Question

Subtract. Simplify, if possible.
10 2/3 - 4 4/5
[__] [__]/[__]

Answer 1

To subtract the mixed numbers \(10 \frac{2}{3}\) and \(4 \frac{4}{5}\), we will first convert them into improper fractions, perform the subtraction, and then simplify the result if possible.

1. Convert \(10 \frac{2}{3}\) to an improper fraction:
\[
10 \frac{2}{3} = \frac{10 \times 3 + 2}{3} = \frac{30 + 2}{3} = \frac{32}{3}
\]

2. Convert \(4 \frac{4}{5}\) to an improper fraction:
\[
4 \frac{4}{5} = \frac{4 \times 5 + 4}{5} = \frac{20 + 4}{5} = \frac{24}{5}
\]

3. Now, we need to subtract the two improper fractions:
\[
\frac{32}{3} - \frac{24}{5}
\]

To subtract these fractions, we need a common denominator. The least common multiple of 3 and 5 is 15.

4. Convert each fraction to have a denominator of 15:
\[
\frac{32}{3} = \frac{32 \times 5}{3 \times 5} = \frac{160}{15}
\]
\[
\frac{24}{5} = \frac{24 \times 3}{5 \times 3} = \frac{72}{15}
\]

5. Now, subtract the fractions:
\[
\frac{160}{15} - \frac{72}{15} = \frac{160 - 72}{15} = \frac{88}{15}
\]

6. Since \(88\) and \(15\) have no common factors, \(\frac{88}{15}\) is already in its simplest form.

7. Convert back to a mixed number:
\[
88 \div 15 = 5 \quad \text{(with a remainder of 13)}
\]
Thus, we have:
\[
5 \frac{13}{15}
\]

The final answer is:
\[
5 \frac{13}{15}
\]

In the requested format, the answer is represented as:
\[
[5] [13]/[15]
\]