Basic Math Examples

$\frac{9}{4} \div (\frac{1}{5} - \frac{3}{20})$

Step 1

Rewrite the division as a fraction.

$\frac{\frac{9}{4}}{\frac{1}{5} - \frac{3}{20}}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$\frac{9}{4} \cdot \frac{1}{\frac{1}{5} - \frac{3}{20}}$

Step 3

Simplify the denominator.

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Step 3.1

To write $\frac{1}{5}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{9}{4} \cdot \frac{1}{\frac{1}{5} \cdot \frac{4}{4} - \frac{3}{20}}$

Step 3.2

Write each expression with a common denominator of $20$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.2.1

Multiply $\frac{1}{5}$ by $\frac{4}{4}$ .

$\frac{9}{4} \cdot \frac{1}{\frac{4}{5 \cdot 4} - \frac{3}{20}}$

Step 3.2.2

Multiply $5$ by $4$ .

$\frac{9}{4} \cdot \frac{1}{\frac{4}{20} - \frac{3}{20}}$

Step 3.3

Combine the numerators over the common denominator.

$\frac{9}{4} \cdot \frac{1}{\frac{4 - 3}{20}}$

Step 3.4

Subtract $3$ from $4$ .

$\frac{9}{4} \cdot \frac{1}{\frac{1}{20}}$

Step 4

Reduce the expression by cancelling the common factors.

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Step 4.1

Multiply the numerator by the reciprocal of the denominator.

$\frac{9}{4} (1 \cdot 20)$

Step 4.2

Multiply $20$ by $1$ .

$\frac{9}{4} \cdot 20$

Step 4.3

Cancel the common factor of $4$ .

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Step 4.3.1

Factor $4$ out of $20$ .

$\frac{9}{4} \cdot (4 (5))$

Step 4.3.2

Cancel the common factor.

$\frac{9}{4} \cdot (4 \cdot 5)$

Step 4.3.3

Rewrite the expression.

$9 \cdot 5$

Step 4.4

Multiply $9$ by $5$ .

$45$