Question

Multiply 5 1/3 x 1 5/6
. Simplify the answer and write as a mixed number.

Answer 1

To multiply the mixed numbers \(5 \frac{1}{3}\) and \(1 \frac{5}{6}\), we first convert them into improper fractions.

1. Convert \(5 \frac{1}{3}\) to an improper fraction:
\[
5 \frac{1}{3} = \frac{5 \times 3 + 1}{3} = \frac{15 + 1}{3} = \frac{16}{3}
\]

2. Convert \(1 \frac{5}{6}\) to an improper fraction:
\[
1 \frac{5}{6} = \frac{1 \times 6 + 5}{6} = \frac{6 + 5}{6} = \frac{11}{6}
\]

Now we will multiply the two improper fractions:
\[
\frac{16}{3} \times \frac{11}{6} = \frac{16 \times 11}{3 \times 6} = \frac{176}{18}
\]

Next, we simplify \(\frac{176}{18}\). We find the greatest common divisor (GCD) of 176 and 18. The GCD is 2. Therefore, we divide both the numerator and the denominator by 2:
\[
\frac{176 \div 2}{18 \div 2} = \frac{88}{9}
\]

Now convert \(\frac{88}{9}\) back to a mixed number.
To do this, we divide 88 by 9:
\[
88 \div 9 = 9 \quad \text{(with a remainder of 7)}
\]
So we can write it as:
\[
\frac{88}{9} = 9 \frac{7}{9}
\]

Thus, the final answer is:
\[
\boxed{9 \frac{7}{9}}
\]