Basic Math Examples

$\frac{21 r^{9}}{7 r^{5}} + \frac{80 r^{8}}{10 r^{4}}$

Step 1

Simplify each term.

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Step 1.1

Cancel the common factor of $21$ and $7$ .

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Step 1.1.1

Factor $7$ out of $21 r^{9}$ .

$\frac{7 (3 r^{9})}{7 r^{5}} + \frac{80 r^{8}}{10 r^{4}}$

Step 1.1.2

Cancel the common factors.

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Step 1.1.2.1

Factor $7$ out of $7 r^{5}$ .

$\frac{7 (3 r^{9})}{7 (r^{5})} + \frac{80 r^{8}}{10 r^{4}}$

Step 1.1.2.2

Cancel the common factor.

$\frac{7 (3 r^{9})}{7 r^{5}} + \frac{80 r^{8}}{10 r^{4}}$

Step 1.1.2.3

Rewrite the expression.

$\frac{3 r^{9}}{r^{5}} + \frac{80 r^{8}}{10 r^{4}}$

Step 1.2

Cancel the common factor of $r^{9}$ and $r^{5}$ .

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Step 1.2.1

Factor $r^{5}$ out of $3 r^{9}$ .

$\frac{r^{5} (3 r^{4})}{r^{5}} + \frac{80 r^{8}}{10 r^{4}}$

Step 1.2.2

Cancel the common factors.

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Step 1.2.2.1

Multiply by $1$ .

$\frac{r^{5} (3 r^{4})}{r^{5} \cdot 1} + \frac{80 r^{8}}{10 r^{4}}$

Step 1.2.2.2

Cancel the common factor.

$\frac{r^{5} (3 r^{4})}{r^{5} \cdot 1} + \frac{80 r^{8}}{10 r^{4}}$

Step 1.2.2.3

Rewrite the expression.

$\frac{3 r^{4}}{1} + \frac{80 r^{8}}{10 r^{4}}$

Step 1.2.2.4

Divide $3 r^{4}$ by $1$ .

$3 r^{4} + \frac{80 r^{8}}{10 r^{4}}$

Step 1.3

Cancel the common factor of $80$ and $10$ .

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Step 1.3.1

Factor $10$ out of $80 r^{8}$ .

$3 r^{4} + \frac{10 (8 r^{8})}{10 r^{4}}$

Step 1.3.2

Cancel the common factors.

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Step 1.3.2.1

Factor $10$ out of $10 r^{4}$ .

$3 r^{4} + \frac{10 (8 r^{8})}{10 (r^{4})}$

Step 1.3.2.2

Cancel the common factor.

$3 r^{4} + \frac{10 (8 r^{8})}{10 r^{4}}$

Step 1.3.2.3

Rewrite the expression.

$3 r^{4} + \frac{8 r^{8}}{r^{4}}$

Step 1.4

Cancel the common factor of $r^{8}$ and $r^{4}$ .

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Step 1.4.1

Factor $r^{4}$ out of $8 r^{8}$ .

$3 r^{4} + \frac{r^{4} (8 r^{4})}{r^{4}}$

Step 1.4.2

Cancel the common factors.

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Step 1.4.2.1

Multiply by $1$ .

$3 r^{4} + \frac{r^{4} (8 r^{4})}{r^{4} \cdot 1}$

Step 1.4.2.2

Cancel the common factor.

$3 r^{4} + \frac{r^{4} (8 r^{4})}{r^{4} \cdot 1}$

Step 1.4.2.3

Rewrite the expression.

$3 r^{4} + \frac{8 r^{4}}{1}$

Step 1.4.2.4

Divide $8 r^{4}$ by $1$ .

$3 r^{4} + 8 r^{4}$

Step 2

Add $3 r^{4}$ and $8 r^{4}$ .

$11 r^{4}$