Question

Find the difference.
5 1/3 - 2 1/6
Simplify your answer completely.
[__] [__]/[__]

Answer 1

To find the difference \( 5 \frac{1}{3} - 2 \frac{1}{6} \), we can follow these steps:

1. Convert the mixed numbers to improper fractions.
- For \( 5 \frac{1}{3} \):
\[
5 \frac{1}{3} = 5 \times 3 + 1 = 15 + 1 = 16 \Rightarrow \frac{16}{3}
\]

- For \( 2 \frac{1}{6} \):
\[
2 \frac{1}{6} = 2 \times 6 + 1 = 12 + 1 = 13 \Rightarrow \frac{13}{6}
\]

2. Now we need to subtract \( \frac{16}{3} - \frac{13}{6} \). To do this, we need a common denominator. The least common multiple of 3 and 6 is 6. Thus, we convert \( \frac{16}{3} \) to have a denominator of 6:
\[
\frac{16}{3} = \frac{16 \times 2}{3 \times 2} = \frac{32}{6}
\]

3. Now, we can perform the subtraction:
\[
\frac{32}{6} - \frac{13}{6} = \frac{32 - 13}{6} = \frac{19}{6}
\]

4. The fraction \( \frac{19}{6} \) is already in its simplest form, but we can convert it back to a mixed number:
- Divide 19 by 6:
- \( 19 \div 6 = 3 \) remainder \( 1 \), so we can write:
\[
\frac{19}{6} = 3 \frac{1}{6}
\]

Thus, the answer in the requested format is:

\[ 3 \] \[ 1 \] / \[ 6 \]