Basic Math Examples

$\frac{8}{11} \cdot (\frac{5}{9} - \frac{1}{6}) \div 1 \frac{5}{9}$

Step 1

Convert $1 \frac{5}{9}$ to an improper fraction.

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Step 1.1

A mixed number is an addition of its whole and fractional parts.

$\frac{8}{11} \cdot (\frac{5}{9} - \frac{1}{6}) \div (1 + \frac{5}{9})$

Step 1.2

Add $1$ and $\frac{5}{9}$ .

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Step 1.2.1

Write $1$ as a fraction with a common denominator.

$\frac{8}{11} \cdot (\frac{5}{9} - \frac{1}{6}) \div (\frac{9}{9} + \frac{5}{9})$

Step 1.2.2

Combine the numerators over the common denominator.

$\frac{8}{11} \cdot (\frac{5}{9} - \frac{1}{6}) \div \frac{9 + 5}{9}$

Step 1.2.3

Add $9$ and $5$ .

$\frac{8}{11} \cdot (\frac{5}{9} - \frac{1}{6}) \div \frac{14}{9}$

Step 2

To divide by a fraction, multiply by its reciprocal.

$\frac{8}{11} \cdot (\frac{5}{9} - \frac{1}{6}) \frac{9}{14}$

Step 3

To write $\frac{5}{9}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{8}{11} \cdot (\frac{5}{9} \cdot \frac{2}{2} - \frac{1}{6}) \frac{9}{14}$

Step 4

To write $- \frac{1}{6}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{8}{11} \cdot (\frac{5}{9} \cdot \frac{2}{2} - \frac{1}{6} \cdot \frac{3}{3}) \frac{9}{14}$

Step 5

Write each expression with a common denominator of $18$ , by multiplying each by an appropriate factor of $1$ .

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Step 5.1

Multiply $\frac{5}{9}$ by $\frac{2}{2}$ .

$\frac{8}{11} \cdot (\frac{5 \cdot 2}{9 \cdot 2} - \frac{1}{6} \cdot \frac{3}{3}) \frac{9}{14}$

Step 5.2

Multiply $9$ by $2$ .

$\frac{8}{11} \cdot (\frac{5 \cdot 2}{18} - \frac{1}{6} \cdot \frac{3}{3}) \frac{9}{14}$

Step 5.3

Multiply $\frac{1}{6}$ by $\frac{3}{3}$ .

$\frac{8}{11} \cdot (\frac{5 \cdot 2}{18} - \frac{3}{6 \cdot 3}) \frac{9}{14}$

Step 5.4

Multiply $6$ by $3$ .

$\frac{8}{11} \cdot (\frac{5 \cdot 2}{18} - \frac{3}{18}) \frac{9}{14}$

Step 6

Combine the numerators over the common denominator.

$\frac{8}{11} \cdot \frac{5 \cdot 2 - 3}{18} \frac{9}{14}$

Step 7

Simplify the numerator.

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Step 7.1

Multiply $5$ by $2$ .

$\frac{8}{11} \cdot \frac{10 - 3}{18} \frac{9}{14}$

Step 7.2

Subtract $3$ from $10$ .

$\frac{8}{11} \cdot \frac{7}{18} \frac{9}{14}$

Step 8

Cancel the common factor of $2$ .

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Step 8.1

Factor $2$ out of $8$ .

$\frac{2 (4)}{11} \cdot \frac{7}{18} \frac{9}{14}$

Step 8.2

Factor $2$ out of $18$ .

$\frac{2 \cdot 4}{11} \cdot \frac{7}{2 \cdot 9} \frac{9}{14}$

Step 8.3

Cancel the common factor.

$\frac{2 \cdot 4}{11} \cdot \frac{7}{2 \cdot 9} \frac{9}{14}$

Step 8.4

Rewrite the expression.

$\frac{4}{11} \cdot \frac{7}{9} \frac{9}{14}$

Step 9

Multiply $\frac{4}{11}$ by $\frac{7}{9}$ .

$\frac{4 \cdot 7}{11 \cdot 9} \cdot \frac{9}{14}$

Step 10

Multiply.

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Step 10.1

Multiply $4$ by $7$ .

$\frac{28}{11 \cdot 9} \cdot \frac{9}{14}$

Step 10.2

Multiply $11$ by $9$ .

$\frac{28}{99} \cdot \frac{9}{14}$

Step 11

Cancel the common factor of $14$ .

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Step 11.1

Factor $14$ out of $28$ .

$\frac{14 (2)}{99} \cdot \frac{9}{14}$

Step 11.2

Cancel the common factor.

$\frac{14 \cdot 2}{99} \cdot \frac{9}{14}$

Step 11.3

Rewrite the expression.

$\frac{2}{99} \cdot 9$

Step 12

Cancel the common factor of $9$ .

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Step 12.1

Factor $9$ out of $99$ .

$\frac{2}{9 (11)} \cdot 9$

Step 12.2

Cancel the common factor.

$\frac{2}{9 \cdot 11} \cdot 9$

Step 12.3

Rewrite the expression.

$\frac{2}{11}$

Step 13

The result can be shown in multiple forms.

Exact Form:

$\frac{2}{11}$

Decimal Form:

$0.\overline{18}$