Basic Math Examples

{(1000 - 20)}^{2} \cdot \frac{1}{1000} + {(5000 - 20)}^{2} \cdot \frac{2}{1000} + {(0 - 20)}^{2} \cdot \frac{997}{1000}

${(1000 - 20)}^{2} \cdot \frac{1}{1000} + {(5000 - 20)}^{2} \cdot \frac{2}{1000} + {(0 - 20)}^{2} \cdot \frac{997}{1000}$

Step 1

Simplify each term.

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Step 1.1

Subtract

20

$20$ from

1000

$1000$ .

980^{2} \cdot \frac{1}{1000} + {(5000 - 20)}^{2} \cdot \frac{2}{1000} + {(0 - 20)}^{2} \cdot \frac{997}{1000}

$980^{2} \cdot \frac{1}{1000} + {(5000 - 20)}^{2} \cdot \frac{2}{1000} + {(0 - 20)}^{2} \cdot \frac{997}{1000}$

Step 1.2

Raise

980

$980$ to the power of

2

$2$ .

960400 \cdot \frac{1}{1000} + {(5000 - 20)}^{2} \cdot \frac{2}{1000} + {(0 - 20)}^{2} \cdot \frac{997}{1000}

$960400 \cdot \frac{1}{1000} + {(5000 - 20)}^{2} \cdot \frac{2}{1000} + {(0 - 20)}^{2} \cdot \frac{997}{1000}$

Step 1.3

Cancel the common factor of

200

$200$ .

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Step 1.3.1

Factor

200

$200$ out of

960400

$960400$ .

200 (4802) \cdot \frac{1}{1000} + {(5000 - 20)}^{2} \cdot \frac{2}{1000} + {(0 - 20)}^{2} \cdot \frac{997}{1000}

$200 (4802) \cdot \frac{1}{1000} + {(5000 - 20)}^{2} \cdot \frac{2}{1000} + {(0 - 20)}^{2} \cdot \frac{997}{1000}$

Step 1.3.2

Factor

200

$200$ out of

1000

$1000$ .

200 \cdot 4802 \cdot \frac{1}{200 \cdot 5} + {(5000 - 20)}^{2} \cdot \frac{2}{1000} + {(0 - 20)}^{2} \cdot \frac{997}{1000}

$200 \cdot 4802 \cdot \frac{1}{200 \cdot 5} + {(5000 - 20)}^{2} \cdot \frac{2}{1000} + {(0 - 20)}^{2} \cdot \frac{997}{1000}$

Step 1.3.3

Cancel the common factor.

$200 \cdot 4802 \cdot \frac{1}{200 \cdot 5} + {(5000 - 20)}^{2} \cdot \frac{2}{1000} + {(0 - 20)}^{2} \cdot \frac{997}{1000}$

Step 1.3.4

Rewrite the expression.

$4802 \cdot \frac{1}{5} + {(5000 - 20)}^{2} \cdot \frac{2}{1000} + {(0 - 20)}^{2} \cdot \frac{997}{1000}$

Step 1.4

Combine

$4802$ and

$\frac{1}{5}$ .

$\frac{4802}{5} + {(5000 - 20)}^{2} \cdot \frac{2}{1000} + {(0 - 20)}^{2} \cdot \frac{997}{1000}$

Step 1.5

Subtract

$20$ from

$5000$ .

$\frac{4802}{5} + 4980^{2} \cdot \frac{2}{1000} + {(0 - 20)}^{2} \cdot \frac{997}{1000}$

Step 1.6

Raise

$4980$ to the power of

$2$ .

$\frac{4802}{5} + 24800400 \cdot \frac{2}{1000} + {(0 - 20)}^{2} \cdot \frac{997}{1000}$

Step 1.7

Cancel the common factor of

$200$ .

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Step 1.7.1

Factor

$200$ out of

$24800400$ .

$\frac{4802}{5} + 200 (124002) \cdot \frac{2}{1000} + {(0 - 20)}^{2} \cdot \frac{997}{1000}$

Step 1.7.2

Factor

$200$ out of

$1000$ .

$\frac{4802}{5} + 200 \cdot 124002 \cdot \frac{2}{200 \cdot 5} + {(0 - 20)}^{2} \cdot \frac{997}{1000}$

Step 1.7.3

Cancel the common factor.

$\frac{4802}{5} + 200 \cdot 124002 \cdot \frac{2}{200 \cdot 5} + {(0 - 20)}^{2} \cdot \frac{997}{1000}$

Step 1.7.4

Rewrite the expression.

$\frac{4802}{5} + 124002 \cdot \frac{2}{5} + {(0 - 20)}^{2} \cdot \frac{997}{1000}$

Step 1.8

Combine

$124002$ and

$\frac{2}{5}$ .

$\frac{4802}{5} + \frac{124002 \cdot 2}{5} + {(0 - 20)}^{2} \cdot \frac{997}{1000}$

Step 1.9

Multiply

$124002$ by

$2$ .

$\frac{4802}{5} + \frac{248004}{5} + {(0 - 20)}^{2} \cdot \frac{997}{1000}$

Step 1.10

Subtract

$20$ from

$0$ .

$\frac{4802}{5} + \frac{248004}{5} + {(- 20)}^{2} \cdot \frac{997}{1000}$

Step 1.11

Raise

$- 20$ to the power of

$2$ .

$\frac{4802}{5} + \frac{248004}{5} + 400 \cdot \frac{997}{1000}$

Step 1.12

Cancel the common factor of

$200$ .

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Step 1.12.1

Factor

$200$ out of

$400$ .

$\frac{4802}{5} + \frac{248004}{5} + 200 (2) \cdot \frac{997}{1000}$

Step 1.12.2

Factor

$200$ out of

$1000$ .

$\frac{4802}{5} + \frac{248004}{5} + 200 \cdot 2 \cdot \frac{997}{200 \cdot 5}$

Step 1.12.3

Cancel the common factor.

$\frac{4802}{5} + \frac{248004}{5} + 200 \cdot 2 \cdot \frac{997}{200 \cdot 5}$

Step 1.12.4

Rewrite the expression.

$\frac{4802}{5} + \frac{248004}{5} + 2 \cdot \frac{997}{5}$

Step 1.13

Combine

$2$ and

$\frac{997}{5}$ .

$\frac{4802}{5} + \frac{248004}{5} + \frac{2 \cdot 997}{5}$

Step 1.14

Multiply

$2$ by

$997$ .

$\frac{4802}{5} + \frac{248004}{5} + \frac{1994}{5}$

Step 2

Combine fractions.

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Step 2.1

Combine the numerators over the common denominator.

$\frac{4802 + 248004 + 1994}{5}$

Step 2.2

Simplify the expression.

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Step 2.2.1

Add

$4802$ and

$248004$ .

$\frac{252806 + 1994}{5}$

Step 2.2.2

Add

$252806$ and

$1994$ .

$\frac{254800}{5}$

Step 2.2.3

Divide

$254800$ by

$5$ .

$50960$