Algebra Examples

$- \frac{14}{9} \div \frac{6}{9} + \frac{8}{9} \cdot (- \frac{3}{2})$

Step 1

Simplify each term.

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Step 1.1

To divide by a fraction, multiply by its reciprocal.

$- \frac{14}{9} \cdot \frac{9}{6} + \frac{8}{9} \cdot (- \frac{3}{2})$

Step 1.2

Cancel the common factor of $2$ .

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Step 1.2.1

Move the leading negative in $- \frac{14}{9}$ into the numerator.

$\frac{- 14}{9} \cdot \frac{9}{6} + \frac{8}{9} \cdot (- \frac{3}{2})$

Step 1.2.2

Factor $2$ out of $- 14$ .

$\frac{2 (- 7)}{9} \cdot \frac{9}{6} + \frac{8}{9} \cdot (- \frac{3}{2})$

Step 1.2.3

Factor $2$ out of $6$ .

$\frac{2 \cdot - 7}{9} \cdot \frac{9}{2 \cdot 3} + \frac{8}{9} \cdot (- \frac{3}{2})$

Step 1.2.4

Cancel the common factor.

$\frac{2 \cdot - 7}{9} \cdot \frac{9}{2 \cdot 3} + \frac{8}{9} \cdot (- \frac{3}{2})$

Step 1.2.5

Rewrite the expression.

$\frac{- 7}{9} \cdot \frac{9}{3} + \frac{8}{9} \cdot (- \frac{3}{2})$

Step 1.3

Cancel the common factor of $9$ .

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Step 1.3.1

Cancel the common factor.

$\frac{- 7}{9} \cdot \frac{9}{3} + \frac{8}{9} \cdot (- \frac{3}{2})$

Step 1.3.2

Rewrite the expression.

$- 7 (\frac{1}{3}) + \frac{8}{9} \cdot (- \frac{3}{2})$

Step 1.4

Combine $- 7$ and $\frac{1}{3}$ .

$\frac{- 7}{3} + \frac{8}{9} \cdot (- \frac{3}{2})$

Step 1.5

Move the negative in front of the fraction.

$- \frac{7}{3} + \frac{8}{9} \cdot (- \frac{3}{2})$

Step 1.6

Cancel the common factor of $2$ .

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Step 1.6.1

Move the leading negative in $- \frac{3}{2}$ into the numerator.

$- \frac{7}{3} + \frac{8}{9} \cdot \frac{- 3}{2}$

Step 1.6.2

Factor $2$ out of $8$ .

$- \frac{7}{3} + \frac{2 (4)}{9} \cdot \frac{- 3}{2}$

Step 1.6.3

Cancel the common factor.

$- \frac{7}{3} + \frac{2 \cdot 4}{9} \cdot \frac{- 3}{2}$

Step 1.6.4

Rewrite the expression.

$- \frac{7}{3} + \frac{4}{9} \cdot - 3$

Step 1.7

Cancel the common factor of $3$ .

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Step 1.7.1

Factor $3$ out of $9$ .

$- \frac{7}{3} + \frac{4}{3 (3)} \cdot - 3$

Step 1.7.2

Factor $3$ out of $- 3$ .

$- \frac{7}{3} + \frac{4}{3 \cdot 3} \cdot (3 \cdot - 1)$

Step 1.7.3

Cancel the common factor.

$- \frac{7}{3} + \frac{4}{3 \cdot 3} \cdot (3 \cdot - 1)$

Step 1.7.4

Rewrite the expression.

$- \frac{7}{3} + \frac{4}{3} \cdot - 1$

Step 1.8

Combine $\frac{4}{3}$ and $- 1$ .

$- \frac{7}{3} + \frac{4 \cdot - 1}{3}$

Step 1.9

Multiply $4$ by $- 1$ .

$- \frac{7}{3} + \frac{- 4}{3}$

Step 1.10

Move the negative in front of the fraction.

$- \frac{7}{3} - \frac{4}{3}$

Step 2

Combine fractions.

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Step 2.1

Combine the numerators over the common denominator.

$\frac{- 7 - 4}{3}$

Step 2.2

Simplify the expression.

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Step 2.2.1

Subtract $4$ from $- 7$ .

$\frac{- 11}{3}$

Step 2.2.2

Move the negative in front of the fraction.

$- \frac{11}{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$- \frac{11}{3}$

Decimal Form:

$- 3.\overline{6}$

Mixed Number Form:

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