Algebra Examples

$\frac{1}{5} - \frac{2}{3} + 1$

Step 1

Find the common denominator.

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Step 1.1

Multiply $\frac{1}{5}$ by $\frac{3}{3}$ .

$\frac{1}{5} \cdot \frac{3}{3} - \frac{2}{3} + 1$

Step 1.2

Multiply $\frac{1}{5}$ by $\frac{3}{3}$ .

$\frac{3}{5 \cdot 3} - \frac{2}{3} + 1$

Step 1.3

Multiply $\frac{2}{3}$ by $\frac{5}{5}$ .

$\frac{3}{5 \cdot 3} - (\frac{2}{3} \cdot \frac{5}{5}) + 1$

Step 1.4

Multiply $\frac{2}{3}$ by $\frac{5}{5}$ .

$\frac{3}{5 \cdot 3} - \frac{2 \cdot 5}{3 \cdot 5} + 1$

Step 1.5

Write $1$ as a fraction with denominator $1$ .

$\frac{3}{5 \cdot 3} - \frac{2 \cdot 5}{3 \cdot 5} + \frac{1}{1}$

Step 1.6

Multiply $\frac{1}{1}$ by $\frac{15}{15}$ .

$\frac{3}{5 \cdot 3} - \frac{2 \cdot 5}{3 \cdot 5} + \frac{1}{1} \cdot \frac{15}{15}$

Step 1.7

Multiply $\frac{1}{1}$ by $\frac{15}{15}$ .

$\frac{3}{5 \cdot 3} - \frac{2 \cdot 5}{3 \cdot 5} + \frac{15}{15}$

Step 1.8

Reorder the factors of $5 \cdot 3$ .

$\frac{3}{3 \cdot 5} - \frac{2 \cdot 5}{3 \cdot 5} + \frac{15}{15}$

Step 1.9

Multiply $3$ by $5$ .

$\frac{3}{15} - \frac{2 \cdot 5}{3 \cdot 5} + \frac{15}{15}$

Step 1.10

Multiply $3$ by $5$ .

$\frac{3}{15} - \frac{2 \cdot 5}{15} + \frac{15}{15}$

Step 2

Combine the numerators over the common denominator.

$\frac{3 - 2 \cdot 5 + 15}{15}$

Step 3

Simplify the expression.

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Step 3.1

Multiply $- 2$ by $5$ .

$\frac{3 - 10 + 15}{15}$

Step 3.2

Subtract $10$ from $3$ .

$\frac{- 7 + 15}{15}$

Step 3.3

Add $- 7$ and $15$ .

$\frac{8}{15}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{8}{15}$

Decimal Form:

$0.5\overline{3}$