Pre-Algebra Examples

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

Step 1

Combine the numerators over the common denominator.

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

Step 2

Simplify by adding numbers.

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Step 2.1

Add $1$ and $1$ .

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

Step 2.2

Add $1$ and $1$ .

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

Step 2.3

Add $2$ and $1$ .

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

Step 3

To write $\frac{2}{5}$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

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

Step 4

To write $\frac{3}{8}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

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

Step 5

Write each expression with a common denominator of $40$ , by multiplying each by an appropriate factor of $1$ .

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Step 5.1

Multiply $\frac{2}{5}$ by $\frac{8}{8}$ .

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

Step 5.2

Multiply $5$ by $8$ .

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

Step 5.3

Multiply $\frac{3}{8}$ by $\frac{5}{5}$ .

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

Step 5.4

Multiply $8$ by $5$ .

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

Step 6

Combine the numerators over the common denominator.

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

Step 7

Simplify the numerator.

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Step 7.1

Multiply $2$ by $8$ .

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

Step 7.2

Multiply $3$ by $5$ .

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

Step 7.3

Add $16$ and $15$ .

$\frac{31}{40}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{31}{40}$

Decimal Form:

$0.775$