Pre-Algebra Examples

$- \frac{8 a - 9 b}{9 a} + \frac{5 a - 8 b}{6 a} + 1$

Step 1

To write $- \frac{8 a - 9 b}{9 a}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{8 a - 9 b}{9 a} \cdot \frac{2}{2} + \frac{5 a - 8 b}{6 a} + 1$

Step 2

To write $\frac{5 a - 8 b}{6 a}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- \frac{8 a - 9 b}{9 a} \cdot \frac{2}{2} + \frac{5 a - 8 b}{6 a} \cdot \frac{3}{3} + 1$

Step 3

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

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Step 3.1

Multiply $\frac{8 a - 9 b}{9 a}$ by $\frac{2}{2}$ .

$- \frac{(8 a - 9 b) \cdot 2}{9 a \cdot 2} + \frac{5 a - 8 b}{6 a} \cdot \frac{3}{3} + 1$

Step 3.2

Multiply $2$ by $9$ .

$- \frac{(8 a - 9 b) \cdot 2}{18 a} + \frac{5 a - 8 b}{6 a} \cdot \frac{3}{3} + 1$

Step 3.3

Multiply $\frac{5 a - 8 b}{6 a}$ by $\frac{3}{3}$ .

$- \frac{(8 a - 9 b) \cdot 2}{18 a} + \frac{(5 a - 8 b) \cdot 3}{6 a \cdot 3} + 1$

Step 3.4

Multiply $3$ by $6$ .

$- \frac{(8 a - 9 b) \cdot 2}{18 a} + \frac{(5 a - 8 b) \cdot 3}{18 a} + 1$

Step 4

Combine the numerators over the common denominator.

$\frac{- (8 a - 9 b) \cdot 2 + (5 a - 8 b) \cdot 3}{18 a} + 1$

Step 5

Simplify the numerator.

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Step 5.1

Apply the distributive property.

$\frac{(- (8 a) - (- 9 b)) \cdot 2 + (5 a - 8 b) \cdot 3}{18 a} + 1$

Step 5.2

Multiply $8$ by $- 1$ .

$\frac{(- 8 a - (- 9 b)) \cdot 2 + (5 a - 8 b) \cdot 3}{18 a} + 1$

Step 5.3

Multiply $- 9$ by $- 1$ .

$\frac{(- 8 a + 9 b) \cdot 2 + (5 a - 8 b) \cdot 3}{18 a} + 1$

Step 5.4

Apply the distributive property.

$\frac{- 8 a \cdot 2 + 9 b \cdot 2 + (5 a - 8 b) \cdot 3}{18 a} + 1$

Step 5.5

Multiply $2$ by $- 8$ .

$\frac{- 16 a + 9 b \cdot 2 + (5 a - 8 b) \cdot 3}{18 a} + 1$

Step 5.6

Multiply $2$ by $9$ .

$\frac{- 16 a + 18 b + (5 a - 8 b) \cdot 3}{18 a} + 1$

Step 5.7

Apply the distributive property.

$\frac{- 16 a + 18 b + 5 a \cdot 3 - 8 b \cdot 3}{18 a} + 1$

Step 5.8

Multiply $3$ by $5$ .

$\frac{- 16 a + 18 b + 15 a - 8 b \cdot 3}{18 a} + 1$

Step 5.9

Multiply $3$ by $- 8$ .

$\frac{- 16 a + 18 b + 15 a - 24 b}{18 a} + 1$

Step 5.10

Add $- 16 a$ and $15 a$ .

$\frac{- a + 18 b - 24 b}{18 a} + 1$

Step 5.11

Subtract $24 b$ from $18 b$ .

$\frac{- a - 6 b}{18 a} + 1$

Step 6

Simplify terms.

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Step 6.1

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

$\frac{- a - 6 b}{18 a} + \frac{18 a}{18 a}$

Step 6.2

Combine the numerators over the common denominator.

$\frac{- a - 6 b + 18 a}{18 a}$

Step 6.3

Add $- a$ and $18 a$ .

$\frac{17 a - 6 b}{18 a}$