To find out how old Gary's brother is, we need to subtract the age difference from Gary's age.
Gary's age: \( 8 \frac{3}{4} \) years
Brother's age difference: \( 3 \frac{7}{12} \) years
Let's convert these mixed numbers to improper fractions to make the subtraction easier.
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Convert Gary's age: \[ 8 \frac{3}{4} = \frac{8 \times 4 + 3}{4} = \frac{32 + 3}{4} = \frac{35}{4} \]
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Convert the brother's age difference: \[ 3 \frac{7}{12} = \frac{3 \times 12 + 7}{12} = \frac{36 + 7}{12} = \frac{43}{12} \]
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Subtract the brother's age difference from Gary's age: Now we need to find a common denominator to subtract these fractions. The least common multiple of 4 and 12 is 12.
Convert Gary's age to have a denominator of 12: \[ \frac{35}{4} = \frac{35 \times 3}{4 \times 3} = \frac{105}{12} \]
Now we can subtract: \[ \frac{105}{12} - \frac{43}{12} = \frac{105 - 43}{12} = \frac{62}{12} \]
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Simplify \(\frac{62}{12}\): \[ \frac{62}{12} = \frac{31}{6} \]
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Convert back to a mixed number: \(\frac{31}{6}\) can also be written as: \[ 5 \frac{1}{6} \]
So, Gary's brother is \( 5 \frac{1}{6} \) years old.
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