Think of the amount 3/5 of an hour.
What do you multiply 3/5 hour by to get 1 hour?
You multiply 3/5 by its reciprocal, 5/3, to get 1, since 3/5 * 5/3 = 15/15 = 1.
Since you multiply the time by 5/3 to get 1 hour, you also multiply the fraction of the allowance by 5/3.
3/4 of the allowance * 5/3 = 15/12 of the allowance = 5/4 of the allowance.
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Here is another way of thinking of this.
Turn this into a unit rate problem.
3/4 allowance for 3/5 of an hour is what unit rate of allowance per hour?
Divide 3/4 allowance per 3/5 hour.
[tex] \dfrac{\frac{3}{4}~allowance}{\frac{3}{5}~hour} = [/tex]
[tex] = \dfrac{\frac{3}{4}}{\frac{3}{5}}\dfrac{allowance}{hour} [/tex]
[tex] = \dfrac{3}{4} \times \dfrac{5}{3}\dfrac{allowance}{hour} [/tex]
[tex] = \dfrac{3 \times 5}{4 \times 3} \dfrac{allowance}{hour} [/tex]
[tex] = \dfrac{5}{4} \dfrac{allowance}{hour} [/tex]
The unit rate is 5/4 of the allowance per hour.
