Pre-Algebra Examples

$\frac{- 20 r^{4} + 56 r^{3} - 44 r^{2} + 21 r + 7}{- 4 r}$

Step 1

Move the negative in front of the fraction.

$- \frac{- 20 r^{4} + 56 r^{3} - 44 r^{2} + 21 r + 7}{4 r}$

Step 2

Factor $- 1$ out of $- 20 r^{4}$ .

$- \frac{- (20 r^{4}) + 56 r^{3} - 44 r^{2} + 21 r + 7}{4 r}$

Step 3

Factor $- 1$ out of $56 r^{3}$ .

$- \frac{- (20 r^{4}) - (- 56 r^{3}) - 44 r^{2} + 21 r + 7}{4 r}$

Step 4

Factor $- 1$ out of $- (20 r^{4}) - (- 56 r^{3})$ .

$- \frac{- (20 r^{4} - 56 r^{3}) - 44 r^{2} + 21 r + 7}{4 r}$

Step 5

Factor $- 1$ out of $- 44 r^{2}$ .

$- \frac{- (20 r^{4} - 56 r^{3}) - (44 r^{2}) + 21 r + 7}{4 r}$

Step 6

Factor $- 1$ out of $- (20 r^{4} - 56 r^{3}) - (44 r^{2})$ .

$- \frac{- (20 r^{4} - 56 r^{3} + 44 r^{2}) + 21 r + 7}{4 r}$

Step 7

Factor $- 1$ out of $21 r$ .

$- \frac{- (20 r^{4} - 56 r^{3} + 44 r^{2}) - (- 21 r) + 7}{4 r}$

Step 8

Factor $- 1$ out of $- (20 r^{4} - 56 r^{3} + 44 r^{2}) - (- 21 r)$ .

$- \frac{- (20 r^{4} - 56 r^{3} + 44 r^{2} - 21 r) + 7}{4 r}$

Step 9

Rewrite $7$ as $- 1 (- 7)$ .

$- \frac{- (20 r^{4} - 56 r^{3} + 44 r^{2} - 21 r) - 1 (- 7)}{4 r}$

Step 10

Factor $- 1$ out of $- (20 r^{4} - 56 r^{3} + 44 r^{2} - 21 r) - 1 (- 7)$ .

$- \frac{- (20 r^{4} - 56 r^{3} + 44 r^{2} - 21 r - 7)}{4 r}$

Step 11

Rewrite $- (20 r^{4} - 56 r^{3} + 44 r^{2} - 21 r - 7)$ as $- 1 (20 r^{4} - 56 r^{3} + 44 r^{2} - 21 r - 7)$ .

$- \frac{- 1 (20 r^{4} - 56 r^{3} + 44 r^{2} - 21 r - 7)}{4 r}$

Step 12

Move the negative in front of the fraction.

$- - \frac{20 r^{4} - 56 r^{3} + 44 r^{2} - 21 r - 7}{4 r}$

Step 13

Multiply $- 1$ by $- 1$ .

$1 \frac{20 r^{4} - 56 r^{3} + 44 r^{2} - 21 r - 7}{4 r}$

Step 14

Multiply $\frac{20 r^{4} - 56 r^{3} + 44 r^{2} - 21 r - 7}{4 r}$ by $1$ .

$\frac{20 r^{4} - 56 r^{3} + 44 r^{2} - 21 r - 7}{4 r}$

Step 15

Split the fraction $\frac{20 r^{4} - 56 r^{3} + 44 r^{2} - 21 r - 7}{4 r}$ into two fractions.

$\frac{20 r^{4} - 56 r^{3} + 44 r^{2} - 21 r}{4 r} + \frac{- 7}{4 r}$

Step 16

Split the fraction $\frac{20 r^{4} - 56 r^{3} + 44 r^{2} - 21 r}{4 r}$ into two fractions.

$\frac{20 r^{4} - 56 r^{3} + 44 r^{2}}{4 r} + \frac{- 21 r}{4 r} + \frac{- 7}{4 r}$

Step 17

Split the fraction $\frac{20 r^{4} - 56 r^{3} + 44 r^{2}}{4 r}$ into two fractions.

$\frac{20 r^{4} - 56 r^{3}}{4 r} + \frac{44 r^{2}}{4 r} + \frac{- 21 r}{4 r} + \frac{- 7}{4 r}$

Step 18

Split the fraction $\frac{20 r^{4} - 56 r^{3}}{4 r}$ into two fractions.

