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

[show answer]

Multiply across

[show answer]

Simplify: reduce and rename

[show answer]

 

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]