Algebra Examples

\frac{5}{10} + \frac{8}{100}

$\frac{5}{10} + \frac{8}{100}$

Step 1

Simplify each term.

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Step 1.1

Cancel the common factor of

5

$5$ and

10

$10$ .

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Step 1.1.1

Factor

5

$5$ out of

5

$5$ .

\frac{5 (1)}{10} + \frac{8}{100}

$\frac{5 (1)}{10} + \frac{8}{100}$

Step 1.1.2

Cancel the common factors.

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Step 1.1.2.1

Factor

5

$5$ out of

10

$10$ .

\frac{5 \cdot 1}{5 \cdot 2} + \frac{8}{100}

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

Step 1.1.2.2

Cancel the common factor.

\frac{5 \cdot 1}{5 \cdot 2} + \frac{8}{100}

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

Step 1.1.2.3

Rewrite the expression.

\frac{1}{2} + \frac{8}{100}

$\frac{1}{2} + \frac{8}{100}$

\frac{1}{2} + \frac{8}{100}

$\frac{1}{2} + \frac{8}{100}$

\frac{1}{2} + \frac{8}{100}

$\frac{1}{2} + \frac{8}{100}$

Step 1.2

Cancel the common factor of

8

$8$ and

100

$100$ .

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Step 1.2.1

Factor

4

$4$ out of

8

$8$ .

\frac{1}{2} + \frac{4 (2)}{100}

$\frac{1}{2} + \frac{4 (2)}{100}$

Step 1.2.2

Cancel the common factors.

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Step 1.2.2.1

Factor

4

$4$ out of

100

$100$ .

\frac{1}{2} + \frac{4 \cdot 2}{4 \cdot 25}

$\frac{1}{2} + \frac{4 \cdot 2}{4 \cdot 25}$

Step 1.2.2.2

Cancel the common factor.

\frac{1}{2} + \frac{4 \cdot 2}{4 \cdot 25}

$\frac{1}{2} + \frac{4 \cdot 2}{4 \cdot 25}$

Step 1.2.2.3

Rewrite the expression.

\frac{1}{2} + \frac{2}{25}

$\frac{1}{2} + \frac{2}{25}$

\frac{1}{2} + \frac{2}{25}

$\frac{1}{2} + \frac{2}{25}$

\frac{1}{2} + \frac{2}{25}

$\frac{1}{2} + \frac{2}{25}$

\frac{1}{2} + \frac{2}{25}

$\frac{1}{2} + \frac{2}{25}$

Step 2

To write

\frac{1}{2}

$\frac{1}{2}$ as a fraction with a common denominator, multiply by

\frac{25}{25}

$\frac{25}{25}$ .

\frac{1}{2} \cdot \frac{25}{25} + \frac{2}{25}

$\frac{1}{2} \cdot \frac{25}{25} + \frac{2}{25}$

Step 3

To write

\frac{2}{25}

$\frac{2}{25}$ as a fraction with a common denominator, multiply by

\frac{2}{2}

$\frac{2}{2}$ .

\frac{1}{2} \cdot \frac{25}{25} + \frac{2}{25} \cdot \frac{2}{2}

$\frac{1}{2} \cdot \frac{25}{25} + \frac{2}{25} \cdot \frac{2}{2}$

Step 4

Write each expression with a common denominator of

50

$50$ , by multiplying each by an appropriate factor of

1

$1$ .

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Step 4.1

Multiply

\frac{1}{2}

$\frac{1}{2}$ by

\frac{25}{25}

$\frac{25}{25}$ .

\frac{25}{2 \cdot 25} + \frac{2}{25} \cdot \frac{2}{2}

$\frac{25}{2 \cdot 25} + \frac{2}{25} \cdot \frac{2}{2}$

Step 4.2

Multiply

2

$2$ by

25

$25$ .

\frac{25}{50} + \frac{2}{25} \cdot \frac{2}{2}

$\frac{25}{50} + \frac{2}{25} \cdot \frac{2}{2}$

Step 4.3

Multiply

\frac{2}{25}

$\frac{2}{25}$ by

\frac{2}{2}

$\frac{2}{2}$ .

\frac{25}{50} + \frac{2 \cdot 2}{25 \cdot 2}

$\frac{25}{50} + \frac{2 \cdot 2}{25 \cdot 2}$

Step 4.4

Multiply

25

$25$ by

2

$2$ .

\frac{25}{50} + \frac{2 \cdot 2}{50}

$\frac{25}{50} + \frac{2 \cdot 2}{50}$

\frac{25}{50} + \frac{2 \cdot 2}{50}

$\frac{25}{50} + \frac{2 \cdot 2}{50}$

Step 5

Combine the numerators over the common denominator.

\frac{25 + 2 \cdot 2}{50}

$\frac{25 + 2 \cdot 2}{50}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply

2

$2$ by

2

$2$ .

\frac{25 + 4}{50}

$\frac{25 + 4}{50}$

Step 6.2

Add

25

$25$ and

4

$4$ .

\frac{29}{50}

$\frac{29}{50}$

\frac{29}{50}

$\frac{29}{50}$

Step 7

The result can be shown in multiple forms.

Exact Form:

\frac{29}{50}

$\frac{29}{50}$

Decimal Form:

0.58

$0.58$