# How do you divide 2\frac { 5} { 7} \div \frac { 3} { 2}?

Mar 12, 2018

$\frac{38}{21}$

#### Explanation:

First, change the mixed number into an improper fraction.

For $2 \frac{5}{7}$, that's

$\frac{\left(7 \cdot 2\right) + 5}{7} = \frac{19}{7}$

Then you flip the second fraction and add a $\times$ sign, so

$\frac{19}{7} \times \frac{2}{3}$

Multiply the top and bottom numbers

$\frac{38}{21}$

Hope this helps!

Mar 12, 2018

2 5/7-:3/2=color(blue)(38/21=1 17/21

#### Explanation:

Divide:

$2 \frac{5}{7} \div \frac{3}{2}$

First convert $2 \frac{5}{7}$ to an improper fraction. Multiply the denominator by the whole number and then add the numerator. Place this over the denominator $7$.

$2 \frac{5}{7} = \frac{\left(7 \times 2 + 5\right)}{7}$

$2 \frac{5}{7} = \frac{19}{7}$

Rewrite the expression.

$\frac{19}{7} \div \frac{3}{2}$

When dividing by a fraction, invert it and multiply.

$\frac{19}{7} \times \frac{2}{3}$

Multiply the numerators and denominators across.

$\frac{19 \times 2}{7 \times 3}$

Simplify.

$\frac{38}{21}$

$\frac{38}{21}$ can be converted to a mixed number.

Using long division, divide $38$ by $21$ to get the whole number quotient with a remainder. The whole number quotient becomes the whole number of the mixed number, the remainder becomes the numerator, and the divisor $21$ is the denominator.

$38 \div 21 = \text{1 remainder 17}$

$\frac{38}{21} = 1 \frac{17}{21}$