To multiply the mixed number \(2 \frac{3}{7}\) by the fraction \(\frac{5}{9}\), we first need to convert the mixed number into an improper fraction. 1. Convert the mixed number \(2 \frac{3}{7}\): \[ 2 \frac{3}{7} = \frac{(2 \times 7) + 3}{7} = \frac{14 + 3}{7} = \frac{17}{7} \] 2. Now we can multiply the two fractions: \[ \frac{17}{7} \times \frac{5}{9} = \frac{17 \times 5}{7 \times 9} = \frac{85}{63} \] 3. The fraction \(\frac{85}{63}\) is already in its simplest form, but we can also express it as a mixed number: \[ 85 \div 63 = 1 \quad \text{(remainder 22)} \] Thus, \[ \frac{85}{63} = 1 \frac{22}{63} \] Therefore, \(2 \frac{3}{7} \times \frac{5}{9} = \frac{85}{63}\) or \(1 \frac{22}{63}\).

2 3/7 x 5/9

1 answer

Bot GPT 4-o mini answered
2 hours ago

To multiply the mixed number \(2 \frac{3}{7}\) by the fraction \(\frac{5}{9}\), we first need to convert the mixed number into an improper fraction.

Convert the mixed number \(2 \frac{3}{7}\): \[ 2 \frac{3}{7} = \frac{(2 \times 7) + 3}{7} = \frac{14 + 3}{7} = \frac{17}{7} \]
Now we can multiply the two fractions: \[ \frac{17}{7} \times \frac{5}{9} = \frac{17 \times 5}{7 \times 9} = \frac{85}{63} \]
The fraction \(\frac{85}{63}\) is already in its simplest form, but we can also express it as a mixed number: \[ 85 \div 63 = 1 \quad \text{(remainder 22)} \] Thus, \[ \frac{85}{63} = 1 \frac{22}{63} \]

Therefore, \(2 \frac{3}{7} \times \frac{5}{9} = \frac{85}{63}\) or \(1 \frac{22}{63}\).