Basic Math Examples

$1 + \frac{2 b + 6 y}{9 b} - \frac{7 b - 5 y}{6 b}$

Step 1

Simplify terms.

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Step 1.1

Factor $2$ out of $2 b + 6 y$ .

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Step 1.1.1

Factor $2$ out of $2 b$ .

$1 + \frac{2 (b) + 6 y}{9 b} - \frac{7 b - 5 y}{6 b}$

Step 1.1.2

Factor $2$ out of $6 y$ .

$1 + \frac{2 (b) + 2 (3 y)}{9 b} - \frac{7 b - 5 y}{6 b}$

Step 1.1.3

Factor $2$ out of $2 (b) + 2 (3 y)$ .

$1 + \frac{2 (b + 3 y)}{9 b} - \frac{7 b - 5 y}{6 b}$

Step 1.2

Write $1$ as a fraction with a common denominator.

$\frac{9 b}{9 b} + \frac{2 (b + 3 y)}{9 b} - \frac{7 b - 5 y}{6 b}$

Step 1.3

Combine the numerators over the common denominator.

$\frac{9 b + 2 (b + 3 y)}{9 b} - \frac{7 b - 5 y}{6 b}$

Step 2

Simplify the numerator.

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Step 2.1

Apply the distributive property.

$\frac{9 b + 2 b + 2 (3 y)}{9 b} - \frac{7 b - 5 y}{6 b}$

Step 2.2

Multiply $3$ by $2$ .

$\frac{9 b + 2 b + 6 y}{9 b} - \frac{7 b - 5 y}{6 b}$

Step 2.3

Add $9 b$ and $2 b$ .

$\frac{11 b + 6 y}{9 b} - \frac{7 b - 5 y}{6 b}$

Step 3

To write $\frac{11 b + 6 y}{9 b}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{11 b + 6 y}{9 b} \cdot \frac{2}{2} - \frac{7 b - 5 y}{6 b}$

Step 4

To write $- \frac{7 b - 5 y}{6 b}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{11 b + 6 y}{9 b} \cdot \frac{2}{2} - \frac{7 b - 5 y}{6 b} \cdot \frac{3}{3}$

Step 5

Write each expression with a common denominator of $18 b$ , by multiplying each by an appropriate factor of $1$ .

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Step 5.1

Multiply $\frac{11 b + 6 y}{9 b}$ by $\frac{2}{2}$ .

$\frac{(11 b + 6 y) \cdot 2}{9 b \cdot 2} - \frac{7 b - 5 y}{6 b} \cdot \frac{3}{3}$

Step 5.2

Multiply $2$ by $9$ .

$\frac{(11 b + 6 y) \cdot 2}{18 b} - \frac{7 b - 5 y}{6 b} \cdot \frac{3}{3}$

Step 5.3

Multiply $\frac{7 b - 5 y}{6 b}$ by $\frac{3}{3}$ .

$\frac{(11 b + 6 y) \cdot 2}{18 b} - \frac{(7 b - 5 y) \cdot 3}{6 b \cdot 3}$

Step 5.4

Multiply $3$ by $6$ .

$\frac{(11 b + 6 y) \cdot 2}{18 b} - \frac{(7 b - 5 y) \cdot 3}{18 b}$

Step 6

Combine the numerators over the common denominator.

$\frac{(11 b + 6 y) \cdot 2 - (7 b - 5 y) \cdot 3}{18 b}$

Step 7

Simplify the numerator.

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Step 7.1

Apply the distributive property.

$\frac{11 b \cdot 2 + 6 y \cdot 2 - (7 b - 5 y) \cdot 3}{18 b}$

Step 7.2

Multiply $2$ by $11$ .

$\frac{22 b + 6 y \cdot 2 - (7 b - 5 y) \cdot 3}{18 b}$

Step 7.3

Multiply $2$ by $6$ .

$\frac{22 b + 12 y - (7 b - 5 y) \cdot 3}{18 b}$

Step 7.4

Apply the distributive property.

$\frac{22 b + 12 y + (- (7 b) - (- 5 y)) \cdot 3}{18 b}$

Step 7.5

Multiply $7$ by $- 1$ .

$\frac{22 b + 12 y + (- 7 b - (- 5 y)) \cdot 3}{18 b}$

Step 7.6

Multiply $- 5$ by $- 1$ .

$\frac{22 b + 12 y + (- 7 b + 5 y) \cdot 3}{18 b}$

Step 7.7

Apply the distributive property.

$\frac{22 b + 12 y - 7 b \cdot 3 + 5 y \cdot 3}{18 b}$

Step 7.8

Multiply $3$ by $- 7$ .

$\frac{22 b + 12 y - 21 b + 5 y \cdot 3}{18 b}$

Step 7.9

Multiply $3$ by $5$ .

$\frac{22 b + 12 y - 21 b + 15 y}{18 b}$

Step 7.10

Subtract $21 b$ from $22 b$ .

$\frac{b + 12 y + 15 y}{18 b}$

Step 7.11

Add $12 y$ and $15 y$ .

$\frac{b + 27 y}{18 b}$