Evaluate (10/21)÷(-15/7)

$\frac{10}{21} \div (- \frac{15}{7})$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{10}{21} (- \frac{7}{15})$

Step 2

Cancel the common factor of $5$ .

Move the leading negative in $- \frac{7}{15}$ into the numerator.

$\frac{10}{21} \cdot \frac{- 7}{15}$

Factor $5$ out of $10$ .

$\frac{5 (2)}{21} \cdot \frac{- 7}{15}$

Factor $5$ out of $15$ .

$\frac{5 \cdot 2}{21} \cdot \frac{- 7}{5 \cdot 3}$

Cancel the common factor.

$\frac{5 \cdot 2}{21} \cdot \frac{- 7}{5 \cdot 3}$

Rewrite the expression.

$\frac{2}{21} \cdot \frac{- 7}{3}$

Step 3

Cancel the common factor of $7$ .

Factor $7$ out of $21$ .

$\frac{2}{7 (3)} \cdot \frac{- 7}{3}$

Factor $7$ out of $- 7$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 4

Multiply $\frac{2}{3}$ by $\frac{- 1}{3}$ .

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

Step 5

Simplify the expression.

Multiply $2$ by $- 1$ .

$\frac{- 2}{3 \cdot 3}$

Multiply $3$ by $3$ .

$\frac{- 2}{9}$

Move the negative in front of the fraction.

$- \frac{2}{9}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$- \frac{2}{9}$

Decimal Form:

$- 0.\overline{2}$