Precalculus Examples

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

Step 1

Simplify $\frac{a}{2} + \frac{a}{3}$ .

Tap for more steps...

Step 1.1

To write $\frac{a}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Step 1.2

To write $\frac{a}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 1.3

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 1.3.1

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

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

Step 1.3.2

Multiply $2$ by $3$ .

$\frac{a \cdot 3}{6} + \frac{a}{3} \cdot \frac{2}{2} = 5$

Step 1.3.3

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

$\frac{a \cdot 3}{6} + \frac{a \cdot 2}{3 \cdot 2} = 5$

Step 1.3.4

Multiply $3$ by $2$ .

$\frac{a \cdot 3}{6} + \frac{a \cdot 2}{6} = 5$

Step 1.4

Combine the numerators over the common denominator.

$\frac{a \cdot 3 + a \cdot 2}{6} = 5$

Step 1.5

Simplify the numerator.

Tap for more steps...

Step 1.5.1

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

$\frac{3 \cdot a + a \cdot 2}{6} = 5$

Step 1.5.2

Move $2$ to the left of $a$ .

$\frac{3 a + 2 \cdot a}{6} = 5$

Step 1.5.3

Add $3 a$ and $2 a$ .

$\frac{5 a}{6} = 5$

Step 2

Multiply both sides of the equation by $\frac{6}{5}$ .

$\frac{6}{5} \cdot \frac{5 a}{6} = \frac{6}{5} \cdot 5$

Step 3

Simplify both sides of the equation.

Tap for more steps...

Step 3.1

Simplify the left side.

Tap for more steps...

Step 3.1.1

Simplify $\frac{6}{5} \cdot \frac{5 a}{6}$ .

Tap for more steps...

Step 3.1.1.1

Cancel the common factor of $6$ .

Tap for more steps...

Step 3.1.1.1.1

Cancel the common factor.

$\frac{6}{5} \cdot \frac{5 a}{6} = \frac{6}{5} \cdot 5$

Step 3.1.1.1.2

Rewrite the expression.

$\frac{1}{5} (5 a) = \frac{6}{5} \cdot 5$

Step 3.1.1.2

Cancel the common factor of $5$ .

Tap for more steps...

Step 3.1.1.2.1

Factor $5$ out of $5 a$ .

$\frac{1}{5} (5 (a)) = \frac{6}{5} \cdot 5$

Step 3.1.1.2.2

Cancel the common factor.

$\frac{1}{5} (5 a) = \frac{6}{5} \cdot 5$

Step 3.1.1.2.3

Rewrite the expression.

$a = \frac{6}{5} \cdot 5$

Step 3.2

Simplify the right side.

Tap for more steps...

Step 3.2.1

Cancel the common factor of $5$ .

Tap for more steps...

Step 3.2.1.1

Cancel the common factor.

$a = \frac{6}{5} \cdot 5$

Step 3.2.1.2

Rewrite the expression.

$a = 6$