Pre-Algebra Examples

$\frac{3 a}{b c} + \frac{2 b}{a c}$

Step 1

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

$\frac{3 a}{b c} \cdot \frac{a}{a} + \frac{2 b}{a c}$

Step 2

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

$\frac{3 a}{b c} \cdot \frac{a}{a} + \frac{2 b}{a c} \cdot \frac{b}{b}$

Step 3

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

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Step 3.1

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

$\frac{3 a \cdot a}{b c a} + \frac{2 b}{a c} \cdot \frac{b}{b}$

Step 3.2

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

$\frac{3 a \cdot a}{b c a} + \frac{2 b \cdot b}{a c b}$

Step 3.3

Reorder the factors of $b c a$ .

$\frac{3 a \cdot a}{a b c} + \frac{2 b \cdot b}{a c b}$

Step 3.4

Reorder the factors of $a c b$ .

$\frac{3 a \cdot a}{a b c} + \frac{2 b \cdot b}{a b c}$

Step 4

Combine the numerators over the common denominator.

$\frac{3 a \cdot a + 2 b \cdot b}{a b c}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $a$ by $a$ by adding the exponents.

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Step 5.1.1

Move $a$ .

$\frac{3 (a \cdot a) + 2 b \cdot b}{a b c}$

Step 5.1.2

Multiply $a$ by $a$ .

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

Step 5.2

Multiply $b$ by $b$ by adding the exponents.

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Step 5.2.1

Move $b$ .

$\frac{3 a^{2} + 2 (b \cdot b)}{a b c}$

Step 5.2.2

Multiply $b$ by $b$ .

$\frac{3 a^{2} + 2 b^{2}}{a b c}$