Basic Math Examples

$(\frac{15}{16} - \frac{1}{8}) \div (- 9 \frac{3}{4})$

Step 1

Convert $9 \frac{3}{4}$ to an improper fraction.

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Step 1.1

A mixed number is an addition of its whole and fractional parts.

$(\frac{15}{16} - \frac{1}{8}) \div (- (9 + \frac{3}{4}))$

Step 1.2

Add $9$ and $\frac{3}{4}$ .

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Step 1.2.1

To write $9$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$(\frac{15}{16} - \frac{1}{8}) \div (- (9 \cdot \frac{4}{4} + \frac{3}{4}))$

Step 1.2.2

Combine $9$ and $\frac{4}{4}$ .

$(\frac{15}{16} - \frac{1}{8}) \div (- (\frac{9 \cdot 4}{4} + \frac{3}{4}))$

Step 1.2.3

Combine the numerators over the common denominator.

$(\frac{15}{16} - \frac{1}{8}) \div (- \frac{9 \cdot 4 + 3}{4})$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $9$ by $4$ .

$(\frac{15}{16} - \frac{1}{8}) \div (- \frac{36 + 3}{4})$

Step 1.2.4.2

Add $36$ and $3$ .

$(\frac{15}{16} - \frac{1}{8}) \div (- \frac{39}{4})$

Step 2

To divide by a fraction, multiply by its reciprocal.

$(\frac{15}{16} - \frac{1}{8}) (- \frac{4}{39})$

Step 3

To write $- \frac{1}{8}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$(\frac{15}{16} - \frac{1}{8} \cdot \frac{2}{2}) (- \frac{4}{39})$

Step 4

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

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Step 4.1

Multiply $\frac{1}{8}$ by $\frac{2}{2}$ .

$(\frac{15}{16} - \frac{2}{8 \cdot 2}) (- \frac{4}{39})$

Step 4.2

Multiply $8$ by $2$ .

$(\frac{15}{16} - \frac{2}{16}) (- \frac{4}{39})$

Step 5

Simplify the expression.

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Step 5.1

Combine the numerators over the common denominator.

$\frac{15 - 2}{16} (- \frac{4}{39})$

Step 5.2

Subtract $2$ from $15$ .

$\frac{13}{16} (- \frac{4}{39})$

Step 6

Cancel the common factor of $13$ .

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Step 6.1

Move the leading negative in $- \frac{4}{39}$ into the numerator.

$\frac{13}{16} \cdot \frac{- 4}{39}$

Step 6.2

Factor $13$ out of $39$ .

$\frac{13}{16} \cdot \frac{- 4}{13 (3)}$

Step 6.3

Cancel the common factor.

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

Step 6.4

Rewrite the expression.

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

Step 7

Cancel the common factor of $4$ .

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Step 7.1

Factor $4$ out of $16$ .

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

Step 7.2

Factor $4$ out of $- 4$ .

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

Step 7.3

Cancel the common factor.

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

Step 7.4

Rewrite the expression.

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

Step 8

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

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

Step 9

Simplify the expression.

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Step 9.1

Multiply $4$ by $3$ .

$\frac{- 1}{12}$

Step 9.2

Move the negative in front of the fraction.

$- \frac{1}{12}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$- \frac{1}{12}$

Decimal Form:

$- 0.08\overline{3}$