\,\,\displaystyle\frac{1}{15}\)
\(\,\,\,\,\,\,\displaystyle\frac{2}{5}\div6\)
\(\,\,\,\,\,\,\displaystyle\frac{2}{5}\div\frac{6}{1}\)
\(\,\,\,\,\,\,\displaystyle\frac{2}{5}\times\frac{1}{6}\)
\(\,\,\,\,\,\,\displaystyle\frac{2}{30}\)
\(\,\,\,\,\,\,\displaystyle\frac{1}{15}\)
\(\textbf{9)}\) \(\displaystyle\frac{1}{4}\div\frac{5}{8}\)
The answer is \(\displaystyle\frac{2}{5}\)
\(\,\,\,\,\,\,\displaystyle\frac{1}{4}\div\frac{5}{8}\)
\(\,\,\,\,\,\,\displaystyle\frac{1}{4}\times\frac{8}{5}\)
\(\,\,\,\,\,\,\displaystyle\frac{8}{20}\)
\(\,\,\,\,\,\,\displaystyle\frac{8\div4}{20\div4}\)
\(\,\,\,\,\,\,\displaystyle\frac{2}{5}\)
\(\,\,\,\,\,\,\displaystyle\frac{1}{4}\div\frac{5}{8}\)
\(\,\,\,\,\,\,\displaystyle\frac{1}{4}\times\frac{8}{5}\)
\(\,\,\,\,\,\,\displaystyle\frac{8}{20}\)
\(\,\,\,\,\,\,\displaystyle\frac{8\div4}{20\div4}\)
\(\,\,\,\,\,\,\displaystyle\frac{2}{5}\)
\(\textbf{10)}\) \(\displaystyle\frac{3}{5}\div\frac{3}{5}\)
The answer is \(1\)
\(\,\,\,\,\,\,\displaystyle\frac{3}{5}\div\frac{3}{5}\)
\(\,\,\,\,\,\,\displaystyle\frac{3}{5}\times\frac{5}{3}\)
\(\,\,\,\,\,\,\displaystyle\frac{15}{15}\)
\(\,\,\,\,\,\,1\)
\(\,\,\,\,\,\,\displaystyle\frac{3}{5}\div\frac{3}{5}\)
\(\,\,\,\,\,\,\displaystyle\frac{3}{5}\times\frac{5}{3}\)
\(\,\,\,\,\,\,\displaystyle\frac{15}{15}\)
\(\,\,\,\,\,\,1\)
\(\textbf{11)}\) \(\displaystyle\frac{1}{7}\div\frac{5}{2}\)
The answer is \(\displaystyle\frac{2}{35}\)
\(\,\,\,\,\,\,\displaystyle\frac{1}{7}\div\frac{5}{2}\)
\(\,\,\,\,\,\,\displaystyle\frac{1}{7}\times\frac{2}{5}\)
\(\,\,\,\,\,\,\displaystyle\frac{1\times2}{7\times5}\)
\(\,\,\,\,\,\,\displaystyle\frac{2}{35}\)
\(\,\,\,\,\,\,\displaystyle\frac{1}{7}\div\frac{5}{2}\)
\(\,\,\,\,\,\,\displaystyle\frac{1}{7}\times\frac{2}{5}\)
\(\,\,\,\,\,\,\displaystyle\frac{1\times2}{7\times5}\)
\(\,\,\,\,\,\,\displaystyle\frac{2}{35}\)
\(\textbf{12)}\) \(\displaystyle\frac{7}{8}\div\frac{1}{8}\)
The answer is \(7\)
\(\,\,\,\,\,\,\displaystyle\frac{7}{8}\div\frac{1}{8}\)
\(\,\,\,\,\,\,\displaystyle\frac{7}{8}\times\frac{8}{1}\)
\(\,\,\,\,\,\,\displaystyle\frac{56}{8}\)
\(\,\,\,\,\,\,7\)
\(\,\,\,\,\,\,\displaystyle\frac{7}{8}\div\frac{1}{8}\)
\(\,\,\,\,\,\,\displaystyle\frac{7}{8}\times\frac{8}{1}\)
\(\,\,\,\,\,\,\displaystyle\frac{56}{8}\)
\(\,\,\,\,\,\,7\)
\(\textbf{13)}\) \(\displaystyle\frac{5}{8}\div5\)
