Basic Math Examples

$\frac{2}{5} \div (\frac{3}{12} - \frac{3}{4})$

Step 1

Rewrite the division as a fraction.

$\frac{\frac{2}{5}}{\frac{3}{12} - \frac{3}{4}}$

Step 2

Cancel the common factor of $3$ and $12$ .

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Step 2.1

Factor $3$ out of $3$ .

$\frac{\frac{2}{5}}{\frac{3 (1)}{12} - \frac{3}{4}}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $3$ out of $12$ .

$\frac{\frac{2}{5}}{\frac{3 \cdot 1}{3 \cdot 4} - \frac{3}{4}}$

Step 2.2.2

Cancel the common factor.

$\frac{\frac{2}{5}}{\frac{3 \cdot 1}{3 \cdot 4} - \frac{3}{4}}$

Step 2.2.3

Rewrite the expression.

$\frac{\frac{2}{5}}{\frac{1}{4} - \frac{3}{4}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$\frac{2}{5} \cdot \frac{1}{\frac{1}{4} - \frac{3}{4}}$

Step 4

Simplify the denominator.

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Step 4.1

Combine the numerators over the common denominator.

$\frac{2}{5} \cdot \frac{1}{\frac{1 - 3}{4}}$

Step 4.2

Subtract $3$ from $1$ .

$\frac{2}{5} \cdot \frac{1}{\frac{- 2}{4}}$

Step 4.3

Reduce the expression by cancelling the common factors.

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Step 4.3.1

Cancel the common factor of $- 2$ and $4$ .

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Step 4.3.1.1

Factor $2$ out of $- 2$ .

$\frac{2}{5} \cdot \frac{1}{\frac{2 (- 1)}{4}}$

Step 4.3.1.2

Cancel the common factors.

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Step 4.3.1.2.1

Factor $2$ out of $4$ .

$\frac{2}{5} \cdot \frac{1}{\frac{2 \cdot - 1}{2 \cdot 2}}$

Step 4.3.1.2.2

Cancel the common factor.

$\frac{2}{5} \cdot \frac{1}{\frac{2 \cdot - 1}{2 \cdot 2}}$

Step 4.3.1.2.3

Rewrite the expression.

$\frac{2}{5} \cdot \frac{1}{\frac{- 1}{2}}$

Step 4.3.2

Move the negative in front of the fraction.

$\frac{2}{5} \cdot \frac{1}{- \frac{1}{2}}$

Step 5

Reduce the expression by cancelling the common factors.

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Step 5.1

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

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Step 5.1.1

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

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

Step 5.1.2

Move the negative in front of the fraction.

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

Step 5.2

Multiply the numerator by the reciprocal of the denominator.

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

Step 6

Multiply $- (1 \cdot 2)$ .

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Step 6.1

Multiply $2$ by $1$ .

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

Step 6.2

Multiply $- 1$ by $2$ .

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

Step 7

Multiply $\frac{2}{5} \cdot - 2$ .

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Step 7.1

Combine $\frac{2}{5}$ and $- 2$ .

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

Step 7.2

Multiply $2$ by $- 2$ .

$\frac{- 4}{5}$

Step 8

Move the negative in front of the fraction.

$- \frac{4}{5}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$- \frac{4}{5}$

Decimal Form:

$- 0.8$