Algebra Examples

$\frac{1}{4} + \frac{9}{10} y - \frac{3}{5} y + \frac{7}{8}$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Combine $\frac{9}{10}$ and $y$ .

$\frac{1}{4} + \frac{9 y}{10} - \frac{3}{5} y + \frac{7}{8}$

Step 1.2

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

$\frac{1}{4} + \frac{9 y}{10} - \frac{y \cdot 3}{5} + \frac{7}{8}$

Step 1.3

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

$\frac{1}{4} + \frac{9 y}{10} - \frac{3 y}{5} + \frac{7}{8}$

Step 2

To write $\frac{1}{4}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{9 y}{10} - \frac{3 y}{5} + \frac{1}{4} \cdot \frac{2}{2} + \frac{7}{8}$

Step 3

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 3.1

Multiply $\frac{1}{4}$ by $\frac{2}{2}$ .

$\frac{9 y}{10} - \frac{3 y}{5} + \frac{2}{4 \cdot 2} + \frac{7}{8}$

Step 3.2

Multiply $4$ by $2$ .

$\frac{9 y}{10} - \frac{3 y}{5} + \frac{2}{8} + \frac{7}{8}$

Step 4

Combine the numerators over the common denominator.

$\frac{9 y}{10} - \frac{3 y}{5} + \frac{2 + 7}{8}$

Step 5

Add $2$ and $7$ .

$\frac{9 y}{10} - \frac{3 y}{5} + \frac{9}{8}$

Step 6

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

$\frac{9 y}{10} - \frac{3 y}{5} \cdot \frac{2}{2} + \frac{9}{8}$

Step 7

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 7.1

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

$\frac{9 y}{10} - \frac{3 y \cdot 2}{5 \cdot 2} + \frac{9}{8}$

Step 7.2

Multiply $5$ by $2$ .

$\frac{9 y}{10} - \frac{3 y \cdot 2}{10} + \frac{9}{8}$

Step 8

Combine the numerators over the common denominator.

$\frac{9 y - 3 y \cdot 2}{10} + \frac{9}{8}$

Step 9

Simplify the numerator.

Tap for more steps...

Step 9.1

Factor $3 y$ out of $9 y - 3 y \cdot 2$ .

Tap for more steps...

Step 9.1.1

Factor $3 y$ out of $9 y$ .

$\frac{3 y (3) - 3 y \cdot 2}{10} + \frac{9}{8}$

Step 9.1.2

Factor $3 y$ out of $- 3 y \cdot 2$ .

$\frac{3 y (3) + 3 y (- 1 \cdot 2)}{10} + \frac{9}{8}$

Step 9.1.3

Factor $3 y$ out of $3 y (3) + 3 y (- 1 \cdot 2)$ .

$\frac{3 y (3 - 1 \cdot 2)}{10} + \frac{9}{8}$

Step 9.2

Multiply $- 1$ by $2$ .

$\frac{3 y (3 - 2)}{10} + \frac{9}{8}$

Step 9.3

Subtract $2$ from $3$ .

$\frac{3 y \cdot 1}{10} + \frac{9}{8}$

Step 9.4

Multiply $3$ by $1$ .

$\frac{3 y}{10} + \frac{9}{8}$