# How do you evaluate 3\frac { 2} { 3} \cdot 2\frac { 1} { 4} ?

Aug 13, 2017

$8 \frac{1}{4}$

#### Explanation:

$3 \frac{2}{3} \cdot 2 \frac{1}{4}$

First, we convert the mixed fractions into improper fractions by multiplying the whole number by the respective denominator, adding the product to the respective numerator, and placing the result above the same denominator.

$3 \frac{2}{3} \implies \frac{11}{3}$, and

$2 \frac{1}{4} \implies \frac{9}{4}$

Now, we can write the same expression as:

$\frac{11}{3} \cdot \frac{9}{4}$

Since $9$ is divisible by $3$, we reduce the fractions.

$\frac{11}{1 \cancel{3}} \cdot \frac{3 \cancel{9}}{4}$

$\frac{11}{1} \cdot \frac{3}{4}$

Now multiply the numerators with each other, and the denominators with each other.

$\frac{11 \times 3}{1 \times 4} = \frac{33}{4}$

Hence, we get,

$\frac{33}{4}$

This can be reduced to a mixed fraction by dividing $33$ by $4$, writing the whole number and keeping the remnant over the same denominator.

$33 \div 4 = 8$ with a remnant of $1$.

$8 \frac{1}{4}$