Algebra Examples

$a - \frac{2}{5} = \frac{1}{10}$

Step 1

Add $\frac{2}{5}$ to both sides of the equation.

$a = \frac{1}{10} + \frac{2}{5}$

Step 2

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

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

Step 3

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

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Step 3.1

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

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

Step 3.2

Multiply $5$ by $2$ .

$a = \frac{1}{10} + \frac{2 \cdot 2}{10}$

Step 4

Combine the numerators over the common denominator.

$a = \frac{1 + 2 \cdot 2}{10}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $2$ by $2$ .

$a = \frac{1 + 4}{10}$

Step 5.2

Add $1$ and $4$ .

$a = \frac{5}{10}$

Step 6

Cancel the common factor of $5$ and $10$ .

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Step 6.1

Factor $5$ out of $5$ .

$a = \frac{5 (1)}{10}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $5$ out of $10$ .

$a = \frac{5 \cdot 1}{5 \cdot 2}$

Step 6.2.2

Cancel the common factor.

$a = \frac{5 \cdot 1}{5 \cdot 2}$

Step 6.2.3

Rewrite the expression.

$a = \frac{1}{2}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$a = \frac{1}{2}$

Decimal Form:

$a = 0.5$