Question

Multiply 1 2/3 by 6 1/2 . Convert the answer to be a mixed number.(1 point) Responses 10 5/6 10 Start Fraction 5 over 6 End Fraction 11 1/6 11 Start Fraction 1 over 6 End Fraction 65/6 Start Fraction 65 over 6 End Fraction 18/5

Answer 1

To multiply the mixed numbers \(1 \frac{2}{3}\) and \(6 \frac{1}{2}\), we first need to convert them to improper fractions.

1. Convert \(1 \frac{2}{3}\):
\[
1 \frac{2}{3} = \frac{3 \times 1 + 2}{3} = \frac{3 + 2}{3} = \frac{5}{3}
\]

2. Convert \(6 \frac{1}{2}\):
\[
6 \frac{1}{2} = \frac{2 \times 6 + 1}{2} = \frac{12 + 1}{2} = \frac{13}{2}
\]

Now multiply the two improper fractions:
\[
\frac{5}{3} \times \frac{13}{2} = \frac{5 \times 13}{3 \times 2} = \frac{65}{6}
\]

Now we convert \(\frac{65}{6}\) to a mixed number. To do this, divide 65 by 6:
- \(65 \div 6 = 10\) remainder \(5\).

So, \(\frac{65}{6} = 10 \frac{5}{6}\).

Therefore, the answer is:
\[
10 \frac{5}{6}
\]
This corresponds to the first response option: **10 5/6**.