## Complex Fractions

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# Complex Fractions

A complex fraction is a fraction whose numerator and/or denominator contain fractions. Here are some examples of complex fractions:

$\frac{3}{\frac{4}{5}}$

$\frac{\frac{4}{7}}{3}$ $\frac{\frac{2}{3}}{\frac{5}{8}}$

You can change a complex fraction to a regular fraction by multiplying it by 1 in a form that “clears” the fractions.

$\frac{\frac{2}{3}}{\frac{5}{8}}=\frac{\frac{2}{3}}{\frac{5}{8}}\times \frac{24}{24}=\frac{\frac{48}{3}}{\frac{120}{8}}=\frac{16}{15}$

You can use this idea to divide fractions.

Consider the problem $\frac{3}{4}$ ÷ $\frac{5}{6}$.

Write the division problem as a complex fraction.

Multiply the complex fraction by 1 in a form that will clear the fractions in the numerator and denominator, giving a regular fraction. The result is the solution to $\frac{3}{4}$ ÷ $\frac{5}{6}$.

Use multiplication to check that the result from Part 2 is the solution to the division problem.

Use the complex fraction method to find 2$\frac{1}{3}$ ÷ $\frac{1}{2}$. (You will need to write 2$\frac{1}{3}$ as a fraction.)