The answer is \(\displaystyle\frac{1}{8}\)
\(\,\,\,\,\,\,\displaystyle\frac{5}{8}\div5\)
\(\,\,\,\,\,\,\displaystyle\frac{5}{8}\div\frac{5}{1}\)
\(\,\,\,\,\,\,\displaystyle\frac{5}{8}\times\frac{1}{5}\)
\(\,\,\,\,\,\,\displaystyle\frac{5}{40}\)
\(\,\,\,\,\,\,\displaystyle\frac{1}{8}\)
\(\,\,\,\,\,\,\displaystyle\frac{5}{8}\div5\)
\(\,\,\,\,\,\,\displaystyle\frac{5}{8}\div\frac{5}{1}\)
\(\,\,\,\,\,\,\displaystyle\frac{5}{8}\times\frac{1}{5}\)
\(\,\,\,\,\,\,\displaystyle\frac{5}{40}\)
\(\,\,\,\,\,\,\displaystyle\frac{1}{8}\)
\(\textbf{14)}\) \(\displaystyle\frac{2}{3}\div\frac{1}{5}\)
The answer is \(\displaystyle\frac{10}{3}=3\frac{1}{3}\)
\(\,\,\,\,\,\,\displaystyle\frac{2}{3}\div\frac{1}{5}\)
\(\,\,\,\,\,\,\displaystyle\frac{2}{3}\times\frac{5}{1}\)
\(\,\,\,\,\,\,\displaystyle\frac{10}{3}\)
\(\,\,\,\,\,\,\displaystyle10\div3=3\text{ remainder }1\)
\(\,\,\,\,\,\,\displaystyle3\frac{1}{3}\)
\(\,\,\,\,\,\,\displaystyle\frac{2}{3}\div\frac{1}{5}\)
\(\,\,\,\,\,\,\displaystyle\frac{2}{3}\times\frac{5}{1}\)
\(\,\,\,\,\,\,\displaystyle\frac{10}{3}\)
\(\,\,\,\,\,\,\displaystyle10\div3=3\text{ remainder }1\)
\(\,\,\,\,\,\,\displaystyle3\frac{1}{3}\)
\(\textbf{15)}\) \(\displaystyle\frac{6}{7}\div\frac{7}{6}\)
The answer is \(\displaystyle\frac{36}{49}\)
\(\,\,\,\,\,\,\displaystyle\frac{6}{7}\div\frac{7}{6}\)
\(\,\,\,\,\,\,\displaystyle\frac{6}{7}\times\frac{6}{7}\)
\(\,\,\,\,\,\,\displaystyle\frac{6\times6}{7\times7}\)
\(\,\,\,\,\,\,\displaystyle\frac{36}{49}\)
\(\,\,\,\,\,\,\displaystyle\frac{6}{7}\div\frac{7}{6}\)
\(\,\,\,\,\,\,\displaystyle\frac{6}{7}\times\frac{6}{7}\)
\(\,\,\,\,\,\,\displaystyle\frac{6\times6}{7\times7}\)
\(\,\,\,\,\,\,\displaystyle\frac{36}{49}\)
\(\textbf{16)}\) \(\displaystyle\frac{3}{4}\div\frac{2}{5}\)
The answer is \(\displaystyle\frac{15}{8}=1\frac{7}{8}\)
\(\,\,\,\,\,\,\displaystyle\frac{3}{4}\div\frac{2}{5}\)
\(\,\,\,\,\,\,\displaystyle\frac{3}{4}\times\frac{5}{2}\)
\(\,\,\,\,\,\,\displaystyle\frac{15}{8}\)
\(\,\,\,\,\,\,\displaystyle1\frac{7}{8}\)
\(\,\,\,\,\,\,\displaystyle\frac{3}{4}\div\frac{2}{5}\)
\(\,\,\,\,\,\,\displaystyle\frac{3}{4}\times\frac{5}{2}\)
\(\,\,\,\,\,\,\displaystyle\frac{15}{8}\)
\(\,\,\,\,\,\,\displaystyle1\frac{7}{8}\)
\(\textbf{17)}\) \(8\div\displaystyle\frac{2}{3}\)
The answer is \(12\)
\(\,\,\,\,\,\,\displaystyle8\div\frac{2}{3}\)
