Basic Math Examples

\frac{2 \cdot 9 - 7 \cdot 2}{3 \cdot 10^{2} + 2 \cdot (- 8^{3})}

$\frac{2 \cdot 9 - 7 \cdot 2}{3 \cdot 10^{2} + 2 \cdot (- 8^{3})}$

Step 1

Simplify the numerator.

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Step 1.1

Multiply

2

$2$ by

9

$9$ .

\frac{18 - 7 \cdot 2}{3 \cdot 10^{2} + 2 \cdot - 1 \cdot 8^{3}}

$\frac{18 - 7 \cdot 2}{3 \cdot 10^{2} + 2 \cdot - 1 \cdot 8^{3}}$

Step 1.2

Multiply

- 7

$- 7$ by

2

$2$ .

\frac{18 - 14}{3 \cdot 10^{2} + 2 \cdot - 1 \cdot 8^{3}}

$\frac{18 - 14}{3 \cdot 10^{2} + 2 \cdot - 1 \cdot 8^{3}}$

Step 1.3

Subtract

14

$14$ from

18

$18$ .

\frac{4}{3 \cdot 10^{2} + 2 \cdot - 1 \cdot 8^{3}}

$\frac{4}{3 \cdot 10^{2} + 2 \cdot - 1 \cdot 8^{3}}$

\frac{4}{3 \cdot 10^{2} + 2 \cdot - 1 \cdot 8^{3}}

$\frac{4}{3 \cdot 10^{2} + 2 \cdot - 1 \cdot 8^{3}}$

Step 2

Simplify the denominator.

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Step 2.1

Multiply

2

$2$ by

- 1

$- 1$ .

\frac{4}{3 \cdot 10^{2} - 2 \cdot 8^{3}}

$\frac{4}{3 \cdot 10^{2} - 2 \cdot 8^{3}}$

Step 2.2

Raise

8

$8$ to the power of

3

$3$ .

\frac{4}{3 \cdot 10^{2} - 2 \cdot 512}

$\frac{4}{3 \cdot 10^{2} - 2 \cdot 512}$

Step 2.3

Multiply

- 2

$- 2$ by

512

$512$ .

\frac{4}{3 \cdot 10^{2} - 1024}

$\frac{4}{3 \cdot 10^{2} - 1024}$

Step 2.4

Convert

- 1024

$- 1024$ to scientific notation.

\frac{4}{3 \cdot 10^{2} - 1.024 \cdot 10^{3}}

$\frac{4}{3 \cdot 10^{2} - 1.024 \cdot 10^{3}}$

Step 2.5

Move the decimal point in

3

$3$ to the left by

$1$ place and increase the power of

$10^{2}$ by

$1$ .

$\frac{4}{0.3 \cdot 10^{3} - 1.024 \cdot 10^{3}}$

Step 2.6

Factor

$10^{3}$ out of

$0.3 \cdot 10^{3} - 1.024 \cdot 10^{3}$ .

$\frac{4}{(0.3 - 1.024) \cdot 10^{3}}$

Step 2.7

Subtract

$1.024$ from

$0.3$ .

$\frac{4}{- 0.724 \cdot 10^{3}}$

Step 2.8

Move the decimal point in

$- 0.724$ to the right by

$1$ place and decrease the power of

$10^{3}$ by

$1$ .

$\frac{4}{- 7.24 \cdot 10^{2}}$

Step 2.9

Raise

$10$ to the power of

$2$ .

$\frac{4}{- 7.24 \cdot 100}$

Step 3

Reduce the expression by cancelling the common factors.

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Step 3.1

Multiply

$- 7.24$ by

$100$ .

$\frac{4}{- 724}$

Step 3.2

Cancel the common factor of

$4$ and

$- 724$ .

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Step 3.2.1

Factor

$4$ out of

$4$ .

$\frac{4 (1)}{- 724}$

Step 3.2.2

Cancel the common factors.

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Step 3.2.2.1

Factor

$4$ out of

$- 724$ .

$\frac{4 \cdot 1}{4 \cdot - 181}$

Step 3.2.2.2

Cancel the common factor.

$\frac{4 \cdot 1}{4 \cdot - 181}$

Step 3.2.2.3

Rewrite the expression.

$\frac{1}{- 181}$

Step 3.3

Simplify the expression.

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Step 3.3.1

Move the negative in front of the fraction.

$- \frac{1}{181}$

Step 3.3.2

Divide

$1$ by

$181$ .

$- 1 \cdot 0.00552486$

Step 3.3.3

Multiply

$- 1$ by

$0.00552486$ .

$- 0.00552486$