Basic Math Examples

$\frac{2}{5} + \frac{a}{2} = \frac{4}{5} + 2 a$

Step 1

Move all terms containing $a$ to the left side of the equation.

Tap for more steps...

Step 1.1

Subtract $2 a$ from both sides of the equation.

$\frac{2}{5} + \frac{a}{2} - 2 a = \frac{4}{5}$

Step 1.2

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

$\frac{2}{5} + \frac{a}{2} - 2 a \cdot \frac{2}{2} = \frac{4}{5}$

Step 1.3

Combine $- 2 a$ and $\frac{2}{2}$ .

$\frac{2}{5} + \frac{a}{2} + \frac{- 2 a \cdot 2}{2} = \frac{4}{5}$

Step 1.4

Combine the numerators over the common denominator.

$\frac{2}{5} + \frac{a - 2 a \cdot 2}{2} = \frac{4}{5}$

Step 1.5

Simplify each term.

Tap for more steps...

Step 1.5.1

Simplify the numerator.

Tap for more steps...

Step 1.5.1.1

Factor $a$ out of $a - 2 a \cdot 2$ .

Tap for more steps...

Step 1.5.1.1.1

Raise $a$ to the power of $1$ .

$\frac{2}{5} + \frac{a^{1} - 2 a \cdot 2}{2} = \frac{4}{5}$

Step 1.5.1.1.2

Factor $a$ out of $a^{1}$ .

$\frac{2}{5} + \frac{a \cdot 1 - 2 a \cdot 2}{2} = \frac{4}{5}$

Step 1.5.1.1.3

Factor $a$ out of $- 2 a \cdot 2$ .

$\frac{2}{5} + \frac{a \cdot 1 + a (- 2 \cdot 2)}{2} = \frac{4}{5}$

Step 1.5.1.1.4

Factor $a$ out of $a \cdot 1 + a (- 2 \cdot 2)$ .

$\frac{2}{5} + \frac{a (1 - 2 \cdot 2)}{2} = \frac{4}{5}$

Step 1.5.1.2

Multiply $- 2$ by $2$ .

$\frac{2}{5} + \frac{a (1 - 4)}{2} = \frac{4}{5}$

Step 1.5.1.3

Subtract $4$ from $1$ .

$\frac{2}{5} + \frac{a \cdot - 3}{2} = \frac{4}{5}$

Step 1.5.2

Move $- 3$ to the left of $a$ .

$\frac{2}{5} + \frac{- 3 \cdot a}{2} = \frac{4}{5}$

Step 1.5.3

Move the negative in front of the fraction.

$\frac{2}{5} - \frac{3 a}{2} = \frac{4}{5}$

Step 2

Move all terms not containing $a$ to the right side of the equation.

Tap for more steps...

Step 2.1

Subtract $\frac{2}{5}$ from both sides of the equation.

$- \frac{3 a}{2} = \frac{4}{5} - \frac{2}{5}$

Step 2.2

Combine the numerators over the common denominator.

$- \frac{3 a}{2} = \frac{4 - 2}{5}$

Step 2.3

Subtract $2$ from $4$ .

$- \frac{3 a}{2} = \frac{2}{5}$

Step 3

Multiply both sides of the equation by $- \frac{2}{3}$ .

$- \frac{2}{3} (- \frac{3 a}{2}) = - \frac{2}{3} \cdot \frac{2}{5}$

Step 4

Simplify both sides of the equation.

Tap for more steps...

Step 4.1

Simplify the left side.

Tap for more steps...

Step 4.1.1

Simplify $- \frac{2}{3} (- \frac{3 a}{2})$ .

Tap for more steps...

Step 4.1.1.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 4.1.1.1.1

Move the leading negative in $- \frac{2}{3}$ into the numerator.

$\frac{- 2}{3} (- \frac{3 a}{2}) = - \frac{2}{3} \cdot \frac{2}{5}$

Step 4.1.1.1.2

Move the leading negative in $- \frac{3 a}{2}$ into the numerator.

$\frac{- 2}{3} \cdot \frac{- 3 a}{2} = - \frac{2}{3} \cdot \frac{2}{5}$

Step 4.1.1.1.3

Factor $2$ out of $- 2$ .

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

Step 4.1.1.1.4

Cancel the common factor.

$\frac{2 \cdot - 1}{3} \cdot \frac{- 3 a}{2} = - \frac{2}{3} \cdot \frac{2}{5}$

Step 4.1.1.1.5

Rewrite the expression.

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

Step 4.1.1.2

Cancel the common factor of $3$ .

Tap for more steps...

Step 4.1.1.2.1

Factor $3$ out of $- 3 a$ .

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

Step 4.1.1.2.2

Cancel the common factor.

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

Step 4.1.1.2.3

Rewrite the expression.

$- - a = - \frac{2}{3} \cdot \frac{2}{5}$

Step 4.1.1.3

Multiply.

Tap for more steps...

Step 4.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 a = - \frac{2}{3} \cdot \frac{2}{5}$

Step 4.1.1.3.2

Multiply $a$ by $1$ .

$a = - \frac{2}{3} \cdot \frac{2}{5}$

Step 4.2

Simplify the right side.

Tap for more steps...

Step 4.2.1

Multiply $- \frac{2}{3} \cdot \frac{2}{5}$ .

Tap for more steps...

Step 4.2.1.1

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

$a = - \frac{2 \cdot 2}{5 \cdot 3}$

Step 4.2.1.2

Multiply $2$ by $2$ .

$a = - \frac{4}{5 \cdot 3}$

Step 4.2.1.3

Multiply $5$ by $3$ .

$a = - \frac{4}{15}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$a = - \frac{4}{15}$

Decimal Form:

$a = - 0.2\overline{6}$