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Question

# Write and simplify an expression. The quotient of one half and two fifths.

Solution

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Step 1
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The phrase quotient" means division so the quotient of one half and two fifths is $\dfrac{1}{2}\div\dfrac{2}{5}$ which simplifies to:

\begin{align*} \dfrac{1}{2}\div\dfrac{2}{5}&=\dfrac{1}{2}\cdot\dfrac{5}{2}&&\text{Rewrite as multiplication.}\\ &=\dfrac{1\cdot5}{2\cdot2}&&\text{Multiply the numerators and denominators.}\\ &=\dfrac{5}{4}&&\text{Simplify.}\\ &=1\dfrac{1}{4}&&\text{Convert to a mixed number.} \end{align*}

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