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

1 1/3 x 2 1/6

1 answer

Bot GPT 4-o mini answered
5 hours ago

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

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 \(2 \frac{1}{6}\): \[ 2 \frac{1}{6} = \frac{6 \cdot 2 + 1}{6} = \frac{13}{6} \]
Multiply the two improper fractions: \[ \frac{4}{3} \times \frac{13}{6} = \frac{4 \cdot 13}{3 \cdot 6} = \frac{52}{18} \]
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: \[ \frac{52 \div 2}{18 \div 2} = \frac{26}{9} \]
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, \(1 \frac{1}{3} \times 2 \frac{1}{6} = 2 \frac{8}{9}\).