Find unknown 2

Find unknown denominator:

2/3 -5/? = 1/4

Correct result:

d =  12

Solution:

$$\begin{gathered} {\displaystyle \frac{2}{3}}-{\displaystyle \frac{5}{d}}={\displaystyle \frac{1}{4}} \\ {\displaystyle \frac{2}{3}}\cdot 12d-{\displaystyle \frac{5}{d}}\cdot 12d={\displaystyle \frac{1}{4}}\cdot 12d \\ 4\cdot 2\cdot d-5\cdot 12=1\cdot 3\cdot d \\ 5d=60=12 \\ d=12 \\ \text{ Verifying Solution: } \\ r={\displaystyle \frac{2}{3}}-{\displaystyle \frac{5}{d}}={\displaystyle \frac{2}{3}}-{\displaystyle \frac{5}{12}}={\displaystyle \frac{1}{4}}=0.25 \end{gathered}$$

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