Basic Math Examples

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

Step 1

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

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Step 1.1

Subtract $5$ from both sides of the equation.

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

Step 1.2

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

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

Step 1.3

Combine $- 5$ and $\frac{2}{2}$ .

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

Step 1.4

Combine the numerators over the common denominator.

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

Step 1.5

Simplify the numerator.

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Step 1.5.1

Multiply $- 5$ by $2$ .

$\frac{a}{4} = \frac{5 - 10}{2}$

Step 1.5.2

Subtract $10$ from $5$ .

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

Step 1.6

Move the negative in front of the fraction.

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

Step 2

Multiply both sides of the equation by $4$ .

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

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Cancel the common factor of $4$ .

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Step 3.1.1.1

Cancel the common factor.

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

Step 3.1.1.2

Rewrite the expression.

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

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $4 (- \frac{5}{2})$ .

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Step 3.2.1.1

Cancel the common factor of $2$ .

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Step 3.2.1.1.1

Move the leading negative in $- \frac{5}{2}$ into the numerator.

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

Step 3.2.1.1.2

Factor $2$ out of $4$ .

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

Step 3.2.1.1.3

Cancel the common factor.

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

Step 3.2.1.1.4

Rewrite the expression.

$a = 2 \cdot - 5$

Step 3.2.1.2

Multiply $2$ by $- 5$ .

$a = - 10$