Question

Subtract. Answer as a mixed number in simplest form.
20 3/4 - 16 5/8 = [__] [__]/[__]

Answer 1

To subtract the mixed numbers \( 20 \frac{3}{4} \) and \( 16 \frac{5}{8} \), we will first convert them into improper fractions.

1. Convert \( 20 \frac{3}{4} \) to an improper fraction:
\[
20 \frac{3}{4} = 20 \times 4 + 3 = 80 + 3 = 83, \text{ so } 20 \frac{3}{4} = \frac{83}{4}
\]

2. Convert \( 16 \frac{5}{8} \) to an improper fraction:
\[
16 \frac{5}{8} = 16 \times 8 + 5 = 128 + 5 = 133, \text{ so } 16 \frac{5}{8} = \frac{133}{8}
\]

3. To perform the subtraction, we need a common denominator. The least common multiple of 4 and 8 is 8. Convert \( \frac{83}{4} \) to an equivalent fraction with a denominator of 8:
\[
\frac{83}{4} = \frac{83 \times 2}{4 \times 2} = \frac{166}{8}
\]

4. Now we can subtract:
\[
\frac{166}{8} - \frac{133}{8} = \frac{166 - 133}{8} = \frac{33}{8}
\]

5. Now convert \( \frac{33}{8} \) back to a mixed number:
- Divide 33 by 8, which gives 4 with a remainder:
\[
33 \div 8 = 4 \quad \text{and the remainder is } 33 - 32 = 1
\]
- Thus, \( \frac{33}{8} = 4 \frac{1}{8} \).

Finally, the answer as a mixed number in simplest form is:
\[
\boxed{4 \frac{1}{8}}
\]