Pre-Algebra Examples

$\frac{3 a^{8} b^{8}}{4 a^{7} c b^{7}} + \frac{24 c a^{7} b^{8}}{12 a^{9}}$

Step 1

Simplify each term.

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Step 1.1

Cancel the common factor of $a^{8}$ and $a^{7}$ .

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Step 1.1.1

Factor $a^{7}$ out of $3 a^{8} b^{8}$ .

$\frac{a^{7} (3 a b^{8})}{4 a^{7} c b^{7}} + \frac{24 c a^{7} b^{8}}{12 a^{9}}$

Step 1.1.2

Cancel the common factors.

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Step 1.1.2.1

Factor $a^{7}$ out of $4 a^{7} c b^{7}$ .

$\frac{a^{7} (3 a b^{8})}{a^{7} (4 c b^{7})} + \frac{24 c a^{7} b^{8}}{12 a^{9}}$

Step 1.1.2.2

Cancel the common factor.

$\frac{a^{7} (3 a b^{8})}{a^{7} (4 c b^{7})} + \frac{24 c a^{7} b^{8}}{12 a^{9}}$

Step 1.1.2.3

Rewrite the expression.

$\frac{3 a b^{8}}{4 c b^{7}} + \frac{24 c a^{7} b^{8}}{12 a^{9}}$

Step 1.2

Cancel the common factor of $b^{8}$ and $b^{7}$ .

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Step 1.2.1

Factor $b^{7}$ out of $3 a b^{8}$ .

$\frac{b^{7} (3 a b)}{4 c b^{7}} + \frac{24 c a^{7} b^{8}}{12 a^{9}}$

Step 1.2.2

Cancel the common factors.

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Step 1.2.2.1

Factor $b^{7}$ out of $4 c b^{7}$ .

$\frac{b^{7} (3 a b)}{b^{7} (4 c)} + \frac{24 c a^{7} b^{8}}{12 a^{9}}$

Step 1.2.2.2

Cancel the common factor.

$\frac{b^{7} (3 a b)}{b^{7} (4 c)} + \frac{24 c a^{7} b^{8}}{12 a^{9}}$

Step 1.2.2.3

Rewrite the expression.

$\frac{3 a b}{4 c} + \frac{24 c a^{7} b^{8}}{12 a^{9}}$

Step 1.3

Cancel the common factor of $24$ and $12$ .

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Step 1.3.1

Factor $12$ out of $24 c a^{7} b^{8}$ .

$\frac{3 a b}{4 c} + \frac{12 (2 c a^{7} b^{8})}{12 a^{9}}$

Step 1.3.2

Cancel the common factors.

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Step 1.3.2.1

Factor $12$ out of $12 a^{9}$ .

$\frac{3 a b}{4 c} + \frac{12 (2 c a^{7} b^{8})}{12 (a^{9})}$

Step 1.3.2.2

Cancel the common factor.

$\frac{3 a b}{4 c} + \frac{12 (2 c a^{7} b^{8})}{12 a^{9}}$

Step 1.3.2.3

Rewrite the expression.

$\frac{3 a b}{4 c} + \frac{2 c a^{7} b^{8}}{a^{9}}$

Step 1.4

Cancel the common factor of $a^{7}$ and $a^{9}$ .

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Step 1.4.1

Factor $a^{7}$ out of $2 c a^{7} b^{8}$ .

$\frac{3 a b}{4 c} + \frac{a^{7} (2 c b^{8})}{a^{9}}$

Step 1.4.2

Cancel the common factors.

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Step 1.4.2.1

Factor $a^{7}$ out of $a^{9}$ .

$\frac{3 a b}{4 c} + \frac{a^{7} (2 c b^{8})}{a^{7} a^{2}}$

Step 1.4.2.2

Cancel the common factor.

$\frac{3 a b}{4 c} + \frac{a^{7} (2 c b^{8})}{a^{7} a^{2}}$

Step 1.4.2.3

Rewrite the expression.

$\frac{3 a b}{4 c} + \frac{2 c b^{8}}{a^{2}}$

Step 2

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

$\frac{3 a b}{4 c} \cdot \frac{a^{2}}{a^{2}} + \frac{2 c b^{8}}{a^{2}}$

Step 3

To write $\frac{2 c b^{8}}{a^{2}}$ as a fraction with a common denominator, multiply by $\frac{4 c}{4 c}$ .

$\frac{3 a b}{4 c} \cdot \frac{a^{2}}{a^{2}} + \frac{2 c b^{8}}{a^{2}} \cdot \frac{4 c}{4 c}$

Step 4

Write each expression with a common denominator of $4 c a^{2}$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

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

$\frac{3 a b a^{2}}{4 c a^{2}} + \frac{2 c b^{8}}{a^{2}} \cdot \frac{4 c}{4 c}$

Step 4.2

Multiply $\frac{2 c b^{8}}{a^{2}}$ by $\frac{4 c}{4 c}$ .

$\frac{3 a b a^{2}}{4 c a^{2}} + \frac{2 c b^{8} (4 c)}{a^{2} (4 c)}$

Step 4.3

Reorder the factors of $4 c a^{2}$ .

$\frac{3 a b a^{2}}{4 a^{2} c} + \frac{2 c b^{8} (4 c)}{a^{2} (4 c)}$

Step 4.4

Reorder the factors of $a^{2} (4 c)$ .

$\frac{3 a b a^{2}}{4 a^{2} c} + \frac{2 c b^{8} (4 c)}{4 a^{2} c}$

Step 5

Combine the numerators over the common denominator.

$\frac{3 a b a^{2} + 2 c b^{8} (4 c)}{4 a^{2} c}$

Step 6

Simplify the numerator.

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Step 6.1

Factor $b$ out of $3 a b a^{2} + 2 c b^{8} (4 c)$ .

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Step 6.1.1

Factor $b$ out of $3 a b a^{2}$ .

$\frac{b (3 a \cdot a^{2}) + 2 c b^{8} (4 c)}{4 a^{2} c}$

Step 6.1.2

Factor $b$ out of $2 c b^{8} (4 c)$ .

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

Step 6.1.3

Factor $b$ out of $b (3 a \cdot a^{2}) + b (2 c b^{7} (4 c))$ .

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

Step 6.2

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

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Step 6.2.1

Move $a^{2}$ .

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

Step 6.2.2

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

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Step 6.2.2.1

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

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

Step 6.2.2.2

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

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

Step 6.2.3

Add $2$ and $1$ .

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

Step 6.3

Multiply $c$ by $c$ by adding the exponents.

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Step 6.3.1

Move $c$ .

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

Step 6.3.2

Multiply $c$ by $c$ .

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

Step 6.4

Multiply $4$ by $2$ .

$\frac{b (3 a^{3} + 8 c^{2} b^{7})}{4 a^{2} c}$