Question

What is the product of 3 1/5 times 5/6 then the answer in simplest from?

Answer 1

a. three and five over eleven
b. three and one over six
c. two and two over three
d. two and one over four

Answer 2

Here are two ways you could work this:

1) convert to improper fractions:

\[3\frac{1}{5} = \frac{3*5+1}{5} = \frac{16}{5}\]Multiply \[\frac{16}{5}*\frac{5}{6} = \frac{16}{\cancel{5}}*\frac{\cancel{5}}{6} = \frac{16}{6}\]now reduce the fraction and convert to a mixed number

2) use the distributive property:
\[3\frac{1}{5}*\frac{5}{6} = (3+\frac{1}{5})*\frac{5}{6} = 3*\frac{5}{6} + \frac{1}{5}*\frac{5}6 = \frac{3*5}{6}+\frac{1}{\cancel{5}}*\frac{\cancel{5}}6 \]\[\qquad= \frac{15}{6} + \frac{1}{6} = \frac{16}{6}\]

Again, reduce fraction and convert to a mixed number.