Original number

Joe divided a number by 2 1/4 to get 2/3. What was the original number?

Correct answer:

x =  1.5

Step-by-step explanation:

$$\begin{gathered} a=2{\displaystyle \frac{1}{4}}=2+{\displaystyle \frac{1}{4}}={\displaystyle \frac{2\cdot 4+1}{4}}={\displaystyle \frac{9}{4}}=2.25 \\ b=2\mathrm{/}3={\displaystyle \frac{2}{3}}\doteq 0.6667 \\ x\mathrm{/}a=b \\ x\mathrm{/}2.25=0.666666666667 \\ 0.444444x=0.666667 \\ x={\displaystyle \frac{3}{2}}=1.5={\displaystyle \frac{3}{2}}=1\frac{1}{2}=1.5 \end{gathered}$$

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