\(\,\,\,\,\,\,\displaystyle\frac{8}{1}\times\frac{3}{2}\)
\(\,\,\,\,\,\,\displaystyle\frac{24}{2}\)
\(\,\,\,\,\,\,12\)
\(\,\,\,\,\,\,\displaystyle8\div\frac{2}{3}\)
\(\,\,\,\,\,\,\displaystyle\frac{8}{1}\times\frac{3}{2}\)
\(\,\,\,\,\,\,\displaystyle\frac{24}{2}\)
\(\,\,\,\,\,\,12\)
\(\textbf{18)}\) \(\displaystyle\frac{9}{10}\div\frac{3}{4}\)
The answer is \(\displaystyle\frac{6}{5}=1\frac{1}{5}\)
\(\,\,\,\,\,\,\displaystyle\frac{9}{10}\div\frac{3}{4}\)
\(\,\,\,\,\,\,\displaystyle\frac{9}{10}\times\frac{4}{3}\)
\(\,\,\,\,\,\,\displaystyle\frac{36}{30}\)
\(\,\,\,\,\,\,\displaystyle\frac{36\div6}{30\div6}=\frac{6}{5}\)
\(\,\,\,\,\,\,\displaystyle1\frac{1}{5}\)
\(\,\,\,\,\,\,\displaystyle\frac{9}{10}\div\frac{3}{4}\)
\(\,\,\,\,\,\,\displaystyle\frac{9}{10}\times\frac{4}{3}\)
\(\,\,\,\,\,\,\displaystyle\frac{36}{30}\)
\(\,\,\,\,\,\,\displaystyle\frac{36\div6}{30\div6}=\frac{6}{5}\)
\(\,\,\,\,\,\,\displaystyle1\frac{1}{5}\)
\(\textbf{19)}\) \(\displaystyle\frac{7}{12}\div\frac{7}{18}\)
The answer is \(\displaystyle\frac{3}{2}=1\frac{1}{2}\)
\(\,\,\,\,\,\,\displaystyle\frac{7}{12}\div\frac{7}{18}\)
\(\,\,\,\,\,\,\displaystyle\frac{7}{12}\times\frac{18}{7}\)
\(\,\,\,\,\,\,\displaystyle\frac{126}{84}\)
\(\,\,\,\,\,\,\displaystyle\frac{126\div42}{84\div42}=\frac{3}{2}\)
\(\,\,\,\,\,\,\displaystyle1\frac{1}{2}\)
\(\,\,\,\,\,\,\displaystyle\frac{7}{12}\div\frac{7}{18}\)
\(\,\,\,\,\,\,\displaystyle\frac{7}{12}\times\frac{18}{7}\)
\(\,\,\,\,\,\,\displaystyle\frac{126}{84}\)
\(\,\,\,\,\,\,\displaystyle\frac{126\div42}{84\div42}=\frac{3}{2}\)
\(\,\,\,\,\,\,\displaystyle1\frac{1}{2}\)
\(\textbf{20)}\) \(\displaystyle\frac{5}{6}\div\frac{10}{9}\)
The answer is \(\displaystyle\frac{3}{4}\)
\(\,\,\,\,\,\,\displaystyle\frac{5}{6}\div\frac{10}{9}\)
\(\,\,\,\,\,\,\displaystyle\frac{5}{6}\times\frac{9}{10}\)
\(\,\,\,\,\,\,\displaystyle\frac{45}{60}\)
\(\,\,\,\,\,\,\displaystyle\frac{45\div15}{60\div15}\)
\(\,\,\,\,\,\,\displaystyle\frac{3}{4}\)
\(\,\,\,\,\,\,\displaystyle\frac{5}{6}\div\frac{10}{9}\)
\(\,\,\,\,\,\,\displaystyle\frac{5}{6}\times\frac{9}{10}\)
\(\,\,\,\,\,\,\displaystyle\frac{45}{60}\)
\(\,\,\,\,\,\,\displaystyle\frac{45\div15}{60\div15}\)
\(\,\,\,\,\,\,\displaystyle\frac{3}{4}\)
\(\textbf{21)}\) \(\displaystyle1\frac{1}{2}\div\frac{3}{4}\)
The answer is \(2\)
Convert the mixed number into an improper fraction.
