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

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

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	[show answer] $\frac{5}{4}\times~\frac{18}{5}\,=$
Multiply across	[show answer] $\frac{90}{20}\,=$
Simplify: reduce and rename	[show answer] $\frac{90}{20}\,=\,\frac{9}{2}\,=\,4\frac{1}{2}$

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

Duane Habecker, Created with GeoGebra

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]

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