Question

5 9/10 x 5 1/10

Answer 1

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:
\[
\boxed{30 \frac{9}{100}}
\]