Pre-Algebra Examples

\frac{1}{5} + \frac{1}{8} + \frac{1}{8} + \frac{1}{5} + \frac{1}{8}

$\frac{1}{5} + \frac{1}{8} + \frac{1}{8} + \frac{1}{5} + \frac{1}{8}$

Step 1

Combine the numerators over the common denominator.

\frac{1 + 1}{5} + \frac{1 + 1 + 1}{8}

$\frac{1 + 1}{5} + \frac{1 + 1 + 1}{8}$

Step 2

Simplify by adding numbers.

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Step 2.1

Add

1

$1$ and

1

$1$ .

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

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

Step 2.2

Add

1

$1$ and

1

$1$ .

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

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

Step 2.3

Add

2

$2$ and

1

$1$ .

\frac{2}{5} + \frac{3}{8}

$\frac{2}{5} + \frac{3}{8}$

\frac{2}{5} + \frac{3}{8}

$\frac{2}{5} + \frac{3}{8}$

Step 3

To write

\frac{2}{5}

$\frac{2}{5}$ as a fraction with a common denominator, multiply by

\frac{8}{8}

$\frac{8}{8}$ .

\frac{2}{5} \cdot \frac{8}{8} + \frac{3}{8}

$\frac{2}{5} \cdot \frac{8}{8} + \frac{3}{8}$

Step 4

To write

\frac{3}{8}

$\frac{3}{8}$ as a fraction with a common denominator, multiply by

\frac{5}{5}

$\frac{5}{5}$ .

\frac{2}{5} \cdot \frac{8}{8} + \frac{3}{8} \cdot \frac{5}{5}

$\frac{2}{5} \cdot \frac{8}{8} + \frac{3}{8} \cdot \frac{5}{5}$

Step 5

Write each expression with a common denominator of

40

$40$ , by multiplying each by an appropriate factor of

1

$1$ .

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Step 5.1

Multiply

\frac{2}{5}

$\frac{2}{5}$ by

\frac{8}{8}

$\frac{8}{8}$ .

\frac{2 \cdot 8}{5 \cdot 8} + \frac{3}{8} \cdot \frac{5}{5}

$\frac{2 \cdot 8}{5 \cdot 8} + \frac{3}{8} \cdot \frac{5}{5}$

Step 5.2

Multiply

5

$5$ by

8

$8$ .

\frac{2 \cdot 8}{40} + \frac{3}{8} \cdot \frac{5}{5}

$\frac{2 \cdot 8}{40} + \frac{3}{8} \cdot \frac{5}{5}$

Step 5.3

Multiply

\frac{3}{8}

$\frac{3}{8}$ by

\frac{5}{5}

$\frac{5}{5}$ .

\frac{2 \cdot 8}{40} + \frac{3 \cdot 5}{8 \cdot 5}

$\frac{2 \cdot 8}{40} + \frac{3 \cdot 5}{8 \cdot 5}$

Step 5.4

Multiply

8

$8$ by

5

$5$ .

\frac{2 \cdot 8}{40} + \frac{3 \cdot 5}{40}

$\frac{2 \cdot 8}{40} + \frac{3 \cdot 5}{40}$

\frac{2 \cdot 8}{40} + \frac{3 \cdot 5}{40}

$\frac{2 \cdot 8}{40} + \frac{3 \cdot 5}{40}$

Step 6

Combine the numerators over the common denominator.

\frac{2 \cdot 8 + 3 \cdot 5}{40}

$\frac{2 \cdot 8 + 3 \cdot 5}{40}$

Step 7

Simplify the numerator.

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Step 7.1

Multiply

2

$2$ by

8

$8$ .

\frac{16 + 3 \cdot 5}{40}

$\frac{16 + 3 \cdot 5}{40}$

Step 7.2

Multiply

3

$3$ by

5

$5$ .

\frac{16 + 15}{40}

$\frac{16 + 15}{40}$

Step 7.3

Add

16

$16$ and

15

$15$ .

\frac{31}{40}

$\frac{31}{40}$

\frac{31}{40}

$\frac{31}{40}$

Step 8

The result can be shown in multiple forms.

Exact Form:

\frac{31}{40}

$\frac{31}{40}$

Decimal Form:

0.775

$0.775$