Evaluate (5/16)÷(3/8-2/5)

$\frac{5}{16} \div (\frac{3}{8} - \frac{2}{5})$

Step 1

Rewrite the division as a fraction.

$\frac{\frac{5}{16}}{\frac{3}{8} - \frac{2}{5}}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$\frac{5}{16} \cdot \frac{1}{\frac{3}{8} - \frac{2}{5}}$

Step 3

Simplify the denominator.

To write $\frac{3}{8}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{5}{16} \cdot \frac{1}{\frac{3}{8} \cdot \frac{5}{5} - \frac{2}{5}}$

To write $- \frac{2}{5}$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{5}{16} \cdot \frac{1}{\frac{3}{8} \cdot \frac{5}{5} - \frac{2}{5} \cdot \frac{8}{8}}$

Write each expression with a common denominator of $40$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{3}{8}$ by $\frac{5}{5}$ .

$\frac{5}{16} \cdot \frac{1}{\frac{3 \cdot 5}{8 \cdot 5} - \frac{2}{5} \cdot \frac{8}{8}}$

Multiply $8$ by $5$ .

$\frac{5}{16} \cdot \frac{1}{\frac{3 \cdot 5}{40} - \frac{2}{5} \cdot \frac{8}{8}}$

Multiply $\frac{2}{5}$ by $\frac{8}{8}$ .

$\frac{5}{16} \cdot \frac{1}{\frac{3 \cdot 5}{40} - \frac{2 \cdot 8}{5 \cdot 8}}$

Multiply $5$ by $8$ .

$\frac{5}{16} \cdot \frac{1}{\frac{3 \cdot 5}{40} - \frac{2 \cdot 8}{40}}$

Combine the numerators over the common denominator.

$\frac{5}{16} \cdot \frac{1}{\frac{3 \cdot 5 - 2 \cdot 8}{40}}$

Simplify the numerator.

Multiply $3$ by $5$ .

$\frac{5}{16} \cdot \frac{1}{\frac{15 - 2 \cdot 8}{40}}$

Multiply $- 2$ by $8$ .

$\frac{5}{16} \cdot \frac{1}{\frac{15 - 16}{40}}$

Subtract $16$ from $15$ .

$\frac{5}{16} \cdot \frac{1}{\frac{- 1}{40}}$

Move the negative in front of the fraction.

$\frac{5}{16} \cdot \frac{1}{- \frac{1}{40}}$

Step 4

Reduce the expression by cancelling the common factors.

Cancel the common factor of $1$ and $- 1$ .

Rewrite $1$ as $- 1 (- 1)$ .

$\frac{5}{16} \cdot \frac{- 1 (- 1)}{- \frac{1}{40}}$

Move the negative in front of the fraction.

$\frac{5}{16} (- \frac{1}{\frac{1}{40}})$

Multiply the numerator by the reciprocal of the denominator.

$\frac{5}{16} (- (1 \cdot 40))$

Step 5

Multiply $- (1 \cdot 40)$ .

Multiply $40$ by $1$ .

$\frac{5}{16} (- 1 \cdot 40)$

Multiply $- 1$ by $40$ .

$\frac{5}{16} \cdot - 40$

Step 6

Cancel the common factor of $8$ .

Factor $8$ out of $16$ .

$\frac{5}{8 (2)} \cdot - 40$

Factor $8$ out of $- 40$ .

$\frac{5}{8 \cdot 2} \cdot (8 \cdot - 5)$

Cancel the common factor.

$\frac{5}{8 \cdot 2} \cdot (8 \cdot - 5)$

Rewrite the expression.

$\frac{5}{2} \cdot - 5$

Step 7

Combine $\frac{5}{2}$ and $- 5$ .

$\frac{5 \cdot - 5}{2}$

Step 8

Simplify the expression.

Multiply $5$ by $- 5$ .

$\frac{- 25}{2}$

Move the negative in front of the fraction.

$- \frac{25}{2}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$- \frac{25}{2}$

Decimal Form:

$- 12.5$

Mixed Number Form:

$- 12 \frac{1}{2}$

Evaluate (5/16)÷(3/8-2/5)

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