Basic Math Examples

$(\frac{36}{5} - \frac{33}{8}) \div \frac{5}{4}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$(\frac{36}{5} - \frac{33}{8}) \frac{4}{5}$

Step 2

To write $\frac{36}{5}$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$(\frac{36}{5} \cdot \frac{8}{8} - \frac{33}{8}) \frac{4}{5}$

Step 3

To write $- \frac{33}{8}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$(\frac{36}{5} \cdot \frac{8}{8} - \frac{33}{8} \cdot \frac{5}{5}) \frac{4}{5}$

Step 4

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

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Step 4.1

Multiply $\frac{36}{5}$ by $\frac{8}{8}$ .

$(\frac{36 \cdot 8}{5 \cdot 8} - \frac{33}{8} \cdot \frac{5}{5}) \frac{4}{5}$

Step 4.2

Multiply $5$ by $8$ .

$(\frac{36 \cdot 8}{40} - \frac{33}{8} \cdot \frac{5}{5}) \frac{4}{5}$

Step 4.3

Multiply $\frac{33}{8}$ by $\frac{5}{5}$ .

$(\frac{36 \cdot 8}{40} - \frac{33 \cdot 5}{8 \cdot 5}) \frac{4}{5}$

Step 4.4

Multiply $8$ by $5$ .

$(\frac{36 \cdot 8}{40} - \frac{33 \cdot 5}{40}) \frac{4}{5}$

Step 5

Combine the numerators over the common denominator.

$\frac{36 \cdot 8 - 33 \cdot 5}{40} \cdot \frac{4}{5}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $36$ by $8$ .

$\frac{288 - 33 \cdot 5}{40} \cdot \frac{4}{5}$

Step 6.2

Multiply $- 33$ by $5$ .

$\frac{288 - 165}{40} \cdot \frac{4}{5}$

Step 6.3

Subtract $165$ from $288$ .

$\frac{123}{40} \cdot \frac{4}{5}$

Step 7

Cancel the common factor of $4$ .

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Step 7.1

Factor $4$ out of $40$ .

$\frac{123}{4 (10)} \cdot \frac{4}{5}$

Step 7.2

Cancel the common factor.

$\frac{123}{4 \cdot 10} \cdot \frac{4}{5}$

Step 7.3

Rewrite the expression.

$\frac{123}{10} \cdot \frac{1}{5}$

Step 8

Multiply $\frac{123}{10}$ by $\frac{1}{5}$ .

$\frac{123}{10 \cdot 5}$

Step 9

Multiply $10$ by $5$ .

$\frac{123}{50}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$\frac{123}{50}$

Decimal Form:

$2.46$

Mixed Number Form:

$2 \frac{23}{50}$