\(\,\,\,\,\,\,\displaystyle1\frac{1}{2}=\frac{3}{2}\)
\(\,\,\,\,\,\,\displaystyle\frac{3}{2}\div\frac{3}{4}\)
\(\,\,\,\,\,\,\displaystyle\frac{3}{2}\times\frac{4}{3}\)
\(\,\,\,\,\,\,\displaystyle\frac{12}{6}\)
\(\,\,\,\,\,\,2\)
Convert the mixed number into an improper fraction.
\(\,\,\,\,\,\,\displaystyle1\frac{1}{2}=\frac{3}{2}\)
\(\,\,\,\,\,\,\displaystyle\frac{3}{2}\div\frac{3}{4}\)
\(\,\,\,\,\,\,\displaystyle\frac{3}{2}\times\frac{4}{3}\)
\(\,\,\,\,\,\,\displaystyle\frac{12}{6}\)
\(\,\,\,\,\,\,2\)
\(\textbf{22)}\) \(\displaystyle2\frac{1}{4}\div1\frac{1}{2}\)
The answer is \(\displaystyle1\frac{1}{2}\)
Convert both mixed numbers into improper fractions.
\(\,\,\,\,\,\,\displaystyle2\frac{1}{4}=\frac{9}{4}\)
\(\,\,\,\,\,\,\displaystyle1\frac{1}{2}=\frac{3}{2}\)
\(\,\,\,\,\,\,\displaystyle\frac{9}{4}\div\frac{3}{2}\)
\(\,\,\,\,\,\,\displaystyle\frac{9}{4}\times\frac{2}{3}\)
\(\,\,\,\,\,\,\displaystyle\frac{18}{12}\)
\(\,\,\,\,\,\,\displaystyle\frac{18\div6}{12\div6}=\frac{3}{2}\)
\(\,\,\,\,\,\,\displaystyle1\frac{1}{2}\)
Convert both mixed numbers into improper fractions.
\(\,\,\,\,\,\,\displaystyle2\frac{1}{4}=\frac{9}{4}\)
\(\,\,\,\,\,\,\displaystyle1\frac{1}{2}=\frac{3}{2}\)
\(\,\,\,\,\,\,\displaystyle\frac{9}{4}\div\frac{3}{2}\)
\(\,\,\,\,\,\,\displaystyle\frac{9}{4}\times\frac{2}{3}\)
\(\,\,\,\,\,\,\displaystyle\frac{18}{12}\)
\(\,\,\,\,\,\,\displaystyle\frac{18\div6}{12\div6}=\frac{3}{2}\)
\(\,\,\,\,\,\,\displaystyle1\frac{1}{2}\)
Related Pages
\(\bullet\text{ Reducing Fractions}\)
\(\,\,\,\,\,\,\,\,\frac{9}{15}=\frac{3}{5}…\)
\(\bullet\text{ Comparing Fractions}\)
\(\,\,\,\,\,\,\,\,\frac{3}{4} \bigcirc \frac{4}{5}…\)
\(\bullet\text{ Adding and Subtracting Fractions}\)
\(\,\,\,\,\,\,\,\,\frac{4}{5}+\frac{2}{3}…\)
\(\bullet\text{ Multiplying Fractions}\)
\(\,\,\,\,\,\,\,\,\frac{2}{5}\times\frac{5}{8}…\)
\(\bullet\text{ Dividing Fractions}\)
\(\,\,\,\,\,\,\,\,\frac{2}{7}\div\frac{1}{5}…\)
\(\bullet\text{ Improper Fractions and Mixed Numbers}\)
\(\,\,\,\,\,\,\,\,\frac{35}{4}=8\frac{3}{4}…\)
\(\bullet\text{ Dividing Mixed Numbers}\)
\(\,\,\,\,\,\,\,\,3 \frac{2}{3}÷1 \frac{1}{5}…\)