Basic Math Examples

$4 \cdot 10 + 8 + 4 \cdot \frac{1}{10} + 2 \cdot \frac{1}{100} + 2 \cdot \frac{1}{1000}$

Step 1

Simplify each term.

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Step 1.1

Multiply $4$ by $10$ .

$40 + 8 + 4 \cdot \frac{1}{10} + 2 \cdot \frac{1}{100} + 2 \cdot \frac{1}{1000}$

Step 1.2

Cancel the common factor of $2$ .

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Step 1.2.1

Factor $2$ out of $4$ .

$40 + 8 + 2 (2) \cdot \frac{1}{10} + 2 \cdot \frac{1}{100} + 2 \cdot \frac{1}{1000}$

Step 1.2.2

Factor $2$ out of $10$ .

$40 + 8 + 2 \cdot 2 \cdot \frac{1}{2 \cdot 5} + 2 \cdot \frac{1}{100} + 2 \cdot \frac{1}{1000}$

Step 1.2.3

Cancel the common factor.

$40 + 8 + 2 \cdot 2 \cdot \frac{1}{2 \cdot 5} + 2 \cdot \frac{1}{100} + 2 \cdot \frac{1}{1000}$

Step 1.2.4

Rewrite the expression.

$40 + 8 + 2 \cdot \frac{1}{5} + 2 \cdot \frac{1}{100} + 2 \cdot \frac{1}{1000}$

Step 1.3

Combine $2$ and $\frac{1}{5}$ .

$40 + 8 + \frac{2}{5} + 2 \cdot \frac{1}{100} + 2 \cdot \frac{1}{1000}$

Step 1.4

Cancel the common factor of $2$ .

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Step 1.4.1

Factor $2$ out of $100$ .

$40 + 8 + \frac{2}{5} + 2 \cdot \frac{1}{2 (50)} + 2 \cdot \frac{1}{1000}$

Step 1.4.2

Cancel the common factor.

$40 + 8 + \frac{2}{5} + 2 \cdot \frac{1}{2 \cdot 50} + 2 \cdot \frac{1}{1000}$

Step 1.4.3

Rewrite the expression.

$40 + 8 + \frac{2}{5} + \frac{1}{50} + 2 \cdot \frac{1}{1000}$

Step 1.5

Cancel the common factor of $2$ .

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Step 1.5.1

Factor $2$ out of $1000$ .

$40 + 8 + \frac{2}{5} + \frac{1}{50} + 2 \cdot \frac{1}{2 (500)}$

Step 1.5.2

Cancel the common factor.

$40 + 8 + \frac{2}{5} + \frac{1}{50} + 2 \cdot \frac{1}{2 \cdot 500}$

Step 1.5.3

Rewrite the expression.

$40 + 8 + \frac{2}{5} + \frac{1}{50} + \frac{1}{500}$

Step 2

Find the common denominator.

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Step 2.1

Write $40$ as a fraction with denominator $1$ .

$\frac{40}{1} + 8 + \frac{2}{5} + \frac{1}{50} + \frac{1}{500}$

Step 2.2

Multiply $\frac{40}{1}$ by $\frac{500}{500}$ .

$\frac{40}{1} \cdot \frac{500}{500} + 8 + \frac{2}{5} + \frac{1}{50} + \frac{1}{500}$

Step 2.3

Multiply $\frac{40}{1}$ by $\frac{500}{500}$ .

$\frac{40 \cdot 500}{500} + 8 + \frac{2}{5} + \frac{1}{50} + \frac{1}{500}$

Step 2.4

Write $8$ as a fraction with denominator $1$ .

$\frac{40 \cdot 500}{500} + \frac{8}{1} + \frac{2}{5} + \frac{1}{50} + \frac{1}{500}$

Step 2.5

Multiply $\frac{8}{1}$ by $\frac{500}{500}$ .

$\frac{40 \cdot 500}{500} + \frac{8}{1} \cdot \frac{500}{500} + \frac{2}{5} + \frac{1}{50} + \frac{1}{500}$

Step 2.6

Multiply $\frac{8}{1}$ by $\frac{500}{500}$ .

$\frac{40 \cdot 500}{500} + \frac{8 \cdot 500}{500} + \frac{2}{5} + \frac{1}{50} + \frac{1}{500}$

Step 2.7

Multiply $\frac{2}{5}$ by $\frac{100}{100}$ .

$\frac{40 \cdot 500}{500} + \frac{8 \cdot 500}{500} + \frac{2}{5} \cdot \frac{100}{100} + \frac{1}{50} + \frac{1}{500}$

Step 2.8

Multiply $\frac{2}{5}$ by $\frac{100}{100}$ .

$\frac{40 \cdot 500}{500} + \frac{8 \cdot 500}{500} + \frac{2 \cdot 100}{5 \cdot 100} + \frac{1}{50} + \frac{1}{500}$

Step 2.9

Multiply $\frac{1}{50}$ by $\frac{10}{10}$ .

$\frac{40 \cdot 500}{500} + \frac{8 \cdot 500}{500} + \frac{2 \cdot 100}{5 \cdot 100} + \frac{1}{50} \cdot \frac{10}{10} + \frac{1}{500}$

Step 2.10

Multiply $\frac{1}{50}$ by $\frac{10}{10}$ .

$\frac{40 \cdot 500}{500} + \frac{8 \cdot 500}{500} + \frac{2 \cdot 100}{5 \cdot 100} + \frac{10}{50 \cdot 10} + \frac{1}{500}$

Step 2.11

Multiply $5$ by $100$ .

$\frac{40 \cdot 500}{500} + \frac{8 \cdot 500}{500} + \frac{2 \cdot 100}{500} + \frac{10}{50 \cdot 10} + \frac{1}{500}$

Step 2.12

Reorder the factors of $50 \cdot 10$ .

$\frac{40 \cdot 500}{500} + \frac{8 \cdot 500}{500} + \frac{2 \cdot 100}{500} + \frac{10}{10 \cdot 50} + \frac{1}{500}$

Step 2.13

Multiply $10$ by $50$ .

$\frac{40 \cdot 500}{500} + \frac{8 \cdot 500}{500} + \frac{2 \cdot 100}{500} + \frac{10}{500} + \frac{1}{500}$

Step 3

Combine the numerators over the common denominator.

$\frac{40 \cdot 500 + 8 \cdot 500 + 2 \cdot 100 + 10 + 1}{500}$

Step 4

Simplify each term.

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Step 4.1

Multiply $40$ by $500$ .

$\frac{20000 + 8 \cdot 500 + 2 \cdot 100 + 10 + 1}{500}$

Step 4.2

Multiply $8$ by $500$ .

$\frac{20000 + 4000 + 2 \cdot 100 + 10 + 1}{500}$

Step 4.3

Multiply $2$ by $100$ .

$\frac{20000 + 4000 + 200 + 10 + 1}{500}$

Step 5

Simplify by adding numbers.

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Step 5.1

Add $20000$ and $4000$ .

$\frac{24000 + 200 + 10 + 1}{500}$

Step 5.2

Add $24000$ and $200$ .

$\frac{24200 + 10 + 1}{500}$

Step 5.3

Add $24200$ and $10$ .

$\frac{24210 + 1}{500}$

Step 5.4

Add $24210$ and $1$ .

$\frac{24211}{500}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{24211}{500}$

Decimal Form:

$48.422$

Mixed Number Form:

$48 \frac{211}{500}$