Algebra Examples

$1 + 4.25 n + \frac{3}{2} p - 3 + (- 2 p) + \frac{5}{4} n$

Step 1

Remove parentheses.

$1 + 4.25 n + \frac{3}{2} p - 3 - 2 p + \frac{5}{4} n$

Step 2

Simplify each term.

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Step 2.1

Combine $\frac{3}{2}$ and $p$ .

$1 + 4.25 n + \frac{3 p}{2} - 3 - 2 p + \frac{5}{4} n$

Step 2.2

Combine $\frac{5}{4}$ and $n$ .

$1 + 4.25 n + \frac{3 p}{2} - 3 - 2 p + \frac{5 n}{4}$

Step 3

Subtract $3$ from $1$ .

$4.25 n + \frac{3 p}{2} - 2 - 2 p + \frac{5 n}{4}$

Step 4

To write $4.25 n$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{3 p}{2} - 2 - 2 p + 4.25 n \cdot \frac{4}{4} + \frac{5 n}{4}$

Step 5

Simplify terms.

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Step 5.1

Combine $4.25 n$ and $\frac{4}{4}$ .

$\frac{3 p}{2} - 2 - 2 p + \frac{4.25 n \cdot 4}{4} + \frac{5 n}{4}$

Step 5.2

Combine the numerators over the common denominator.

$\frac{3 p}{2} - 2 - 2 p + \frac{4.25 n \cdot 4 + 5 n}{4}$

Step 6

Simplify each term.

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Step 6.1

Simplify the numerator.

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Step 6.1.1

Factor $0.25 n$ out of $4.25 n \cdot 4 + 5 n$ .

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Step 6.1.1.1

Move $n$ .

$\frac{3 p}{2} - 2 - 2 p + \frac{4.25 \cdot 4 n + 5 n}{4}$

Step 6.1.1.2

Factor $0.25 n$ out of $4.25 \cdot 4 n$ .

$\frac{3 p}{2} - 2 - 2 p + \frac{0.25 n (17 \cdot 4) + 5 n}{4}$

Step 6.1.1.3

Factor $0.25 n$ out of $5 n$ .

$\frac{3 p}{2} - 2 - 2 p + \frac{0.25 n (17 \cdot 4) + 0.25 n (20)}{4}$

Step 6.1.1.4

Factor $0.25 n$ out of $0.25 n (17 \cdot 4) + 0.25 n (20)$ .

$\frac{3 p}{2} - 2 - 2 p + \frac{0.25 n (17 \cdot 4 + 20)}{4}$

Step 6.1.2

Combine exponents.

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Step 6.1.2.1

Multiply $17$ by $4$ .

$\frac{3 p}{2} - 2 - 2 p + \frac{0.25 n (68 + 20)}{4}$

Step 6.1.2.2

Multiply $68 + 20$ by $0.25$ .

$\frac{3 p}{2} - 2 - 2 p + \frac{22 n}{4}$

Step 6.2

Cancel the common factor of $22$ and $4$ .

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Step 6.2.1

Factor $2$ out of $22 n$ .

$\frac{3 p}{2} - 2 - 2 p + \frac{2 (11 n)}{4}$

Step 6.2.2

Cancel the common factors.

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Step 6.2.2.1

Factor $2$ out of $4$ .

$\frac{3 p}{2} - 2 - 2 p + \frac{2 (11 n)}{2 (2)}$

Step 6.2.2.2

Cancel the common factor.

$\frac{3 p}{2} - 2 - 2 p + \frac{2 (11 n)}{2 \cdot 2}$

Step 6.2.2.3

Rewrite the expression.

$\frac{3 p}{2} - 2 - 2 p + \frac{11 n}{2}$

Step 7

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

$\frac{3 p}{2} - 2 p \cdot \frac{2}{2} - 2 + \frac{11 n}{2}$

Step 8

Combine $- 2 p$ and $\frac{2}{2}$ .

$\frac{3 p}{2} + \frac{- 2 p \cdot 2}{2} - 2 + \frac{11 n}{2}$

Step 9

Combine the numerators over the common denominator.

$\frac{3 p - 2 p \cdot 2}{2} - 2 + \frac{11 n}{2}$

Step 10

Combine the numerators over the common denominator.

$- 2 + \frac{3 p - 2 p \cdot 2 + 11 n}{2}$

Step 11

Multiply $2$ by $- 2$ .

$- 2 + \frac{3 p - 4 p + 11 n}{2}$

Step 12

Subtract $4 p$ from $3 p$ .

$- 2 + \frac{- p + 11 n}{2}$

Step 13

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

$- 2 \cdot \frac{2}{2} + \frac{- p + 11 n}{2}$

Step 14

Combine $- 2$ and $\frac{2}{2}$ .

$\frac{- 2 \cdot 2}{2} + \frac{- p + 11 n}{2}$

Step 15

Combine the numerators over the common denominator.

$\frac{- 2 \cdot 2 - p + 11 n}{2}$

Step 16

Multiply $- 2$ by $2$ .

$\frac{- 4 - p + 11 n}{2}$

Step 17

Rewrite $- 4$ as $- 1 (4)$ .

$\frac{- 1 (4) - p + 11 n}{2}$

Step 18

Factor $- 1$ out of $- p$ .

$\frac{- 1 (4) - (p) + 11 n}{2}$

Step 19

Factor $- 1$ out of $- 1 (4) - (p)$ .

$\frac{- 1 (4 + p) + 11 n}{2}$

Step 20

Factor $- 1$ out of $11 n$ .

$\frac{- 1 (4 + p) - (- 11 n)}{2}$

Step 21

Factor $- 1$ out of $- 1 (4 + p) - (- 11 n)$ .

$\frac{- 1 (4 + p - 11 n)}{2}$

Step 22

Move the negative in front of the fraction.

$- \frac{4 + p - 11 n}{2}$