$\frac{20 r^{4}}{4 r} + \frac{- 56 r^{3}}{4 r} + \frac{44 r^{2}}{4 r} + \frac{- 21 r}{4 r} + \frac{- 7}{4 r}$

Step 19

Cancel the common factor of $20$ and $4$ .

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Step 19.1

Factor $4$ out of $20 r^{4}$ .

$\frac{4 (5 r^{4})}{4 r} + \frac{- 56 r^{3}}{4 r} + \frac{44 r^{2}}{4 r} + \frac{- 21 r}{4 r} + \frac{- 7}{4 r}$

Step 19.2

Cancel the common factors.

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Step 19.2.1

Factor $4$ out of $4 r$ .

$\frac{4 (5 r^{4})}{4 (r)} + \frac{- 56 r^{3}}{4 r} + \frac{44 r^{2}}{4 r} + \frac{- 21 r}{4 r} + \frac{- 7}{4 r}$

Step 19.2.2

Cancel the common factor.

$\frac{4 (5 r^{4})}{4 r} + \frac{- 56 r^{3}}{4 r} + \frac{44 r^{2}}{4 r} + \frac{- 21 r}{4 r} + \frac{- 7}{4 r}$

Step 19.2.3

Rewrite the expression.

$\frac{5 r^{4}}{r} + \frac{- 56 r^{3}}{4 r} + \frac{44 r^{2}}{4 r} + \frac{- 21 r}{4 r} + \frac{- 7}{4 r}$

Step 20

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

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Step 20.1

Factor $r$ out of $5 r^{4}$ .

$\frac{r (5 r^{3})}{r} + \frac{- 56 r^{3}}{4 r} + \frac{44 r^{2}}{4 r} + \frac{- 21 r}{4 r} + \frac{- 7}{4 r}$

Step 20.2

Cancel the common factors.

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Step 20.2.1

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

$\frac{r (5 r^{3})}{r^{1}} + \frac{- 56 r^{3}}{4 r} + \frac{44 r^{2}}{4 r} + \frac{- 21 r}{4 r} + \frac{- 7}{4 r}$

Step 20.2.2

Factor $r$ out of $r^{1}$ .

$\frac{r (5 r^{3})}{r \cdot 1} + \frac{- 56 r^{3}}{4 r} + \frac{44 r^{2}}{4 r} + \frac{- 21 r}{4 r} + \frac{- 7}{4 r}$

Step 20.2.3

Cancel the common factor.

$\frac{r (5 r^{3})}{r \cdot 1} + \frac{- 56 r^{3}}{4 r} + \frac{44 r^{2}}{4 r} + \frac{- 21 r}{4 r} + \frac{- 7}{4 r}$

Step 20.2.4

Rewrite the expression.

$\frac{5 r^{3}}{1} + \frac{- 56 r^{3}}{4 r} + \frac{44 r^{2}}{4 r} + \frac{- 21 r}{4 r} + \frac{- 7}{4 r}$

Step 20.2.5

Divide $5 r^{3}$ by $1$ .

$5 r^{3} + \frac{- 56 r^{3}}{4 r} + \frac{44 r^{2}}{4 r} + \frac{- 21 r}{4 r} + \frac{- 7}{4 r}$

Step 21

Cancel the common factor of $- 56$ and $4$ .

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Step 21.1

Factor $4$ out of $- 56 r^{3}$ .

$5 r^{3} + \frac{4 (- 14 r^{3})}{4 r} + \frac{44 r^{2}}{4 r} + \frac{- 21 r}{4 r} + \frac{- 7}{4 r}$

Step 21.2

Cancel the common factors.

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Step 21.2.1

Factor $4$ out of $4 r$ .

$5 r^{3} + \frac{4 (- 14 r^{3})}{4 (r)} + \frac{44 r^{2}}{4 r} + \frac{- 21 r}{4 r} + \frac{- 7}{4 r}$

Step 21.2.2

Cancel the common factor.

$5 r^{3} + \frac{4 (- 14 r^{3})}{4 r} + \frac{44 r^{2}}{4 r} + \frac{- 21 r}{4 r} + \frac{- 7}{4 r}$

Step 21.2.3

Rewrite the expression.

$5 r^{3} + \frac{- 14 r^{3}}{r} + \frac{44 r^{2}}{4 r} + \frac{- 21 r}{4 r} + \frac{- 7}{4 r}$

Step 22

Cancel the common factor of $r^{3}$ and $r$ .

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Step 22.1

Factor $r$ out of $- 14 r^{3}$ .

$5 r^{3} + \frac{r (- 14 r^{2})}{r} + \frac{44 r^{2}}{4 r} + \frac{- 21 r}{4 r} + \frac{- 7}{4 r}$

Step 22.2

Cancel the common factors.

