Basic Math Examples

$\frac{1}{2} \div \frac{2}{3} \div \frac{2}{3} - (\frac{4}{5} \cdot \frac{5}{6})$

Step 1

Simplify each term.

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Step 1.1

To divide by a fraction, multiply by its reciprocal.

$\frac{1}{2} \div \frac{2}{3} \cdot \frac{3}{2} - (\frac{4}{5} \cdot \frac{5}{6})$

Step 1.2

To divide by a fraction, multiply by its reciprocal.

$\frac{1}{2} \cdot \frac{3}{2} \frac{3}{2} - (\frac{4}{5} \cdot \frac{5}{6})$

Step 1.3

Multiply $\frac{1}{2} \cdot \frac{3}{2}$ .

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Step 1.3.1

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

$\frac{3}{2 \cdot 2} \cdot \frac{3}{2} - (\frac{4}{5} \cdot \frac{5}{6})$

Step 1.3.2

Multiply $2$ by $2$ .

$\frac{3}{4} \cdot \frac{3}{2} - (\frac{4}{5} \cdot \frac{5}{6})$

Step 1.4

Multiply $\frac{3}{4} \cdot \frac{3}{2}$ .

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Step 1.4.1

Multiply $\frac{3}{4}$ by $\frac{3}{2}$ .

$\frac{3 \cdot 3}{4 \cdot 2} - (\frac{4}{5} \cdot \frac{5}{6})$

Step 1.4.2

Multiply $3$ by $3$ .

$\frac{9}{4 \cdot 2} - (\frac{4}{5} \cdot \frac{5}{6})$

Step 1.4.3

Multiply $4$ by $2$ .

$\frac{9}{8} - (\frac{4}{5} \cdot \frac{5}{6})$

Step 1.5

Cancel the common factor of $2$ .

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Step 1.5.1

Factor $2$ out of $4$ .

$\frac{9}{8} - (\frac{2 (2)}{5} \cdot \frac{5}{6})$

Step 1.5.2

Factor $2$ out of $6$ .

$\frac{9}{8} - (\frac{2 \cdot 2}{5} \cdot \frac{5}{2 \cdot 3})$

Step 1.5.3

Cancel the common factor.

$\frac{9}{8} - (\frac{2 \cdot 2}{5} \cdot \frac{5}{2 \cdot 3})$

Step 1.5.4

Rewrite the expression.

$\frac{9}{8} - (\frac{2}{5} \cdot \frac{5}{3})$

Step 1.6

Cancel the common factor of $5$ .

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Step 1.6.1

Cancel the common factor.

$\frac{9}{8} - (\frac{2}{5} \cdot \frac{5}{3})$

Step 1.6.2

Rewrite the expression.

$\frac{9}{8} - (2 \cdot \frac{1}{3})$

Step 1.7

Combine $2$ and $\frac{1}{3}$ .

$\frac{9}{8} - \frac{2}{3}$

Step 2

To write $\frac{9}{8}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{9}{8} \cdot \frac{3}{3} - \frac{2}{3}$

Step 3

To write $- \frac{2}{3}$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{9}{8} \cdot \frac{3}{3} - \frac{2}{3} \cdot \frac{8}{8}$

Step 4

Write each expression with a common denominator of $24$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{9}{8}$ by $\frac{3}{3}$ .

$\frac{9 \cdot 3}{8 \cdot 3} - \frac{2}{3} \cdot \frac{8}{8}$

Step 4.2

Multiply $8$ by $3$ .

$\frac{9 \cdot 3}{24} - \frac{2}{3} \cdot \frac{8}{8}$

Step 4.3

Multiply $\frac{2}{3}$ by $\frac{8}{8}$ .

$\frac{9 \cdot 3}{24} - \frac{2 \cdot 8}{3 \cdot 8}$

Step 4.4

Multiply $3$ by $8$ .

$\frac{9 \cdot 3}{24} - \frac{2 \cdot 8}{24}$

Step 5

Combine the numerators over the common denominator.

$\frac{9 \cdot 3 - 2 \cdot 8}{24}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $9$ by $3$ .

$\frac{27 - 2 \cdot 8}{24}$

Step 6.2

Multiply $- 2$ by $8$ .

$\frac{27 - 16}{24}$

Step 6.3

Subtract $16$ from $27$ .

$\frac{11}{24}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{11}{24}$

Decimal Form:

$0.458\overline{3}$