Algebra Examples

10.5

$10.5$

Step 1

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

1

$1$ number to the right of the decimal point, place the decimal number over

10^{1}

$10^{1}$

(10)

$(10)$ . Next, add the whole number to the left of the decimal.

10 \frac{5}{10}

$10 \frac{5}{10}$

Step 2

Reduce the fractional part of the mixed number.

10 \frac{1}{2}

$10 \frac{1}{2}$

Step 3

Convert

10 \frac{1}{2}

$10 \frac{1}{2}$ to an improper fraction.

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Step 3.1

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

10 + \frac{1}{2}

$10 + \frac{1}{2}$

Step 3.2

Add

10

$10$ and

\frac{1}{2}

$\frac{1}{2}$ .

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Step 3.2.1

To write

10

$10$ as a fraction with a common denominator, multiply by

\frac{2}{2}

$\frac{2}{2}$ .

10 \cdot \frac{2}{2} + \frac{1}{2}

$10 \cdot \frac{2}{2} + \frac{1}{2}$

Step 3.2.2

Combine

10

$10$ and

\frac{2}{2}

$\frac{2}{2}$ .

\frac{10 \cdot 2}{2} + \frac{1}{2}

$\frac{10 \cdot 2}{2} + \frac{1}{2}$

Step 3.2.3

Combine the numerators over the common denominator.

\frac{10 \cdot 2 + 1}{2}

$\frac{10 \cdot 2 + 1}{2}$

Step 3.2.4

Simplify the numerator.

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Step 3.2.4.1

Multiply

10

$10$ by

2

$2$ .

\frac{20 + 1}{2}

$\frac{20 + 1}{2}$

Step 3.2.4.2

Add

20

$20$ and

1

$1$ .

\frac{21}{2}

$\frac{21}{2}$

\frac{21}{2}

$\frac{21}{2}$

\frac{21}{2}

$\frac{21}{2}$

\frac{21}{2}

$\frac{21}{2}$