Basic Math Examples

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

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

Step 1

Convert

1 \frac{5}{6}

$1 \frac{5}{6}$ 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}))

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

Step 1.2

Add

1

$1$ and

\frac{5}{6}

$\frac{5}{6}$ .

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Step 1.2.1

Write

1

$1$ as a fraction with a common denominator.

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

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

Step 1.2.2

Combine the numerators over the common denominator.

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

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

Step 1.2.3

Add

6

$6$ and

5

$5$ .

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

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

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

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

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

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

Step 2

To divide by a fraction, multiply by its reciprocal.

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

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

Step 3

To write

- \frac{2}{3}

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

\frac{3}{3}

$\frac{3}{3}$ .

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

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

Step 4

Write each expression with a common denominator of

9

$9$ , by multiplying each by an appropriate factor of

1

$1$ .

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Step 4.1

Multiply

\frac{2}{3}

$\frac{2}{3}$ by

\frac{3}{3}

$\frac{3}{3}$ .

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

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

Step 4.2

Multiply

3

$3$ by

3

$3$ .

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

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

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

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

Step 5

Combine the numerators over the common denominator.

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

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

Step 6

Simplify the numerator.

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Step 6.1

Multiply

- 2

$- 2$ by

3

$3$ .

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

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

Step 6.2

Subtract

6

$6$ from

7

$7$ .

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

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

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

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

Step 7

Cancel the common factor of

3

$3$ .

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Step 7.1

Move the leading negative in

- \frac{6}{11}

$- \frac{6}{11}$ into the numerator.

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

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

Step 7.2

Factor

3

$3$ out of

9

$9$ .

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

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

Step 7.3

Factor

3

$3$ out of

- 6

$- 6$ .

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

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

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.

$- \frac{2}{33}$