Basic Math Examples

$\frac{5}{12 a^{2} b} - \frac{4}{15 a b^{2}}$

Step 1

To write $\frac{5}{12 a^{2} b}$ as a fraction with a common denominator, multiply by $\frac{5 b}{5 b}$ .

$\frac{5}{12 a^{2} b} \cdot \frac{5 b}{5 b} - \frac{4}{15 a b^{2}}$

Step 2

To write $- \frac{4}{15 a b^{2}}$ as a fraction with a common denominator, multiply by $\frac{4 a}{4 a}$ .

$\frac{5}{12 a^{2} b} \cdot \frac{5 b}{5 b} - \frac{4}{15 a b^{2}} \cdot \frac{4 a}{4 a}$

Step 3

Write each expression with a common denominator of $60 a^{2} b^{2}$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{5}{12 a^{2} b}$ by $\frac{5 b}{5 b}$ .

$\frac{5 (5 b)}{12 a^{2} b (5 b)} - \frac{4}{15 a b^{2}} \cdot \frac{4 a}{4 a}$

Step 3.2

Multiply $5$ by $12$ .

$\frac{5 (5 b)}{60 a^{2} b \cdot b} - \frac{4}{15 a b^{2}} \cdot \frac{4 a}{4 a}$

Step 3.3

Raise $b$ to the power of $1$ .

$\frac{5 (5 b)}{60 a^{2} (b^{1} b)} - \frac{4}{15 a b^{2}} \cdot \frac{4 a}{4 a}$

Step 3.4

Raise $b$ to the power of $1$ .

$\frac{5 (5 b)}{60 a^{2} (b^{1} b^{1})} - \frac{4}{15 a b^{2}} \cdot \frac{4 a}{4 a}$

Step 3.5

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{5 (5 b)}{60 a^{2} b^{1 + 1}} - \frac{4}{15 a b^{2}} \cdot \frac{4 a}{4 a}$

Step 3.6

Add $1$ and $1$ .

$\frac{5 (5 b)}{60 a^{2} b^{2}} - \frac{4}{15 a b^{2}} \cdot \frac{4 a}{4 a}$

Step 3.7

Multiply $\frac{4}{15 a b^{2}}$ by $\frac{4 a}{4 a}$ .

$\frac{5 (5 b)}{60 a^{2} b^{2}} - \frac{4 (4 a)}{15 a b^{2} (4 a)}$

Step 3.8

Multiply $4$ by $15$ .

$\frac{5 (5 b)}{60 a^{2} b^{2}} - \frac{4 (4 a)}{60 a b^{2} a}$

Step 3.9

Raise $a$ to the power of $1$ .

$\frac{5 (5 b)}{60 a^{2} b^{2}} - \frac{4 (4 a)}{60 (a^{1} a) b^{2}}$

Step 3.10

Raise $a$ to the power of $1$ .

$\frac{5 (5 b)}{60 a^{2} b^{2}} - \frac{4 (4 a)}{60 (a^{1} a^{1}) b^{2}}$

Step 3.11

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{5 (5 b)}{60 a^{2} b^{2}} - \frac{4 (4 a)}{60 a^{1 + 1} b^{2}}$

Step 3.12

Add $1$ and $1$ .

$\frac{5 (5 b)}{60 a^{2} b^{2}} - \frac{4 (4 a)}{60 a^{2} b^{2}}$

Step 4

Combine the numerators over the common denominator.

$\frac{5 (5 b) - 4 (4 a)}{60 a^{2} b^{2}}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $5$ by $5$ .

$\frac{25 b - 4 \cdot 4 a}{60 a^{2} b^{2}}$

Step 5.2

Multiply $- 4$ by $4$ .

$\frac{25 b - 16 a}{60 a^{2} b^{2}}$