Question

Subtract. Simplify, if possible.
7 1/6 - 5 1/3
[__] [__]/[__]

Answer 1

To subtract the mixed numbers \(7 \frac{1}{6}\) and \(5 \frac{1}{3}\), follow these steps:

1. **Convert the mixed numbers to improper fractions:**

For \(7 \frac{1}{6}\):
\[
7 \frac{1}{6} = 7 \times 6 + 1 = 42 + 1 = \frac{43}{6}
\]

For \(5 \frac{1}{3}\):
\[
5 \frac{1}{3} = 5 \times 3 + 1 = 15 + 1 = \frac{16}{3}
\]

2. **Find a common denominator for the fractions \(\frac{43}{6}\) and \(\frac{16}{3}\).**

The least common multiple (LCM) of 6 and 3 is 6.
The fraction \(\frac{16}{3}\) needs to be converted to have a denominator of 6:
\[
\frac{16}{3} \times \frac{2}{2} = \frac{32}{6}
\]

3. **Subtract the fractions:**
\[
\frac{43}{6} - \frac{32}{6} = \frac{43 - 32}{6} = \frac{11}{6}
\]

4. **Convert back to a mixed number:**
\(\frac{11}{6}\) can be written as a mixed number. \(11 \div 6\) gives 1 with a remainder of 5:
\[
\frac{11}{6} = 1 \frac{5}{6}
\]

Thus, the result of \(7 \frac{1}{6} - 5 \frac{1}{3}\) is:
\[
\boxed{1} \quad \boxed{5} \quad \boxed{6}
\]