Basic Math Examples

$\frac{1}{2} \div (\frac{13}{16} - \frac{3}{4})$

Step 1

Rewrite the division as a fraction.

$\frac{\frac{1}{2}}{\frac{13}{16} - \frac{3}{4}}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$\frac{1}{2} \cdot \frac{1}{\frac{13}{16} - \frac{3}{4}}$

Step 3

Simplify the denominator.

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Step 3.1

To write $- \frac{3}{4}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{1}{2} \cdot \frac{1}{\frac{13}{16} - \frac{3}{4} \cdot \frac{4}{4}}$

Step 3.2

Write each expression with a common denominator of $16$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.2.1

Multiply $\frac{3}{4}$ by $\frac{4}{4}$ .

$\frac{1}{2} \cdot \frac{1}{\frac{13}{16} - \frac{3 \cdot 4}{4 \cdot 4}}$

Step 3.2.2

Multiply $4$ by $4$ .

$\frac{1}{2} \cdot \frac{1}{\frac{13}{16} - \frac{3 \cdot 4}{16}}$

Step 3.3

Combine the numerators over the common denominator.

$\frac{1}{2} \cdot \frac{1}{\frac{13 - 3 \cdot 4}{16}}$

Step 3.4

Simplify the numerator.

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Step 3.4.1

Multiply $- 3$ by $4$ .

$\frac{1}{2} \cdot \frac{1}{\frac{13 - 12}{16}}$

Step 3.4.2

Subtract $12$ from $13$ .

$\frac{1}{2} \cdot \frac{1}{\frac{1}{16}}$

Step 4

Reduce the expression by cancelling the common factors.

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Step 4.1

Multiply the numerator by the reciprocal of the denominator.

$\frac{1}{2} (1 \cdot 16)$

Step 4.2

Multiply $16$ by $1$ .

$\frac{1}{2} \cdot 16$

Step 4.3

Cancel the common factor of $2$ .

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Step 4.3.1

Factor $2$ out of $16$ .

$\frac{1}{2} \cdot (2 (8))$

Step 4.3.2

Cancel the common factor.

$\frac{1}{2} \cdot (2 \cdot 8)$

Step 4.3.3

Rewrite the expression.

$8$