Pre-Algebra Examples

$\frac{14}{9} \div (- \frac{2}{3}) - \frac{13}{5}$

Step 1

Simplify each term.

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Step 1.1

To divide by a fraction, multiply by its reciprocal.

$\frac{14}{9} (- \frac{3}{2}) - \frac{13}{5}$

Step 1.2

Cancel the common factor of $2$ .

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Step 1.2.1

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

$\frac{14}{9} \cdot \frac{- 3}{2} - \frac{13}{5}$

Step 1.2.2

Factor $2$ out of $14$ .

$\frac{2 (7)}{9} \cdot \frac{- 3}{2} - \frac{13}{5}$

Step 1.2.3

Cancel the common factor.

$\frac{2 \cdot 7}{9} \cdot \frac{- 3}{2} - \frac{13}{5}$

Step 1.2.4

Rewrite the expression.

$\frac{7}{9} \cdot - 3 - \frac{13}{5}$

Step 1.3

Cancel the common factor of $3$ .

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Step 1.3.1

Factor $3$ out of $9$ .

$\frac{7}{3 (3)} \cdot - 3 - \frac{13}{5}$

Step 1.3.2

Factor $3$ out of $- 3$ .

$\frac{7}{3 \cdot 3} \cdot (3 \cdot - 1) - \frac{13}{5}$

Step 1.3.3

Cancel the common factor.

$\frac{7}{3 \cdot 3} \cdot (3 \cdot - 1) - \frac{13}{5}$

Step 1.3.4

Rewrite the expression.

$\frac{7}{3} \cdot - 1 - \frac{13}{5}$

Step 1.4

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

$\frac{7 \cdot - 1}{3} - \frac{13}{5}$

Step 1.5

Multiply $7$ by $- 1$ .

$\frac{- 7}{3} - \frac{13}{5}$

Step 1.6

Move the negative in front of the fraction.

$- \frac{7}{3} - \frac{13}{5}$

Step 2

To write $- \frac{7}{3}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$- \frac{7}{3} \cdot \frac{5}{5} - \frac{13}{5}$

Step 3

To write $- \frac{13}{5}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- \frac{7}{3} \cdot \frac{5}{5} - \frac{13}{5} \cdot \frac{3}{3}$

Step 4

Write each expression with a common denominator of $15$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{7}{3}$ by $\frac{5}{5}$ .

$- \frac{7 \cdot 5}{3 \cdot 5} - \frac{13}{5} \cdot \frac{3}{3}$

Step 4.2

Multiply $3$ by $5$ .

$- \frac{7 \cdot 5}{15} - \frac{13}{5} \cdot \frac{3}{3}$

Step 4.3

Multiply $\frac{13}{5}$ by $\frac{3}{3}$ .

$- \frac{7 \cdot 5}{15} - \frac{13 \cdot 3}{5 \cdot 3}$

Step 4.4

Multiply $5$ by $3$ .

$- \frac{7 \cdot 5}{15} - \frac{13 \cdot 3}{15}$

Step 5

Combine the numerators over the common denominator.

$\frac{- 7 \cdot 5 - 13 \cdot 3}{15}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $- 7$ by $5$ .

$\frac{- 35 - 13 \cdot 3}{15}$

Step 6.2

Multiply $- 13$ by $3$ .

$\frac{- 35 - 39}{15}$

Step 6.3

Subtract $39$ from $- 35$ .

$\frac{- 74}{15}$

Step 7

Move the negative in front of the fraction.

$- \frac{74}{15}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$- \frac{74}{15}$

Decimal Form:

$- 4.9\overline{3}$

Mixed Number Form:

$- 4 \frac{14}{15}$