Basic Math Examples

$\frac{2}{3} \div (\frac{4}{7} - 2)$

Step 1

Rewrite the division as a fraction.

$\frac{\frac{2}{3}}{\frac{4}{7} - 2}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$\frac{2}{3} \cdot \frac{1}{\frac{4}{7} - 2}$

Step 3

Simplify the denominator.

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Step 3.1

To write $- 2$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{2}{3} \cdot \frac{1}{\frac{4}{7} - 2 \cdot \frac{7}{7}}$

Step 3.2

Combine $- 2$ and $\frac{7}{7}$ .

$\frac{2}{3} \cdot \frac{1}{\frac{4}{7} + \frac{- 2 \cdot 7}{7}}$

Step 3.3

Combine the numerators over the common denominator.

$\frac{2}{3} \cdot \frac{1}{\frac{4 - 2 \cdot 7}{7}}$

Step 3.4

Simplify the numerator.

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Step 3.4.1

Multiply $- 2$ by $7$ .

$\frac{2}{3} \cdot \frac{1}{\frac{4 - 14}{7}}$

Step 3.4.2

Subtract $14$ from $4$ .

$\frac{2}{3} \cdot \frac{1}{\frac{- 10}{7}}$

Step 3.5

Move the negative in front of the fraction.

$\frac{2}{3} \cdot \frac{1}{- \frac{10}{7}}$

Step 4

Cancel the common factor of $1$ and $- 1$ .

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Step 4.1

Rewrite $1$ as $- 1 (- 1)$ .

$\frac{2}{3} \cdot \frac{- 1 (- 1)}{- \frac{10}{7}}$

Step 4.2

Move the negative in front of the fraction.

$\frac{2}{3} (- \frac{1}{\frac{10}{7}})$

Step 5

Multiply the numerator by the reciprocal of the denominator.

$\frac{2}{3} (- (1 (\frac{7}{10})))$

Step 6

Multiply $\frac{7}{10}$ by $1$ .

$\frac{2}{3} (- \frac{7}{10})$

Step 7

Cancel the common factor of $2$ .

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Step 7.1

Move the leading negative in $- \frac{7}{10}$ into the numerator.

$\frac{2}{3} \cdot \frac{- 7}{10}$

Step 7.2

Factor $2$ out of $10$ .

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

Step 7.3

Cancel the common factor.

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

Step 7.4

Rewrite the expression.

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

Step 8

Multiply $\frac{1}{3}$ by $\frac{- 7}{5}$ .

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

Step 9

Simplify the expression.

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Step 9.1

Multiply $3$ by $5$ .

$\frac{- 7}{15}$

Step 9.2

Move the negative in front of the fraction.

$- \frac{7}{15}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$- \frac{7}{15}$

Decimal Form:

$- 0.4\overline{6}$