Basic Math Examples

$(- 3 \div 2) \cdot 2^{- 2} + - 15 \div 3^{3}$

Step 1

Simplify each term.

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Step 1.1

Rewrite the division as a fraction.

$\frac{- 3}{2} \cdot 2^{- 2} + - 15 \div 3^{3}$

Step 1.2

Move the negative in front of the fraction.

$- \frac{3}{2} \cdot 2^{- 2} + - 15 \div 3^{3}$

Step 1.3

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$- \frac{3}{2} \cdot \frac{1}{2^{2}} + - 15 \div 3^{3}$

Step 1.4

Raise $2$ to the power of $2$ .

$- \frac{3}{2} \cdot \frac{1}{4} + - 15 \div 3^{3}$

Step 1.5

Multiply $- \frac{3}{2} \cdot \frac{1}{4}$ .

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Step 1.5.1

Multiply $\frac{1}{4}$ by $\frac{3}{2}$ .

$- \frac{3}{4 \cdot 2} + - 15 \div 3^{3}$

Step 1.5.2

Multiply $4$ by $2$ .

$- \frac{3}{8} + - 15 \div 3^{3}$

Step 1.6

Rewrite the division as a fraction.

$- \frac{3}{8} + \frac{- 15}{3^{3}}$

Step 1.7

Raise $3$ to the power of $3$ .

$- \frac{3}{8} + \frac{- 15}{27}$

Step 1.8

Cancel the common factor of $- 15$ and $27$ .

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Step 1.8.1

Factor $3$ out of $- 15$ .

$- \frac{3}{8} + \frac{3 (- 5)}{27}$

Step 1.8.2

Cancel the common factors.

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Step 1.8.2.1

Factor $3$ out of $27$ .

$- \frac{3}{8} + \frac{3 \cdot - 5}{3 \cdot 9}$

Step 1.8.2.2

Cancel the common factor.

$- \frac{3}{8} + \frac{3 \cdot - 5}{3 \cdot 9}$

Step 1.8.2.3

Rewrite the expression.

$- \frac{3}{8} + \frac{- 5}{9}$

Step 1.9

Move the negative in front of the fraction.

$- \frac{3}{8} - \frac{5}{9}$

Step 2

To write $- \frac{3}{8}$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$- \frac{3}{8} \cdot \frac{9}{9} - \frac{5}{9}$

Step 3

To write $- \frac{5}{9}$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$- \frac{3}{8} \cdot \frac{9}{9} - \frac{5}{9} \cdot \frac{8}{8}$

Step 4

Write each expression with a common denominator of $72$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{3}{8}$ by $\frac{9}{9}$ .

$- \frac{3 \cdot 9}{8 \cdot 9} - \frac{5}{9} \cdot \frac{8}{8}$

Step 4.2

Multiply $8$ by $9$ .

$- \frac{3 \cdot 9}{72} - \frac{5}{9} \cdot \frac{8}{8}$

Step 4.3

Multiply $\frac{5}{9}$ by $\frac{8}{8}$ .

$- \frac{3 \cdot 9}{72} - \frac{5 \cdot 8}{9 \cdot 8}$

Step 4.4

Multiply $9$ by $8$ .

$- \frac{3 \cdot 9}{72} - \frac{5 \cdot 8}{72}$

Step 5

Combine the numerators over the common denominator.

$\frac{- 3 \cdot 9 - 5 \cdot 8}{72}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $- 3$ by $9$ .

$\frac{- 27 - 5 \cdot 8}{72}$

Step 6.2

Multiply $- 5$ by $8$ .

$\frac{- 27 - 40}{72}$

Step 6.3

Subtract $40$ from $- 27$ .

$\frac{- 67}{72}$

Step 7

Move the negative in front of the fraction.

$- \frac{67}{72}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$- \frac{67}{72}$

Decimal Form:

$- 0.930\overline{5}$