Basic Math Examples

$\frac{15}{16} \div (\frac{1}{2} - \frac{5}{4})$

Step 1

Rewrite the division as a fraction.

$\frac{\frac{15}{16}}{\frac{1}{2} - \frac{5}{4}}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$\frac{15}{16} \cdot \frac{1}{\frac{1}{2} - \frac{5}{4}}$

Step 3

Simplify the denominator.

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Step 3.1

To write $\frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{15}{16} \cdot \frac{1}{\frac{1}{2} \cdot \frac{2}{2} - \frac{5}{4}}$

Step 3.2

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.2.1

Multiply $\frac{1}{2}$ by $\frac{2}{2}$ .

$\frac{15}{16} \cdot \frac{1}{\frac{2}{2 \cdot 2} - \frac{5}{4}}$

Step 3.2.2

Multiply $2$ by $2$ .

$\frac{15}{16} \cdot \frac{1}{\frac{2}{4} - \frac{5}{4}}$

Step 3.3

Combine the numerators over the common denominator.

$\frac{15}{16} \cdot \frac{1}{\frac{2 - 5}{4}}$

Step 3.4

Subtract $5$ from $2$ .

$\frac{15}{16} \cdot \frac{1}{\frac{- 3}{4}}$

Step 3.5

Move the negative in front of the fraction.

$\frac{15}{16} \cdot \frac{1}{- \frac{3}{4}}$

Step 4

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

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Step 4.1

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

$\frac{15}{16} \cdot \frac{- 1 (- 1)}{- \frac{3}{4}}$

Step 4.2

Move the negative in front of the fraction.

$\frac{15}{16} (- \frac{1}{\frac{3}{4}})$

Step 5

Multiply the numerator by the reciprocal of the denominator.

$\frac{15}{16} (- (1 (\frac{4}{3})))$

Step 6

Multiply $\frac{4}{3}$ by $1$ .

$\frac{15}{16} (- \frac{4}{3})$

Step 7

Cancel the common factor of $3$ .

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Step 7.1

Move the leading negative in $- \frac{4}{3}$ into the numerator.

$\frac{15}{16} \cdot \frac{- 4}{3}$

Step 7.2

Factor $3$ out of $15$ .

$\frac{3 (5)}{16} \cdot \frac{- 4}{3}$

Step 7.3

Cancel the common factor.

$\frac{3 \cdot 5}{16} \cdot \frac{- 4}{3}$

Step 7.4

Rewrite the expression.

$\frac{5}{16} \cdot - 4$

Step 8

Cancel the common factor of $4$ .

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Step 8.1

Factor $4$ out of $16$ .

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

Step 8.2

Factor $4$ out of $- 4$ .

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

Step 8.3

Cancel the common factor.

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

Step 8.4

Rewrite the expression.

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

Step 9

Combine $\frac{5}{4}$ and $- 1$ .

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

Step 10

Simplify the expression.

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Step 10.1

Multiply $5$ by $- 1$ .

$\frac{- 5}{4}$

Step 10.2

Move the negative in front of the fraction.

$- \frac{5}{4}$

Step 11

The result can be shown in multiple forms.

Exact Form:

$- \frac{5}{4}$

Decimal Form:

$- 1.25$

Mixed Number Form:

$- 1 \frac{1}{4}$