How do you evaluate 7\frac { 1} { 3} \times 2\frac { 2} { 5}?

Mar 30, 2017

$\frac{88}{5}$

Explanation:

To multiply that, rewrite the mixed fractions as improper fractions.

Take the denominator of the mixed fraction, multiply it by the whole number and add the numerator. Whatever value you get becomes the numerator of the improper fraction over the denominator of the mixed fraction.

For $7 \frac{1}{3}$, we multiply $3$ by $7$ and add the product to $1$

$\left(3 \cdot 7\right) + 1$

$21 + 1$

$22$

So our numerator is $22$ over our denominator which is $3$

$\therefore$Our improper fraction for $7 \frac{1}{3}$ is $\frac{22}{3}$

For $2 \frac{2}{5}$, we multiply $5$ by $2$ and add the product to $2$

$\left(5 \cdot 2\right) + 2$

$10 + 2$

$12$

So our numerator is $12$ over our denominator which is $5$

$\therefore$Our improper fraction for $2 \frac{2}{5}$ is $\frac{12}{5}$

Now back to our question;

$7 \frac{1}{3} \cdot 2 \frac{2}{5}$

$\frac{22}{3} \cdot \frac{12}{5}$

Multiply the numerator and the denominator

$\frac{264}{15} = \frac{88 \cdot \cancel{3}}{5 \cdot \cancel{3}}$

$\Rightarrow \frac{88}{5}$