Basic Math Examples

7.826

$7.826$

Step 1

Convert the decimal number to a fraction by placing the decimal number over a power of ten. Since there are

3

$3$ numbers to the right of the decimal point, place the decimal number over

10^{3}

$10^{3}$

(1000)

$(1000)$ . Next, add the whole number to the left of the decimal.

7 \frac{826}{1000}

$7 \frac{826}{1000}$

Step 2

Reduce the fractional part of the mixed number.

7 \frac{413}{500}

$7 \frac{413}{500}$

Step 3

Convert

7 \frac{413}{500}

$7 \frac{413}{500}$ to an improper fraction.

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Step 3.1

A mixed number is an addition of its whole and fractional parts.

7 + \frac{413}{500}

$7 + \frac{413}{500}$

Step 3.2

Add

7

$7$ and

\frac{413}{500}

$\frac{413}{500}$ .

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Step 3.2.1

To write

7

$7$ as a fraction with a common denominator, multiply by

\frac{500}{500}

$\frac{500}{500}$ .

7 \cdot \frac{500}{500} + \frac{413}{500}

$7 \cdot \frac{500}{500} + \frac{413}{500}$

Step 3.2.2

Combine

7

$7$ and

\frac{500}{500}

$\frac{500}{500}$ .

\frac{7 \cdot 500}{500} + \frac{413}{500}

$\frac{7 \cdot 500}{500} + \frac{413}{500}$

Step 3.2.3

Combine the numerators over the common denominator.

\frac{7 \cdot 500 + 413}{500}

$\frac{7 \cdot 500 + 413}{500}$

Step 3.2.4

Simplify the numerator.

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Step 3.2.4.1

Multiply

7

$7$ by

500

$500$ .

\frac{3500 + 413}{500}

$\frac{3500 + 413}{500}$

Step 3.2.4.2

Add

3500

$3500$ and

413

$413$ .

\frac{3913}{500}

$\frac{3913}{500}$

\frac{3913}{500}

$\frac{3913}{500}$

\frac{3913}{500}

$\frac{3913}{500}$

\frac{3913}{500}

$\frac{3913}{500}$