Algebra Examples

$\frac{3}{4} a b - \frac{5}{12} a b$

Step 1

Simplify each term.

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Step 1.1

Multiply $\frac{3}{4} (a b)$ .

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Step 1.1.1

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

$\frac{a \cdot 3}{4} b - \frac{5}{12} \cdot (a b)$

Step 1.1.2

Combine $\frac{a \cdot 3}{4}$ and $b$ .

$\frac{a \cdot 3 b}{4} - \frac{5}{12} \cdot (a b)$

Step 1.2

Move $3$ to the left of $a$ .

$\frac{3 \cdot a b}{4} - \frac{5}{12} \cdot (a b)$

Step 1.3

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

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Step 1.3.1

Combine $a$ and $\frac{5}{12}$ .

$\frac{3 a b}{4} - \frac{a \cdot 5}{12} b$

Step 1.3.2

Combine $b$ and $\frac{a \cdot 5}{12}$ .

$\frac{3 a b}{4} - \frac{b (a \cdot 5)}{12}$

Step 1.4

Move $5$ to the left of $b a$ .

$\frac{3 a b}{4} - \frac{5 b a}{12}$

Step 2

Combine $\frac{3 a b}{4}$ and $- \frac{5 b a}{12}$ using a common denominator.

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Step 2.1

Move $b$ .

$\frac{3 a b}{4} - \frac{5 a b}{12}$

Step 2.2

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

$\frac{3 a b}{4} \cdot \frac{3}{3} - \frac{5 a b}{12}$

Step 2.3

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

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Step 2.3.1

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

$\frac{3 a b \cdot 3}{4 \cdot 3} - \frac{5 a b}{12}$

Step 2.3.2

Multiply $4$ by $3$ .

$\frac{3 a b \cdot 3}{12} - \frac{5 a b}{12}$

Step 2.4

Combine the numerators over the common denominator.

$\frac{3 a b \cdot 3 - 5 a b}{12}$

Step 3

Simplify the numerator.

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Step 3.1

Factor $a b$ out of $3 a b \cdot 3 - 5 a b$ .

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Step 3.1.1

Factor $a b$ out of $3 a b \cdot 3$ .

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

Step 3.1.2

Factor $a b$ out of $- 5 a b$ .

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

Step 3.1.3

Factor $a b$ out of $a b (3 \cdot 3) + a b (- 5)$ .

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

Step 3.2

Multiply $3$ by $3$ .

$\frac{a b (9 - 5)}{12}$

Step 3.3

Subtract $5$ from $9$ .

$\frac{a b \cdot 4}{12}$

Step 4

Cancel the common factor of $4$ and $12$ .

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Step 4.1

Factor $4$ out of $a b \cdot 4$ .

$\frac{4 \cdot (a b)}{12}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $4$ out of $12$ .

$\frac{4 \cdot (a b)}{4 \cdot 3}$

Step 4.2.2

Cancel the common factor.

$\frac{4 \cdot (a b)}{4 \cdot 3}$

Step 4.2.3

Rewrite the expression.

$\frac{a b}{3}$