## Multiplying fractions

It is a three-step process to multiply mixed numbers:

1. Convert mixed numbers into fractions
2. Multiply across
3. Simplify: reduce and rename

$$3\frac{1}{3}\times~\,2\frac{1}{4}\,=$$

Convert mixed numbers into fractions: $$\frac{10}{3}\times~\,\frac{9}{4}\,=$$

Multiply across:  $$\frac{90}{12}\,=$$

Simplify- reduce and rename:  $$\frac{90}{12}\,=\,\frac{30}{4}\,=\,\frac{15}{2}\,=\,7\frac{1}{2}$$

Example

 The problem $4\frac{1}{2}\times~2\frac{1}{6}\,=$ Convert mixed numbers into fractions $\frac{9}{2}\times~\frac{13}{6}\,=$ Multiply across $\frac{117}{12}\,=$ Simplify: reduce and rename $\frac{117}{12}\,=\,\frac{39}{4}\,=\,9\frac{3}{4}$

Example

 The problem $1\frac{1}{4}\times~3\frac{3}{5}\,=$ Convert mixed numbers into fractions $\frac{5}{4}\times~\frac{18}{5}\,=$ Multiply across $\frac{90}{20}\,=$ Simplify: reduce and rename $\frac{90}{20}\,=\,\frac{9}{2}\,=\,4\frac{1}{2}$

What if one of your numbers is a whole number instead of a mixed number?

Duane Habecker, Created with GeoGebra

For more practice with fractions, please try this Fraction Calculator.

# Self-Check

Q1: $\,\,\,5\frac{1}{2}\,\times~\,1\frac{1}{3}\,=\,\,\,\,$ [show answer]

Q2: $\,\,\,2\frac{4}{5}\,\times~\,1\frac{1}{6}\,=\,\,\,\,$ [show answer]

Q3: $\,\,\,5\frac{1}{2}\,\times~\,2\frac{1}{5}\,=\,\,\,\,$ [show answer]