Basic Math Examples

$\frac{a}{2} - \frac{3}{4 b} + \frac{5 a}{6} - \frac{11}{12 b}$

Step 1

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

$\frac{a}{2} \cdot \frac{2 b}{2 b} - \frac{3}{4 b} + \frac{5 a}{6} - \frac{11}{12 b}$

Step 2

Write each expression with a common denominator of $4 b$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.1

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

$\frac{a (2 b)}{2 (2 b)} - \frac{3}{4 b} + \frac{5 a}{6} - \frac{11}{12 b}$

Step 2.2

Multiply $2$ by $2$ .

$\frac{a (2 b)}{4 b} - \frac{3}{4 b} + \frac{5 a}{6} - \frac{11}{12 b}$

Step 3

Combine the numerators over the common denominator.

$\frac{a (2 b) - 3}{4 b} + \frac{5 a}{6} - \frac{11}{12 b}$

Step 4

Move $2$ to the left of $a$ .

$\frac{2 a b - 3}{4 b} + \frac{5 a}{6} - \frac{11}{12 b}$

Step 5

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

$\frac{2 a b - 3}{4 b} \cdot \frac{3}{3} + \frac{5 a}{6} - \frac{11}{12 b}$

Step 6

To write $\frac{5 a}{6}$ as a fraction with a common denominator, multiply by $\frac{2 b}{2 b}$ .

$\frac{2 a b - 3}{4 b} \cdot \frac{3}{3} + \frac{5 a}{6} \cdot \frac{2 b}{2 b} - \frac{11}{12 b}$

Step 7

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

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Step 7.1

Multiply $\frac{2 a b - 3}{4 b}$ by $\frac{3}{3}$ .

$\frac{(2 a b - 3) \cdot 3}{4 b \cdot 3} + \frac{5 a}{6} \cdot \frac{2 b}{2 b} - \frac{11}{12 b}$

Step 7.2

Multiply $3$ by $4$ .

$\frac{(2 a b - 3) \cdot 3}{12 b} + \frac{5 a}{6} \cdot \frac{2 b}{2 b} - \frac{11}{12 b}$

Step 7.3

Multiply $\frac{5 a}{6}$ by $\frac{2 b}{2 b}$ .

$\frac{(2 a b - 3) \cdot 3}{12 b} + \frac{5 a (2 b)}{6 (2 b)} - \frac{11}{12 b}$

Step 7.4

Multiply $2$ by $6$ .

$\frac{(2 a b - 3) \cdot 3}{12 b} + \frac{5 a (2 b)}{12 b} - \frac{11}{12 b}$

Step 8

Combine the numerators over the common denominator.

$\frac{(2 a b - 3) \cdot 3 + 5 a (2 b)}{12 b} - \frac{11}{12 b}$

Step 9

Combine the numerators over the common denominator.

$\frac{(2 a b - 3) \cdot 3 + 5 a (2 b) - 11}{12 b}$

Step 10

Simplify the numerator.

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Step 10.1

Simplify each term.

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Step 10.1.1

Apply the distributive property.

$\frac{2 a b \cdot 3 - 3 \cdot 3 + 5 a (2 b) - 11}{12 b}$

Step 10.1.2

Multiply $3$ by $2$ .

$\frac{6 a b - 3 \cdot 3 + 5 a (2 b) - 11}{12 b}$

Step 10.1.3

Multiply $- 3$ by $3$ .

$\frac{6 a b - 9 + 5 a (2 b) - 11}{12 b}$

Step 10.1.4

Rewrite using the commutative property of multiplication.

$\frac{6 a b - 9 + 5 \cdot 2 a b - 11}{12 b}$

Step 10.1.5

Multiply $5$ by $2$ .

$\frac{6 a b - 9 + 10 a b - 11}{12 b}$

Step 10.2

Add $6 a b$ and $10 a b$ .

$\frac{16 a b - 9 - 11}{12 b}$

Step 10.3

Subtract $11$ from $- 9$ .

$\frac{16 a b - 20}{12 b}$

Step 11

Cancel the common factor of $16 a b - 20$ and $12$ .

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Step 11.1

Factor $4$ out of $16 a b$ .

$\frac{4 (4 a b) - 20}{12 b}$

Step 11.2

Factor $4$ out of $- 20$ .

$\frac{4 (4 a b) + 4 (- 5)}{12 b}$

Step 11.3

Factor $4$ out of $4 (4 a b) + 4 (- 5)$ .

$\frac{4 (4 a b - 5)}{12 b}$

Step 11.4

Cancel the common factors.

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Step 11.4.1

Factor $4$ out of $12 b$ .

$\frac{4 (4 a b - 5)}{4 (3 b)}$

Step 11.4.2

Cancel the common factor.

$\frac{4 (4 a b - 5)}{4 (3 b)}$

Step 11.4.3

Rewrite the expression.

$\frac{4 a b - 5}{3 b}$