Question

Gary is 8 and 3/4
years old. His brother is 3 and 7/12
years younger than he is. How many years old is Gary’s brother?(1 point)
Responses

Answer 1

To find Gary's brother's age, we need to subtract the age difference from Gary's age.

1. **Convert Gary's age to a fraction:**
Gary is 8 and 3/4 years old.
\[
8 \frac{3}{4} = \frac{8 \times 4 + 3}{4} = \frac{32 + 3}{4} = \frac{35}{4}
\]

2. **Convert the age difference to a fraction:**
Gary's brother is 3 and 7/12 years younger than Gary.
\[
3 \frac{7}{12} = \frac{3 \times 12 + 7}{12} = \frac{36 + 7}{12} = \frac{43}{12}
\]

3. **Subtract the age difference from Gary's age:**
\[
\text{Age of Gary's brother} = \text{Gary's age} - \text{Age difference}
\]
\[
= \frac{35}{4} - \frac{43}{12}
\]

4. **Find a common denominator to perform the subtraction:**
The least common multiple of 4 and 12 is 12.

Convert \(\frac{35}{4}\) to have a denominator of 12:
\[
\frac{35}{4} = \frac{35 \times 3}{4 \times 3} = \frac{105}{12}
\]

5. **Now perform the subtraction:**
\[
\frac{105}{12} - \frac{43}{12} = \frac{105 - 43}{12} = \frac{62}{12}
\]

6. **Simplify the fraction:**
\[
\frac{62}{12} = \frac{31}{6}
\]

7. **Convert \(\frac{31}{6}\) to a mixed number:**
\[
\frac{31}{6} = 5 \frac{1}{6}
\]

Therefore, Gary’s brother is **5 and 1/6 years old**.