Question

Subtract and simplify:

8 1/2 − 5 2/3 = _____

Answer 1

To subtract \( 8 \frac{1}{2} \) and \( 5 \frac{2}{3} \), we first convert the mixed numbers into improper fractions.

Starting with \( 8 \frac{1}{2} \):
\[
8 \frac{1}{2} = 8 + \frac{1}{2} = \frac{8 \times 2 + 1}{2} = \frac{16 + 1}{2} = \frac{17}{2}
\]

Now for \( 5 \frac{2}{3} \):
\[
5 \frac{2}{3} = 5 + \frac{2}{3} = \frac{5 \times 3 + 2}{3} = \frac{15 + 2}{3} = \frac{17}{3}
\]

Next, we need to subtract \( \frac{17}{2} - \frac{17}{3} \). To do this, we need a common denominator. The least common multiple of 2 and 3 is 6.

Convert \( \frac{17}{2} \) to a fraction with a denominator of 6:
\[
\frac{17}{2} = \frac{17 \times 3}{2 \times 3} = \frac{51}{6}
\]

Convert \( \frac{17}{3} \) to a fraction with a denominator of 6:
\[
\frac{17}{3} = \frac{17 \times 2}{3 \times 2} = \frac{34}{6}
\]

Now we can subtract the fractions:
\[
\frac{51}{6} - \frac{34}{6} = \frac{51 - 34}{6} = \frac{17}{6}
\]

Now, we simplify \( \frac{17}{6} \). This fraction is already in simplest form, but we can convert it back to a mixed number if desired:
\[
\frac{17}{6} = 2 \frac{5}{6}
\]

Thus, the final answer is:
\[
\boxed{2 \frac{5}{6}}
\]