Pre-Algebra Examples

$\frac{7}{6 a^{2} b} + \frac{3}{4 a b^{3}}$

Step 1

To write $\frac{7}{6 a^{2} b}$ as a fraction with a common denominator, multiply by $\frac{2 b^{2}}{2 b^{2}}$ .

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

Step 2

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

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

Step 3

Write each expression with a common denominator of $12 a^{2} b^{3}$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{7}{6 a^{2} b}$ by $\frac{2 b^{2}}{2 b^{2}}$ .

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

Step 3.2

Multiply $2$ by $6$ .

$\frac{7 (2 b^{2})}{12 a^{2} b \cdot b^{2}} + \frac{3}{4 a b^{3}} \cdot \frac{3 a}{3 a}$

Step 3.3

Multiply $b$ by $b^{2}$ by adding the exponents.

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Step 3.3.1

Move $b^{2}$ .

$\frac{7 (2 b^{2})}{12 a^{2} (b^{2} b)} + \frac{3}{4 a b^{3}} \cdot \frac{3 a}{3 a}$

Step 3.3.2

Multiply $b^{2}$ by $b$ .

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Step 3.3.2.1

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

$\frac{7 (2 b^{2})}{12 a^{2} (b^{2} b^{1})} + \frac{3}{4 a b^{3}} \cdot \frac{3 a}{3 a}$

Step 3.3.2.2

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

$\frac{7 (2 b^{2})}{12 a^{2} b^{2 + 1}} + \frac{3}{4 a b^{3}} \cdot \frac{3 a}{3 a}$

Step 3.3.3

Add $2$ and $1$ .

$\frac{7 (2 b^{2})}{12 a^{2} b^{3}} + \frac{3}{4 a b^{3}} \cdot \frac{3 a}{3 a}$

Step 3.4

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

$\frac{7 (2 b^{2})}{12 a^{2} b^{3}} + \frac{3 (3 a)}{4 a b^{3} (3 a)}$

Step 3.5

Multiply $3$ by $4$ .

$\frac{7 (2 b^{2})}{12 a^{2} b^{3}} + \frac{3 (3 a)}{12 a b^{3} a}$

Step 3.6

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

$\frac{7 (2 b^{2})}{12 a^{2} b^{3}} + \frac{3 (3 a)}{12 (a^{1} a) b^{3}}$

Step 3.7

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

$\frac{7 (2 b^{2})}{12 a^{2} b^{3}} + \frac{3 (3 a)}{12 (a^{1} a^{1}) b^{3}}$

Step 3.8

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

$\frac{7 (2 b^{2})}{12 a^{2} b^{3}} + \frac{3 (3 a)}{12 a^{1 + 1} b^{3}}$

Step 3.9

Add $1$ and $1$ .

$\frac{7 (2 b^{2})}{12 a^{2} b^{3}} + \frac{3 (3 a)}{12 a^{2} b^{3}}$

Step 4

Combine the numerators over the common denominator.

$\frac{7 (2 b^{2}) + 3 (3 a)}{12 a^{2} b^{3}}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $7$ by $2$ .

$\frac{14 b^{2} + 3 \cdot 3 a}{12 a^{2} b^{3}}$

Step 5.2

Multiply $3$ by $3$ .

$\frac{14 b^{2} + 9 a}{12 a^{2} b^{3}}$