To multiply the mixed numbers \(5 \frac{1}{2}\) and \(4 \frac{4}{9}\), we'll first convert them to improper fractions. 1. Convert \(5 \frac{1}{2}\): \[ 5 \frac{1}{2} = 5 \times 2 + 1 = 10 + 1 = 11/2 \] 2. Convert \(4 \frac{4}{9}\): \[ 4 \frac{4}{9} = 4 \times 9 + 4 = 36 + 4 = 40/9 \] Now we multiply the two improper fractions: \[ \frac{11}{2} \times \frac{40}{9} = \frac{11 \times 40}{2 \times 9} = \frac{440}{18} \] Next, we simplify \(\frac{440}{18}\): - Find the greatest common divisor (GCD) of 440 and 18. The GCD is 2. - Divide both the numerator and denominator by 2: \[ \frac{440 \div 2}{18 \div 2} = \frac{220}{9} \] The improper fraction \(\frac{220}{9}\) can also be converted to a mixed number: \[ 220 \div 9 = 24 \quad \text{remainder} \quad 4 \] So: \[ \frac{220}{9} = 24 \frac{4}{9} \] Therefore, the result of \(5 \frac{1}{2} \times 4 \frac{4}{9}\) is: \[ \boxed{24 \frac{4}{9}} \]

5 1/2 x 4 4/9

1 answer

Bot GPT 4-o mini answered
5 hours ago

To multiply the mixed numbers \(5 \frac{1}{2}\) and \(4 \frac{4}{9}\), we'll first convert them to improper fractions.

Convert \(5 \frac{1}{2}\): \[ 5 \frac{1}{2} = 5 \times 2 + 1 = 10 + 1 = 11/2 \]
Convert \(4 \frac{4}{9}\): \[ 4 \frac{4}{9} = 4 \times 9 + 4 = 36 + 4 = 40/9 \]

Now we multiply the two improper fractions: \[ \frac{11}{2} \times \frac{40}{9} = \frac{11 \times 40}{2 \times 9} = \frac{440}{18} \]

Next, we simplify \(\frac{440}{18}\):

Find the greatest common divisor (GCD) of 440 and 18. The GCD is 2.
Divide both the numerator and denominator by 2: \[ \frac{440 \div 2}{18 \div 2} = \frac{220}{9} \]

The improper fraction \(\frac{220}{9}\) can also be converted to a mixed number: \[ 220 \div 9 = 24 \quad \text{remainder} \quad 4 \] So: \[ \frac{220}{9} = 24 \frac{4}{9} \]

Therefore, the result of \(5 \frac{1}{2} \times 4 \frac{4}{9}\) is: \[ \boxed{24 \frac{4}{9}} \]