Pre-Algebra Examples

$\frac{1}{5} \cdot (9 y + 2) + \frac{1}{10} \cdot (2 y - 1)$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Apply the distributive property.

$\frac{1}{5} (9 y) + \frac{1}{5} \cdot 2 + \frac{1}{10} \cdot (2 y - 1)$

Step 1.2

Multiply $\frac{1}{5} (9 y)$ .

Tap for more steps...

Step 1.2.1

Combine $9$ and $\frac{1}{5}$ .

$\frac{9}{5} y + \frac{1}{5} \cdot 2 + \frac{1}{10} \cdot (2 y - 1)$

Step 1.2.2

Combine $\frac{9}{5}$ and $y$ .

$\frac{9 y}{5} + \frac{1}{5} \cdot 2 + \frac{1}{10} \cdot (2 y - 1)$

Step 1.3

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

$\frac{9 y}{5} + \frac{2}{5} + \frac{1}{10} \cdot (2 y - 1)$

Step 1.4

Apply the distributive property.

$\frac{9 y}{5} + \frac{2}{5} + \frac{1}{10} (2 y) + \frac{1}{10} \cdot - 1$

Step 1.5

Cancel the common factor of $2$ .

Tap for more steps...

Step 1.5.1

Factor $2$ out of $10$ .

$\frac{9 y}{5} + \frac{2}{5} + \frac{1}{2 (5)} (2 y) + \frac{1}{10} \cdot - 1$

Step 1.5.2

Factor $2$ out of $2 y$ .

$\frac{9 y}{5} + \frac{2}{5} + \frac{1}{2 (5)} (2 (y)) + \frac{1}{10} \cdot - 1$

Step 1.5.3

Cancel the common factor.

$\frac{9 y}{5} + \frac{2}{5} + \frac{1}{2 \cdot 5} (2 y) + \frac{1}{10} \cdot - 1$

Step 1.5.4

Rewrite the expression.

$\frac{9 y}{5} + \frac{2}{5} + \frac{1}{5} y + \frac{1}{10} \cdot - 1$

Step 1.6

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

$\frac{9 y}{5} + \frac{2}{5} + \frac{y}{5} + \frac{1}{10} \cdot - 1$

Step 1.7

Combine $\frac{1}{10}$ and $- 1$ .

$\frac{9 y}{5} + \frac{2}{5} + \frac{y}{5} + \frac{- 1}{10}$

Step 1.8

Move the negative in front of the fraction.

$\frac{9 y}{5} + \frac{2}{5} + \frac{y}{5} - \frac{1}{10}$

Step 2

Simplify terms.

Tap for more steps...

Step 2.1

Combine the numerators over the common denominator.

$\frac{9 y + 2 + y}{5} + \frac{- 1}{10}$

Step 2.2

Add $9 y$ and $y$ .

$\frac{10 y + 2}{5} + \frac{- 1}{10}$

Step 3

Simplify each term.

Tap for more steps...

Step 3.1

Factor $2$ out of $10 y + 2$ .

Tap for more steps...

Step 3.1.1

Factor $2$ out of $10 y$ .

$\frac{2 (5 y) + 2}{5} + \frac{- 1}{10}$

Step 3.1.2

Factor $2$ out of $2$ .

$\frac{2 (5 y) + 2 (1)}{5} + \frac{- 1}{10}$

Step 3.1.3

Factor $2$ out of $2 (5 y) + 2 (1)$ .

$\frac{2 (5 y + 1)}{5} + \frac{- 1}{10}$

Step 3.2

Move the negative in front of the fraction.

$\frac{2 (5 y + 1)}{5} - \frac{1}{10}$

Step 4

To write $\frac{2 (5 y + 1)}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{2 (5 y + 1)}{5} \cdot \frac{2}{2} - \frac{1}{10}$

Step 5

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

Tap for more steps...

Step 5.1

Multiply $\frac{2 (5 y + 1)}{5}$ by $\frac{2}{2}$ .

$\frac{2 (5 y + 1) \cdot 2}{5 \cdot 2} - \frac{1}{10}$

Step 5.2

Multiply $5$ by $2$ .

$\frac{2 (5 y + 1) \cdot 2}{10} - \frac{1}{10}$

Step 6

Combine the numerators over the common denominator.

$\frac{2 (5 y + 1) \cdot 2 - 1}{10}$

Step 7

Simplify the numerator.

Tap for more steps...

Step 7.1

Apply the distributive property.

$\frac{(2 (5 y) + 2 \cdot 1) \cdot 2 - 1}{10}$

Step 7.2

Multiply $5$ by $2$ .

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

Step 7.3

Multiply $2$ by $1$ .

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

Step 7.4

Apply the distributive property.

$\frac{10 y \cdot 2 + 2 \cdot 2 - 1}{10}$

Step 7.5

Multiply $2$ by $10$ .

$\frac{20 y + 2 \cdot 2 - 1}{10}$

Step 7.6

Multiply $2$ by $2$ .

$\frac{20 y + 4 - 1}{10}$

Step 7.7

Subtract $1$ from $4$ .

$\frac{20 y + 3}{10}$