Algebra Examples

$y - \frac{1}{2} = \frac{1}{5}$

Step 1

Add $\frac{1}{2}$ to both sides of the equation.

$y = \frac{1}{5} + \frac{1}{2}$

Step 2

To write $\frac{1}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$y = \frac{1}{5} \cdot \frac{2}{2} + \frac{1}{2}$

Step 3

To write $\frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$y = \frac{1}{5} \cdot \frac{2}{2} + \frac{1}{2} \cdot \frac{5}{5}$

Step 4

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{1}{5}$ by $\frac{2}{2}$ .

$y = \frac{2}{5 \cdot 2} + \frac{1}{2} \cdot \frac{5}{5}$

Step 4.2

Multiply $5$ by $2$ .

$y = \frac{2}{10} + \frac{1}{2} \cdot \frac{5}{5}$

Step 4.3

Multiply $\frac{1}{2}$ by $\frac{5}{5}$ .

$y = \frac{2}{10} + \frac{5}{2 \cdot 5}$

Step 4.4

Multiply $2$ by $5$ .

$y = \frac{2}{10} + \frac{5}{10}$

Step 5

Combine the numerators over the common denominator.

$y = \frac{2 + 5}{10}$

Step 6

Add $2$ and $5$ .

$y = \frac{7}{10}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$y = \frac{7}{10}$

Decimal Form:

$y = 0.7$