Basic Math Examples

$\frac{1}{3} \cdot (2 y - 2) + \frac{1}{6} \cdot (8 y + 7)$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Apply the distributive property.

$\frac{1}{3} (2 y) + \frac{1}{3} \cdot - 2 + \frac{1}{6} \cdot (8 y + 7)$

Step 1.2

Multiply $\frac{1}{3} (2 y)$ .

Tap for more steps...

Step 1.2.1

Combine $2$ and $\frac{1}{3}$ .

$\frac{2}{3} y + \frac{1}{3} \cdot - 2 + \frac{1}{6} \cdot (8 y + 7)$

Step 1.2.2

Combine $\frac{2}{3}$ and $y$ .

$\frac{2 y}{3} + \frac{1}{3} \cdot - 2 + \frac{1}{6} \cdot (8 y + 7)$

Step 1.3

Combine $\frac{1}{3}$ and $- 2$ .

$\frac{2 y}{3} + \frac{- 2}{3} + \frac{1}{6} \cdot (8 y + 7)$

Step 1.4

Combine the numerators over the common denominator.

$\frac{2 y - 2}{3} + \frac{1}{6} \cdot (8 y + 7)$

Step 1.5

Factor $2$ out of $2 y - 2$ .

Tap for more steps...

Step 1.5.1

Factor $2$ out of $2 y$ .

$\frac{2 (y) - 2}{3} + \frac{1}{6} \cdot (8 y + 7)$

Step 1.5.2

Factor $2$ out of $- 2$ .

$\frac{2 (y) + 2 (- 1)}{3} + \frac{1}{6} \cdot (8 y + 7)$

Step 1.5.3

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

$\frac{2 (y - 1)}{3} + \frac{1}{6} \cdot (8 y + 7)$

Step 1.6

Apply the distributive property.

$\frac{2 (y - 1)}{3} + \frac{1}{6} (8 y) + \frac{1}{6} \cdot 7$

Step 1.7

Cancel the common factor of $2$ .

Tap for more steps...

Step 1.7.1

Factor $2$ out of $6$ .

$\frac{2 (y - 1)}{3} + \frac{1}{2 (3)} (8 y) + \frac{1}{6} \cdot 7$

Step 1.7.2

Factor $2$ out of $8 y$ .

$\frac{2 (y - 1)}{3} + \frac{1}{2 (3)} (2 (4 y)) + \frac{1}{6} \cdot 7$

Step 1.7.3

Cancel the common factor.

$\frac{2 (y - 1)}{3} + \frac{1}{2 \cdot 3} (2 (4 y)) + \frac{1}{6} \cdot 7$

Step 1.7.4

Rewrite the expression.

$\frac{2 (y - 1)}{3} + \frac{1}{3} (4 y) + \frac{1}{6} \cdot 7$

Step 1.8

Combine $4$ and $\frac{1}{3}$ .

$\frac{2 (y - 1)}{3} + \frac{4}{3} y + \frac{1}{6} \cdot 7$

Step 1.9

Combine $\frac{4}{3}$ and $y$ .

$\frac{2 (y - 1)}{3} + \frac{4 y}{3} + \frac{1}{6} \cdot 7$

Step 1.10

Combine $\frac{1}{6}$ and $7$ .

$\frac{2 (y - 1)}{3} + \frac{4 y}{3} + \frac{7}{6}$

Step 1.11

To write $\frac{4 y}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{2 (y - 1)}{3} + \frac{4 y}{3} \cdot \frac{2}{2} + \frac{7}{6}$

Step 1.12

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

Tap for more steps...

Step 1.12.1

Multiply $\frac{4 y}{3}$ by $\frac{2}{2}$ .

$\frac{2 (y - 1)}{3} + \frac{4 y \cdot 2}{3 \cdot 2} + \frac{7}{6}$

Step 1.12.2

Multiply $3$ by $2$ .

$\frac{2 (y - 1)}{3} + \frac{4 y \cdot 2}{6} + \frac{7}{6}$

Step 1.13

Combine the numerators over the common denominator.

$\frac{2 (y - 1)}{3} + \frac{4 y \cdot 2 + 7}{6}$

Step 1.14

Multiply $2$ by $4$ .

$\frac{2 (y - 1)}{3} + \frac{8 y + 7}{6}$

Step 2

To write $\frac{2 (y - 1)}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{2 (y - 1)}{3} \cdot \frac{2}{2} + \frac{8 y + 7}{6}$

Step 3

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

Tap for more steps...

Step 3.1

Multiply $\frac{2 (y - 1)}{3}$ by $\frac{2}{2}$ .

$\frac{2 (y - 1) \cdot 2}{3 \cdot 2} + \frac{8 y + 7}{6}$

Step 3.2

Multiply $3$ by $2$ .

$\frac{2 (y - 1) \cdot 2}{6} + \frac{8 y + 7}{6}$

Step 4

Combine the numerators over the common denominator.

$\frac{2 (y - 1) \cdot 2 + 8 y + 7}{6}$

Step 5

Simplify the numerator.

Tap for more steps...

Step 5.1

Apply the distributive property.

$\frac{(2 y + 2 \cdot - 1) \cdot 2 + 8 y + 7}{6}$

Step 5.2

Multiply $2$ by $- 1$ .

$\frac{(2 y - 2) \cdot 2 + 8 y + 7}{6}$

Step 5.3

Apply the distributive property.

$\frac{2 y \cdot 2 - 2 \cdot 2 + 8 y + 7}{6}$

Step 5.4

Multiply $2$ by $2$ .

$\frac{4 y - 2 \cdot 2 + 8 y + 7}{6}$

Step 5.5

Multiply $- 2$ by $2$ .

$\frac{4 y - 4 + 8 y + 7}{6}$

Step 5.6

Add $4 y$ and $8 y$ .

$\frac{12 y - 4 + 7}{6}$

Step 5.7

Add $- 4$ and $7$ .

$\frac{12 y + 3}{6}$

Step 5.8

Factor $3$ out of $12 y + 3$ .

Tap for more steps...

Step 5.8.1

Factor $3$ out of $12 y$ .

$\frac{3 (4 y) + 3}{6}$

Step 5.8.2

Factor $3$ out of $3$ .

$\frac{3 (4 y) + 3 (1)}{6}$

Step 5.8.3

Factor $3$ out of $3 (4 y) + 3 (1)$ .

$\frac{3 (4 y + 1)}{6}$

Step 6

Cancel the common factors.

Tap for more steps...

Step 6.1

Factor $3$ out of $6$ .

$\frac{3 (4 y + 1)}{3 \cdot 2}$

Step 6.2

Cancel the common factor.

$\frac{3 (4 y + 1)}{3 \cdot 2}$

Step 6.3

Rewrite the expression.

$\frac{4 y + 1}{2}$