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Examples of Multiplying Fractions
Mixed Fraction Multiplication


Dealing with examples of multiplying fractions generally isn’t the toughest skill to learn in Math.

But it’s still something that people do often have to take care when solving such sums.
Particularly if performing mixed fraction multiplication.




Multiplying a Fraction by a Whole Number:

The most basic multiplying fractions examples are when a fraction is multiplied with a whole number.

Like:     3  ×  \bf{\frac{3}{4}}

With such a sum, one just has to multiply the whole number by the numerator of the fraction.



Examples    


(1.1) 
3  ×  \bf{\frac{3}{4}}   =   \boldsymbol{\frac{3 \space \times \space 3}{4}}   =   \bf{\frac{9}{4}}

(1.2) 
2  ×  \bf{\frac{5}{2}}   =   \boldsymbol{\frac{2 \space \times \space 5}{2}}   =   \bf{\frac{10}{2}}   =   5

(1.3) 
5  ×  –\bf{\frac{1}{4}}   =   \boldsymbol{\frac{5 \space \times \space -1}{4}}   =   \bf{\frac{-5}{4}}





Multiplying a Fraction by a Fraction:

When you are required to multiply a fraction by another fraction, things don’t work too differently.
The numbers on the top and bottom of the fractions both multiply each other.


Examples    


(2.1) 

\bf{\frac{1}{3}}  ×  \bf{\frac{3}{4}}   =   \boldsymbol{\frac{1 \space \times \space 3}{3 \space \times \space 4}}   =   \bf{\frac{3}{12}}   =   \bf{\frac{1}{4}}



(2.2) 

\bf{\frac{8}{5}}  ×  \bf{\frac{7}{8}}   =   \boldsymbol{\frac{8 \space \times \space 7}{5 \space \times \space 8}}  =   \bf{\frac{56}{40}}   =   \bf{\frac{7}{5}}



(2.3) 

–\bf{\frac{1}{2}}  ×  \bf{\frac{4}{5}}   =   \boldsymbol{\frac{\text{-}1 \space \times \space 4}{2 \space \times \space 5}}   =   \bf{\frac{\text{-}4}{10}}   =   –\bf{\frac{2}{5}}



(2.4) 

–\bf{\frac{2}{5}}  ×  –\bf{\frac{5}{7}}   =   \boldsymbol{\frac{\text{-}2 \space \times \space 5}{5 \space \times \space \text{-}7}}   =   =   \bf{\frac{\text{-}10}{\text{-}35}}   =   \bf{\frac{2}{7}}






Examples of Multiplying Fractions,
Mixed Fraction Multiplication


When examples of multiplying fractions deals with mixed fraction multiplication, an effective approach is to convert the mixed fractions into improper fractions before performing the multiplication.
Then once the multiplication is complete, we can convert the result back to mixed fraction form.

The examples below show such situations.

Information on conversion from mixed fractions to improper fractions and vice versa can be seen on the  mixed numbers and fractions  page.



Examples    


(3.1) 

1\bf{\frac{3}{4}} × 2\bf{\frac{1}{2}}   =   (\boldsymbol{\frac{1 \space \times \space 4 \space + \space 3}{4}})  ×  (\boldsymbol{\frac{2 \space \times \space 2 \space + \space 1}{2}})

=   \bf{\frac{7}{4}} × \bf{\frac{5}{2}}   =   \bf{\frac{35}{8}}   =   2\bf{\frac{3}{8}}



(3.2) 

4\bf{\frac{1}{5}} × 3\bf{\frac{2}{7}}   =   (\boldsymbol{\frac{4 \space \times \space 5 \space + \space 1}{5}})  ×  (\boldsymbol{\frac{3 \space \times \space 7 \space + \space 2}{7}})

=   \bf{\frac{21}{5}} × \bf{\frac{23}{7}}   =   \bf{\frac{483}{35}}   =   \bf{\frac{69}{5}}   =   13\bf{\frac{4}{5}}



(3.3) 

–1\bf{\frac{2}{3}} × 2\bf{\frac{1}{4}}   =   –(\boldsymbol{\frac{1 \space \times \space 3 \space + \space 2}{3}})  ×  (\boldsymbol{\frac{2 \space \times \space 4 \space + \space 1}{4}})

=   –\bf{\frac{5}{3}} × \bf{\frac{9}{4}}   =   –\bf{\frac{45}{12}}   =   –\bf{\frac{15}{4}}   =   – 3\bf{\frac{3}{4}}





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