Question

1 1/3 x 2 1/6

Answer 1

To multiply the mixed numbers \(1 \frac{1}{3}\) and \(2 \frac{1}{6}\), follow these steps:

1. Convert the mixed numbers to improper fractions:
- For \(1 \frac{1}{3}\):
\[
1 \frac{1}{3} = \frac{3 \cdot 1 + 1}{3} = \frac{4}{3}
\]
- For \(2 \frac{1}{6}\):
\[
2 \frac{1}{6} = \frac{6 \cdot 2 + 1}{6} = \frac{13}{6}
\]

2. Multiply the two improper fractions:
\[
\frac{4}{3} \times \frac{13}{6} = \frac{4 \cdot 13}{3 \cdot 6} = \frac{52}{18}
\]

3. Simplify the fraction \( \frac{52}{18} \):
- Find the greatest common divisor (GCD) of 52 and 18, which is 2.
- Divide both the numerator and the denominator by 2:
\[
\frac{52 \div 2}{18 \div 2} = \frac{26}{9}
\]

4. Convert back to a mixed number:
- Divide 26 by 9:
\[
26 \div 9 = 2 \quad \text{(remainder } 8 \text{)}
\]
- Therefore, \( \frac{26}{9} = 2 \frac{8}{9} \).

So, \(1 \frac{1}{3} \times 2 \frac{1}{6} = 2 \frac{8}{9}\).