Question

Find the difference.
9 1/2 - 6 1/4
Simplify your answer completely.
[__] [__]/[__]

Answer 1

To find the difference \( 9 \frac{1}{2} - 6 \frac{1}{4} \), we can follow these steps:

1. Convert the mixed numbers to improper fractions.
- For \( 9 \frac{1}{2} \):
\[
9 \frac{1}{2} = 9 \times 2 + 1 = 18 + 1 = 19 \quad \Rightarrow \quad \frac{19}{2}
\]
- For \( 6 \frac{1}{4} \):
\[
6 \frac{1}{4} = 6 \times 4 + 1 = 24 + 1 = 25 \quad \Rightarrow \quad \frac{25}{4}
\]

2. Now perform the subtraction:
\[
\frac{19}{2} - \frac{25}{4}
\]

3. We need a common denominator to subtract these fractions. The least common multiple of \( 2 \) and \( 4 \) is \( 4 \). We can rewrite \( \frac{19}{2} \) with a denominator of \( 4 \):
\[
\frac{19}{2} = \frac{19 \times 2}{2 \times 2} = \frac{38}{4}
\]

4. Now we can subtract the fractions:
\[
\frac{38}{4} - \frac{25}{4} = \frac{38 - 25}{4} = \frac{13}{4}
\]

5. Convert the improper fraction \( \frac{13}{4} \) back to a mixed number:
\[
13 \div 4 = 3 \quad \text{(whole number)} \quad \text{with a remainder of } 1
\]
So, \( \frac{13}{4} = 3 \frac{1}{4} \).

Thus, the final answer is:
\[
\text{Difference: } 3 \frac{1}{4} \quad [3] [1] / [4]
\]