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Wize High School Grade 9 Math Textbook > Rational Numbers

Mixed Numbers (Multiplying & Dividing)

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Multiplying & Dividing Mixed Numbers

Improper Fraction Method

The quickest way to multiply and divide mixed numbers is to first convert them to improper fractions.

Example 1
314×2253\dfrac{1}{4}\times2\dfrac{2}{5}

=134×125=\dfrac{13}{4}\times\dfrac{12}{5}

=134 1×12 35=\dfrac{13}{\cancel4^{~1}}\times\dfrac{\cancel{12}^{~3}}{5}

=13×31×5=\dfrac{13\times3}{1\times5}

=395=\dfrac{39}{5} or 7457\dfrac{4}{5}
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Example 2
314÷2253\dfrac{1}{4}\div2\dfrac{2}{5}

=134÷125=\dfrac{13}{4}\div\dfrac{12}{5}

=134×512=\dfrac{13}{4}\times\dfrac{5}{12}

=13×54×12=\dfrac{13\times5}{4\times12}

=6548=\dfrac{65}{48} or 117481\dfrac{17}{48}

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Area Model Method (for Multiplying Mixed Numbers)

We can treat the multiplication of two mixed numbers as the area of a rectangle.

Example 3
314×2253\dfrac{1}{4}\times2\dfrac{2}{5}

First represent this as an area of a rectangle.

Then add up the areas of each piece of the rectangle.


2×3+2×14+25×3+25×14\bcf{2\times3}+\bcth{2\times\dfrac{1}{4}}+\bcfi{\dfrac{2}{5}\times3}+\bct{\dfrac{2}{5}\times\dfrac{1}{4}}

=6+12+65+110=6+\dfrac{1}{2}+\dfrac{6}{5}+\dfrac{1}{10}

We need to find a common denominator:
=6×101×10+1×52×5+6×25×2+110=\dfrac{6\bm{\colorbox{yellow}{$\times10$}}}{1\bm{\colorbox{yellow}{$\times10$}}}+\dfrac{1\bm{\colorbox{yellow}{$\times5$}}}{2\bm{\colorbox{yellow}{$\times5$}}}+\dfrac{6\bm{\colorbox{yellow}{$\times2$}}}{5\bm{\colorbox{yellow}{$\times2$}}}+\dfrac{1}{10}

=6010+510+1210+110=\dfrac{60}{10}+\dfrac{5}{10}+\dfrac{12}{10}+\dfrac{1}{10}

=60+5+12+110=\dfrac{60+5+12+1}{10}

=7810=\dfrac{78}{10}

=395=\dfrac{39}{5} or 7457\dfrac{4}{5}

Practice: Multiplying & Dividing Mixed Numbers

Calculate −335×(−556)-3\dfrac{3}{5}\times\left(-5\dfrac{5}{6}\right)

Practice: Multiplying & Dividing Mixed Numbers

Calculate −335×(−556)-3\dfrac{3}{5}\times\left(-5\dfrac{5}{6}\right)

Practice: Multiplying & Dividing Mixed Numbers

Calculate −159÷415-1\dfrac{5}{9}\div4\dfrac{1}{5}