Algebra Examples

$\frac{1}{2} y^{5} + \frac{1}{3} y^{5}$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Combine $\frac{1}{2}$ and $y^{5}$ .

$\frac{y^{5}}{2} + \frac{1}{3} y^{5}$

Step 1.2

Combine $\frac{1}{3}$ and $y^{5}$ .

$\frac{y^{5}}{2} + \frac{y^{5}}{3}$

Step 2

To write $\frac{y^{5}}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{y^{5}}{2} \cdot \frac{3}{3} + \frac{y^{5}}{3}$

Step 3

To write $\frac{y^{5}}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{y^{5}}{2} \cdot \frac{3}{3} + \frac{y^{5}}{3} \cdot \frac{2}{2}$

Step 4

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

Tap for more steps...

Step 4.1

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

$\frac{y^{5} \cdot 3}{2 \cdot 3} + \frac{y^{5}}{3} \cdot \frac{2}{2}$

Step 4.2

Multiply $2$ by $3$ .

$\frac{y^{5} \cdot 3}{6} + \frac{y^{5}}{3} \cdot \frac{2}{2}$

Step 4.3

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

$\frac{y^{5} \cdot 3}{6} + \frac{y^{5} \cdot 2}{3 \cdot 2}$

Step 4.4

Multiply $3$ by $2$ .

$\frac{y^{5} \cdot 3}{6} + \frac{y^{5} \cdot 2}{6}$

Step 5

Combine the numerators over the common denominator.

$\frac{y^{5} \cdot 3 + y^{5} \cdot 2}{6}$

Step 6

Simplify the numerator.

Tap for more steps...

Step 6.1

Move $3$ to the left of $y^{5}$ .

$\frac{3 \cdot y^{5} + y^{5} \cdot 2}{6}$

Step 6.2

Move $2$ to the left of $y^{5}$ .

$\frac{3 y^{5} + 2 \cdot y^{5}}{6}$

Step 6.3

Add $3 y^{5}$ and $2 y^{5}$ .

$\frac{5 y^{5}}{6}$