# How do you multiply 2\frac { 5} { 8} \times 3\frac { 1} { 7}?

Aug 28, 2017

See a solution process below:

#### Explanation:

First, we need to convert the two mixed numbers into improper fractions:

$2 \frac{5}{8} \times 3 \frac{1}{7} \implies \left(2 + \frac{5}{8}\right) \times \left(3 + \frac{1}{7}\right) \implies$

$\left(\left[\frac{8}{8} \times 2\right] + \frac{5}{8}\right) \times \left(\left[\frac{7}{7} \times 3\right] + \frac{1}{7}\right) \implies$

$\left(\frac{16}{8} + \frac{5}{8}\right) \times \left(\frac{21}{7} + \frac{1}{7}\right) \implies \frac{21}{8} \times \frac{22}{7}$

Next, to multiply the two fractions we will multiply the numerators over the denominators multiplied:

$\frac{21}{8} \times \frac{22}{7} \implies \frac{21 \times 22}{8 \times 7} \implies \frac{462}{56}$

Now, if necessary we can convert the improper fraction into a mixed number:

$\frac{462}{56} \implies \frac{448}{56} + \frac{14}{56} \implies 8 + \frac{14 \times 1}{14 \times 4} \implies 8 + \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{14}}} \times 1}{\textcolor{red}{\cancel{\textcolor{b l a c k}{14}}} \times 4} \implies$

$8 + \frac{1}{4} = 8 \frac{1}{4}$

Aug 28, 2017

The answer is $\frac{33}{4}$ or $8 \frac{1}{4}$.

Refer to the explanation for the process.

#### Explanation:

Multiply:

$2 \frac{5}{8} \times 3 \frac{1}{7}$

Convert each mixed fraction to an improper fraction by multiplying the denominator by the whole number and adding the numerator, and putting the result over the denominator: $a \frac{b}{c} = \frac{\left(c \times a + b\right)}{c}$.

$2 \frac{5}{8} = \frac{\left(8 \times 2 + 5\right)}{8} = \frac{\left(16 + 5\right)}{8} = \frac{21}{8}$

$3 \frac{1}{7} = \frac{\left(7 \times 3 + 1\right)}{7} = \frac{\left(21 + 1\right)}{7} = \frac{22}{7}$

Now multiply the numerators of both fractions and the denominators of both fractions.

$\frac{21}{8} \times \frac{22}{7} = \frac{462}{56}$

Simplify by dividing the numerator and denominator by $14$. I determined this partially by trial and error.

$\frac{462 \div 14}{56 \div 14} = \frac{33}{4}$

Convert the improper fraction to a mixed number by dividing the numerator by the denominator to get the whole number, then take the remainder and place it over the denominator.

$33 \div 4 = 8$ R 1

The mixed number is $8 \frac{1}{4}$.