Basic Math Examples

$\frac{1}{5} a - \frac{1}{15} = \frac{1}{5}$

Step 1

Combine $\frac{1}{5}$ and $a$ .

$\frac{a}{5} - \frac{1}{15} = \frac{1}{5}$

Step 2

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

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Step 2.1

Add $\frac{1}{15}$ to both sides of the equation.

$\frac{a}{5} = \frac{1}{5} + \frac{1}{15}$

Step 2.2

To write $\frac{1}{5}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{a}{5} = \frac{1}{5} \cdot \frac{3}{3} + \frac{1}{15}$

Step 2.3

Write each expression with a common denominator of $15$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.3.1

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

$\frac{a}{5} = \frac{3}{5 \cdot 3} + \frac{1}{15}$

Step 2.3.2

Multiply $5$ by $3$ .

$\frac{a}{5} = \frac{3}{15} + \frac{1}{15}$

Step 2.4

Combine the numerators over the common denominator.

$\frac{a}{5} = \frac{3 + 1}{15}$

Step 2.5

Add $3$ and $1$ .

$\frac{a}{5} = \frac{4}{15}$

Step 3

Multiply both sides of the equation by $5$ .

$5 \frac{a}{5} = 5 (\frac{4}{15})$

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Cancel the common factor of $5$ .

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Step 4.1.1.1

Cancel the common factor.

$5 \frac{a}{5} = 5 (\frac{4}{15})$

Step 4.1.1.2

Rewrite the expression.

$a = 5 (\frac{4}{15})$

Step 4.2

Simplify the right side.

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Step 4.2.1

Cancel the common factor of $5$ .

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Step 4.2.1.1

Factor $5$ out of $15$ .

$a = 5 \frac{4}{5 (3)}$

Step 4.2.1.2

Cancel the common factor.

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

Step 4.2.1.3

Rewrite the expression.

$a = \frac{4}{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$a = \frac{4}{3}$

Decimal Form:

$a = 1.\overline{3}$

Mixed Number Form:

$a = 1 \frac{1}{3}$