Pre-Algebra Examples

$\frac{5}{2 a} + \frac{7}{3 b} - \frac{2}{b} - \frac{3}{4 a}$

Step 1

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

$\frac{5}{2 a} \cdot \frac{3 b}{3 b} + \frac{7}{3 b} - \frac{2}{b} - \frac{3}{4 a}$

Step 2

To write $\frac{7}{3 b}$ as a fraction with a common denominator, multiply by $\frac{2 a}{2 a}$ .

$\frac{5}{2 a} \cdot \frac{3 b}{3 b} + \frac{7}{3 b} \cdot \frac{2 a}{2 a} - \frac{2}{b} - \frac{3}{4 a}$

Step 3

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

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Step 3.1

Multiply $\frac{5}{2 a}$ by $\frac{3 b}{3 b}$ .

$\frac{5 (3 b)}{2 a (3 b)} + \frac{7}{3 b} \cdot \frac{2 a}{2 a} - \frac{2}{b} - \frac{3}{4 a}$

Step 3.2

Multiply $3$ by $2$ .

$\frac{5 (3 b)}{6 a b} + \frac{7}{3 b} \cdot \frac{2 a}{2 a} - \frac{2}{b} - \frac{3}{4 a}$

Step 3.3

Multiply $\frac{7}{3 b}$ by $\frac{2 a}{2 a}$ .

$\frac{5 (3 b)}{6 a b} + \frac{7 (2 a)}{3 b (2 a)} - \frac{2}{b} - \frac{3}{4 a}$

Step 3.4

Multiply $2$ by $3$ .

$\frac{5 (3 b)}{6 a b} + \frac{7 (2 a)}{6 b a} - \frac{2}{b} - \frac{3}{4 a}$

Step 3.5

Reorder the factors of $6 b a$ .

$\frac{5 (3 b)}{6 a b} + \frac{7 (2 a)}{6 a b} - \frac{2}{b} - \frac{3}{4 a}$

Step 4

Combine the numerators over the common denominator.

$\frac{5 (3 b) + 7 (2 a)}{6 a b} - \frac{2}{b} - \frac{3}{4 a}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $5$ by $3$ .

$\frac{15 b + 7 \cdot 2 a}{6 a b} - \frac{2}{b} - \frac{3}{4 a}$

Step 5.2

Multiply $7$ by $2$ .

$\frac{15 b + 14 a}{6 a b} - \frac{2}{b} - \frac{3}{4 a}$

Step 6

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

$\frac{15 b + 14 a}{6 a b} - \frac{2}{b} \cdot \frac{6 a}{6 a} - \frac{3}{4 a}$

Step 7

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

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Step 7.1

Multiply $\frac{2}{b}$ by $\frac{6 a}{6 a}$ .

$\frac{15 b + 14 a}{6 a b} - \frac{2 (6 a)}{b (6 a)} - \frac{3}{4 a}$

Step 7.2

Reorder the factors of $b (6 a)$ .

$\frac{15 b + 14 a}{6 a b} - \frac{2 (6 a)}{6 a b} - \frac{3}{4 a}$

Step 8

Combine the numerators over the common denominator.

$\frac{15 b + 14 a - 2 (6 a)}{6 a b} - \frac{3}{4 a}$

Step 9

Simplify the numerator.

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Step 9.1

Multiply $- 2$ by $6$ .

$\frac{15 b + 14 a - 12 a}{6 a b} - \frac{3}{4 a}$

Step 9.2

Subtract $12 a$ from $14 a$ .

$\frac{15 b + 2 a}{6 a b} - \frac{3}{4 a}$

Step 10

To write $\frac{15 b + 2 a}{6 a b}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{15 b + 2 a}{6 a b} \cdot \frac{2}{2} - \frac{3}{4 a}$

Step 11

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

$\frac{15 b + 2 a}{6 a b} \cdot \frac{2}{2} - \frac{3}{4 a} \cdot \frac{3 b}{3 b}$

Step 12

Write each expression with a common denominator of $12 a b$ , by multiplying each by an appropriate factor of $1$ .

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Step 12.1

Multiply $\frac{15 b + 2 a}{6 a b}$ by $\frac{2}{2}$ .

$\frac{(15 b + 2 a) \cdot 2}{6 a b \cdot 2} - \frac{3}{4 a} \cdot \frac{3 b}{3 b}$

Step 12.2

Multiply $2$ by $6$ .

$\frac{(15 b + 2 a) \cdot 2}{12 a b} - \frac{3}{4 a} \cdot \frac{3 b}{3 b}$

Step 12.3

Multiply $\frac{3}{4 a}$ by $\frac{3 b}{3 b}$ .

$\frac{(15 b + 2 a) \cdot 2}{12 a b} - \frac{3 (3 b)}{4 a (3 b)}$

Step 12.4

Multiply $3$ by $4$ .

$\frac{(15 b + 2 a) \cdot 2}{12 a b} - \frac{3 (3 b)}{12 a b}$

Step 13

Combine the numerators over the common denominator.

$\frac{(15 b + 2 a) \cdot 2 - 3 (3 b)}{12 a b}$

Step 14

Simplify the numerator.

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Step 14.1

Apply the distributive property.

$\frac{15 b \cdot 2 + 2 a \cdot 2 - 3 \cdot 3 b}{12 a b}$

Step 14.2

Multiply $2$ by $15$ .

$\frac{30 b + 2 a \cdot 2 - 3 \cdot 3 b}{12 a b}$

Step 14.3

Multiply $2$ by $2$ .

$\frac{30 b + 4 a - 3 \cdot 3 b}{12 a b}$

Step 14.4

Multiply $- 3$ by $3$ .

$\frac{30 b + 4 a - 9 b}{12 a b}$

Step 14.5

Subtract $9 b$ from $30 b$ .

$\frac{4 a + 21 b}{12 a b}$