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Algebra Difficulty 1.5 Junior Find the answer

What number should go in the \square to make the equation 34+4=1\frac{3}{4}+\frac{4}{\square}=1 true?

A number or a short expression. Spacing and $ signs are ignored.

Solution

For 34+4=1\frac{3}{4}+\frac{4}{\square}=1 to be true, we must have 4=134=14\frac{4}{\square}=1-\frac{3}{4}=\frac{1}{4}. Since 14=416\frac{1}{4}=\frac{4}{16}, we rewrite the right side using the same numerator to obtain 4=416\frac{4}{\square}=\frac{4}{16}. Therefore, =16\square=16 makes the equation true.

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