To multiply the mixed numbers \(5 \frac{9}{10}\) and \(5 \frac{1}{10}\), follow these steps: 1. Convert the mixed numbers to improper fractions. For \(5 \frac{9}{10}\): \[ 5 \times 10 + 9 = 50 + 9 = 59 \quad \Rightarrow \quad 5 \frac{9}{10} = \frac{59}{10} \] For \(5 \frac{1}{10}\): \[ 5 \times 10 + 1 = 50 + 1 = 51 \quad \Rightarrow \quad 5 \frac{1}{10} = \frac{51}{10} \] 2. Now multiply the improper fractions: \[ \frac{59}{10} \times \frac{51}{10} = \frac{59 \times 51}{10 \times 10} \] Calculate \(59 \times 51\): \[ 59 \times 51 = 3009 \] So we have: \[ \frac{59 \times 51}{100} = \frac{3009}{100} \] 3. Convert the improper fraction back to a mixed number: Divide \(3009\) by \(100\): \[ 3009 \div 100 = 30 \quad \text{R} 9 \] This gives us \(30\) as the whole number and \(9\) as the remainder. Therefore, we express it as: \[ 30 \frac{9}{100} \] Thus, the result of multiplying \(5 \frac{9}{10}\) and \(5 \frac{1}{10}\) is: \[ \boxed{30 \frac{9}{100}} \]

5 9/10 x 5 1/10

1 answer

Bot GPT 4-o mini answered
6 hours ago

To multiply the mixed numbers \(5 \frac{9}{10}\) and \(5 \frac{1}{10}\), follow these steps:

Convert the mixed numbers to improper fractions.

For \(5 \frac{9}{10}\): \[ 5 \times 10 + 9 = 50 + 9 = 59 \quad \Rightarrow \quad 5 \frac{9}{10} = \frac{59}{10} \]

For \(5 \frac{1}{10}\): \[ 5 \times 10 + 1 = 50 + 1 = 51 \quad \Rightarrow \quad 5 \frac{1}{10} = \frac{51}{10} \]
Now multiply the improper fractions: \[ \frac{59}{10} \times \frac{51}{10} = \frac{59 \times 51}{10 \times 10} \]

Calculate \(59 \times 51\): \[ 59 \times 51 = 3009 \]

So we have: \[ \frac{59 \times 51}{100} = \frac{3009}{100} \]
Convert the improper fraction back to a mixed number:

Divide \(3009\) by \(100\): \[ 3009 \div 100 = 30 \quad \text{R} 9 \] This gives us \(30\) as the whole number and \(9\) as the remainder.

Therefore, we express it as: \[ 30 \frac{9}{100} \]

Thus, the result of multiplying \(5 \frac{9}{10}\) and \(5 \frac{1}{10}\) is: \[ \boxed{30 \frac{9}{100}} \]