Basic Math Examples

$(\frac{7}{9} - \frac{2}{3}) \div (- 1 \frac{5}{6})$

Step 1

Convert $1 \frac{5}{6}$ to an improper fraction.

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Step 1.1

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

$(\frac{7}{9} - \frac{2}{3}) \div (- (1 + \frac{5}{6}))$

Step 1.2

Add $1$ and $\frac{5}{6}$ .

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Step 1.2.1

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

$(\frac{7}{9} - \frac{2}{3}) \div (- (\frac{6}{6} + \frac{5}{6}))$

Step 1.2.2

Combine the numerators over the common denominator.

$(\frac{7}{9} - \frac{2}{3}) \div (- \frac{6 + 5}{6})$

Step 1.2.3

Add $6$ and $5$ .

$(\frac{7}{9} - \frac{2}{3}) \div (- \frac{11}{6})$

Step 2

To divide by a fraction, multiply by its reciprocal.

$(\frac{7}{9} - \frac{2}{3}) (- \frac{6}{11})$

Step 3

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

$(\frac{7}{9} - \frac{2}{3} \cdot \frac{3}{3}) (- \frac{6}{11})$

Step 4

Write each expression with a common denominator of $9$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

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

$(\frac{7}{9} - \frac{2 \cdot 3}{3 \cdot 3}) (- \frac{6}{11})$

Step 4.2

Multiply $3$ by $3$ .

$(\frac{7}{9} - \frac{2 \cdot 3}{9}) (- \frac{6}{11})$

Step 5

Combine the numerators over the common denominator.

$\frac{7 - 2 \cdot 3}{9} (- \frac{6}{11})$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $- 2$ by $3$ .

$\frac{7 - 6}{9} (- \frac{6}{11})$

Step 6.2

Subtract $6$ from $7$ .

$\frac{1}{9} (- \frac{6}{11})$

Step 7

Cancel the common factor of $3$ .

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Step 7.1

Move the leading negative in $- \frac{6}{11}$ into the numerator.

$\frac{1}{9} \cdot \frac{- 6}{11}$

Step 7.2

Factor $3$ out of $9$ .

$\frac{1}{3 (3)} \cdot \frac{- 6}{11}$

Step 7.3

Factor $3$ out of $- 6$ .

$\frac{1}{3 \cdot 3} \cdot \frac{3 \cdot - 2}{11}$

Step 7.4

Cancel the common factor.

$\frac{1}{3 \cdot 3} \cdot \frac{3 \cdot - 2}{11}$

Step 7.5

Rewrite the expression.

$\frac{1}{3} \cdot \frac{- 2}{11}$

Step 8

Multiply $\frac{1}{3}$ by $\frac{- 2}{11}$ .

$\frac{- 2}{3 \cdot 11}$

Step 9

Simplify the expression.

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Step 9.1

Multiply $3$ by $11$ .

$\frac{- 2}{33}$

Step 9.2

Move the negative in front of the fraction.

$- \frac{2}{33}$