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A whole number multiplied by a fraction

Multiplication by a whole number is simply repeated addition. For example, we know that 5 × 3 means that we add 3 + 3 + 3 + 3 + 3 and obtain 15.

Similarly, \(8×\dfrac{1}{4}\) is the same as \(\dfrac{1}{4}+\dfrac{1}{4}+\dfrac{1}{4}+\dfrac{1}{4} +\dfrac{1}{4}+\dfrac{1}{4}+\dfrac{1}{4}+\dfrac{1}{4}=2\).

This can be found by writing

\(8×\dfrac{1}{4}=\dfrac{8}{4}=2\)

We can also think of this as 8 lots of \(\dfrac{1}{4}\).

Thus 8 lots of \(\dfrac{1}{4}\), 8 × \(\dfrac{1}{4}\) and \(\dfrac{8}{4}\) are all the same thing, and each is equal to 2.

Example 1

  1. \(20 ×\dfrac{3}{4}\)
  2. \(30 ×\dfrac{5}{6}\)

Solution

  1. \begin{align}20×\dfrac{3}{4}&=\dfrac{20×3}{4}\\\\ &=\dfrac{60}{4}\\\\ &=15\end{align}
  2. \begin{align}30×\dfrac{5}{6}&=\dfrac{30×5}{6}\\\\ &=\dfrac{150}{6}\\\\ &=25\end{align}