Basic Math Examples

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

Step 1

Simplify each term.

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Step 1.1

Subtract $20$ from $1000$ .

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

Step 1.2

Raise $980$ to the power of $2$ .

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

Step 1.3

Cancel the common factor of $200$ .

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Step 1.3.1

Factor $200$ out of $960400$ .

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

Step 1.3.2

Factor $200$ out of $1000$ .

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

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 $5$ .

$50960$