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Step 22.2.1

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

$5 r^{3} + \frac{r (- 14 r^{2})}{r^{1}} + \frac{44 r^{2}}{4 r} + \frac{- 21 r}{4 r} + \frac{- 7}{4 r}$

Step 22.2.2

Factor $r$ out of $r^{1}$ .

$5 r^{3} + \frac{r (- 14 r^{2})}{r \cdot 1} + \frac{44 r^{2}}{4 r} + \frac{- 21 r}{4 r} + \frac{- 7}{4 r}$

Step 22.2.3

Cancel the common factor.

$5 r^{3} + \frac{r (- 14 r^{2})}{r \cdot 1} + \frac{44 r^{2}}{4 r} + \frac{- 21 r}{4 r} + \frac{- 7}{4 r}$

Step 22.2.4

Rewrite the expression.

$5 r^{3} + \frac{- 14 r^{2}}{1} + \frac{44 r^{2}}{4 r} + \frac{- 21 r}{4 r} + \frac{- 7}{4 r}$

Step 22.2.5

Divide $- 14 r^{2}$ by $1$ .

$5 r^{3} - 14 r^{2} + \frac{44 r^{2}}{4 r} + \frac{- 21 r}{4 r} + \frac{- 7}{4 r}$

Step 23

Cancel the common factor of $44$ and $4$ .

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Step 23.1

Factor $4$ out of $44 r^{2}$ .

$5 r^{3} - 14 r^{2} + \frac{4 (11 r^{2})}{4 r} + \frac{- 21 r}{4 r} + \frac{- 7}{4 r}$

Step 23.2

Cancel the common factors.

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Step 23.2.1

Factor $4$ out of $4 r$ .

$5 r^{3} - 14 r^{2} + \frac{4 (11 r^{2})}{4 (r)} + \frac{- 21 r}{4 r} + \frac{- 7}{4 r}$

Step 23.2.2

Cancel the common factor.

$5 r^{3} - 14 r^{2} + \frac{4 (11 r^{2})}{4 r} + \frac{- 21 r}{4 r} + \frac{- 7}{4 r}$

Step 23.2.3

Rewrite the expression.

$5 r^{3} - 14 r^{2} + \frac{11 r^{2}}{r} + \frac{- 21 r}{4 r} + \frac{- 7}{4 r}$

Step 24

Cancel the common factor of $r^{2}$ and $r$ .

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Step 24.1

Factor $r$ out of $11 r^{2}$ .

$5 r^{3} - 14 r^{2} + \frac{r (11 r)}{r} + \frac{- 21 r}{4 r} + \frac{- 7}{4 r}$

Step 24.2

Cancel the common factors.

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Step 24.2.1

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

$5 r^{3} - 14 r^{2} + \frac{r (11 r)}{r^{1}} + \frac{- 21 r}{4 r} + \frac{- 7}{4 r}$

Step 24.2.2

Factor $r$ out of $r^{1}$ .

$5 r^{3} - 14 r^{2} + \frac{r (11 r)}{r \cdot 1} + \frac{- 21 r}{4 r} + \frac{- 7}{4 r}$

Step 24.2.3

Cancel the common factor.

$5 r^{3} - 14 r^{2} + \frac{r (11 r)}{r \cdot 1} + \frac{- 21 r}{4 r} + \frac{- 7}{4 r}$

Step 24.2.4

Rewrite the expression.

$5 r^{3} - 14 r^{2} + \frac{11 r}{1} + \frac{- 21 r}{4 r} + \frac{- 7}{4 r}$

Step 24.2.5

Divide $11 r$ by $1$ .

$5 r^{3} - 14 r^{2} + 11 r + \frac{- 21 r}{4 r} + \frac{- 7}{4 r}$

Step 25

Cancel the common factor of $r$ .

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Step 25.1

Cancel the common factor.

$5 r^{3} - 14 r^{2} + 11 r + \frac{- 21 r}{4 r} + \frac{- 7}{4 r}$

Step 25.2

Rewrite the expression.

$5 r^{3} - 14 r^{2} + 11 r + \frac{- 21}{4} + \frac{- 7}{4 r}$

Step 26

Move the negative in front of the fraction.

$5 r^{3} - 14 r^{2} + 11 r - \frac{21}{4} + \frac{- 7}{4 r}$

Step 27

Move the negative in front of the fraction.

$5 r^{3} - 14 r^{2} + 11 r - \frac{21}{4} - \frac{7}{4 r}$