Basic Math Examples

$(- \frac{2}{5} - \frac{1}{3}) \div \frac{3}{10}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$(- \frac{2}{5} - \frac{1}{3}) \frac{10}{3}$

Step 2

To write $- \frac{2}{5}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$(- \frac{2}{5} \cdot \frac{3}{3} - \frac{1}{3}) \frac{10}{3}$

Step 3

To write $- \frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$(- \frac{2}{5} \cdot \frac{3}{3} - \frac{1}{3} \cdot \frac{5}{5}) \frac{10}{3}$

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 $\frac{2}{5}$ by $\frac{3}{3}$ .

$(- \frac{2 \cdot 3}{5 \cdot 3} - \frac{1}{3} \cdot \frac{5}{5}) \frac{10}{3}$

Step 4.2

Multiply $5$ by $3$ .

$(- \frac{2 \cdot 3}{15} - \frac{1}{3} \cdot \frac{5}{5}) \frac{10}{3}$

Step 4.3

Multiply $\frac{1}{3}$ by $\frac{5}{5}$ .

$(- \frac{2 \cdot 3}{15} - \frac{5}{3 \cdot 5}) \frac{10}{3}$

Step 4.4

Multiply $3$ by $5$ .

$(- \frac{2 \cdot 3}{15} - \frac{5}{15}) \frac{10}{3}$

Step 5

Combine the numerators over the common denominator.

$\frac{- 2 \cdot 3 - 5}{15} \cdot \frac{10}{3}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $- 2$ by $3$ .

$\frac{- 6 - 5}{15} \cdot \frac{10}{3}$

Step 6.2

Subtract $5$ from $- 6$ .

$\frac{- 11}{15} \cdot \frac{10}{3}$

Step 7

Cancel the common factor of $5$ .

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Step 7.1

Factor $5$ out of $15$ .

$\frac{- 11}{5 (3)} \cdot \frac{10}{3}$

Step 7.2

Factor $5$ out of $10$ .

$\frac{- 11}{5 \cdot 3} \cdot \frac{5 \cdot 2}{3}$

Step 7.3

Cancel the common factor.

$\frac{- 11}{5 \cdot 3} \cdot \frac{5 \cdot 2}{3}$

Step 7.4

Rewrite the expression.

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

Step 8

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

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

Step 9

Simplify the expression.

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Step 9.1

Multiply $- 11$ by $2$ .

$\frac{- 22}{3 \cdot 3}$

Step 9.2

Multiply $3$ by $3$ .

$\frac{- 22}{9}$

Step 9.3

Move the negative in front of the fraction.

$- \frac{22}{9}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$- \frac{22}{9}$

Decimal Form:

$- 2.\overline{4}$

Mixed Number Form:

$- 2 \frac{4}{9}$