Algebra Examples

$- \frac{3}{4} (5 p - 12) + 2 (8 - \frac{1}{4} p)$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Apply the distributive property.

$- \frac{3}{4} (5 p) - \frac{3}{4} \cdot - 12 + 2 (8 - \frac{1}{4} p)$

Step 1.2

Multiply $- \frac{3}{4} (5 p)$ .

Tap for more steps...

Step 1.2.1

Multiply $5$ by $- 1$ .

$- 5 (\frac{3}{4}) p - \frac{3}{4} \cdot - 12 + 2 (8 - \frac{1}{4} p)$

Step 1.2.2

Combine $- 5$ and $\frac{3}{4}$ .

$\frac{- 5 \cdot 3}{4} p - \frac{3}{4} \cdot - 12 + 2 (8 - \frac{1}{4} p)$

Step 1.2.3

Multiply $- 5$ by $3$ .

$\frac{- 15}{4} p - \frac{3}{4} \cdot - 12 + 2 (8 - \frac{1}{4} p)$

Step 1.2.4

Combine $\frac{- 15}{4}$ and $p$ .

$\frac{- 15 p}{4} - \frac{3}{4} \cdot - 12 + 2 (8 - \frac{1}{4} p)$

Step 1.3

Cancel the common factor of $4$ .

Tap for more steps...

Step 1.3.1

Move the leading negative in $- \frac{3}{4}$ into the numerator.

$\frac{- 15 p}{4} + \frac{- 3}{4} \cdot - 12 + 2 (8 - \frac{1}{4} p)$

Step 1.3.2

Factor $4$ out of $- 12$ .

$\frac{- 15 p}{4} + \frac{- 3}{4} \cdot (4 (- 3)) + 2 (8 - \frac{1}{4} p)$

Step 1.3.3

Cancel the common factor.

$\frac{- 15 p}{4} + \frac{- 3}{4} \cdot (4 \cdot - 3) + 2 (8 - \frac{1}{4} p)$

Step 1.3.4

Rewrite the expression.

$\frac{- 15 p}{4} - 3 \cdot - 3 + 2 (8 - \frac{1}{4} p)$

Step 1.4

Multiply $- 3$ by $- 3$ .

$\frac{- 15 p}{4} + 9 + 2 (8 - \frac{1}{4} p)$

Step 1.5

Move the negative in front of the fraction.

$- \frac{15 p}{4} + 9 + 2 (8 - \frac{1}{4} p)$

Step 1.6

Combine $p$ and $\frac{1}{4}$ .

$- \frac{15 p}{4} + 9 + 2 (8 - \frac{p}{4})$

Step 1.7

Apply the distributive property.

$- \frac{15 p}{4} + 9 + 2 \cdot 8 + 2 (- \frac{p}{4})$

Step 1.8

Multiply $2$ by $8$ .

$- \frac{15 p}{4} + 9 + 16 + 2 (- \frac{p}{4})$

Step 1.9

Cancel the common factor of $2$ .

Tap for more steps...

Step 1.9.1

Move the leading negative in $- \frac{p}{4}$ into the numerator.

$- \frac{15 p}{4} + 9 + 16 + 2 \frac{- p}{4}$

Step 1.9.2

Factor $2$ out of $4$ .

$- \frac{15 p}{4} + 9 + 16 + 2 \frac{- p}{2 (2)}$

Step 1.9.3

Cancel the common factor.

$- \frac{15 p}{4} + 9 + 16 + 2 \frac{- p}{2 \cdot 2}$

Step 1.9.4

Rewrite the expression.

$- \frac{15 p}{4} + 9 + 16 + \frac{- p}{2}$

Step 1.10

Move the negative in front of the fraction.

$- \frac{15 p}{4} + 9 + 16 - \frac{p}{2}$

Step 2

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

$- \frac{15 p}{4} - \frac{p}{2} \cdot \frac{2}{2} + 9 + 16$

Step 3

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 3.1

Multiply $\frac{p}{2}$ by $\frac{2}{2}$ .

$- \frac{15 p}{4} - \frac{p \cdot 2}{2 \cdot 2} + 9 + 16$

Step 3.2

Multiply $2$ by $2$ .

$- \frac{15 p}{4} - \frac{p \cdot 2}{4} + 9 + 16$

Step 4

Combine the numerators over the common denominator.

$\frac{- 15 p - p \cdot 2}{4} + 9 + 16$

Step 5

Find the common denominator.

Tap for more steps...

Step 5.1

Write $9$ as a fraction with denominator $1$ .

$\frac{- 15 p - p \cdot 2}{4} + \frac{9}{1} + 16$

Step 5.2

Multiply $\frac{9}{1}$ by $\frac{4}{4}$ .

$\frac{- 15 p - p \cdot 2}{4} + \frac{9}{1} \cdot \frac{4}{4} + 16$

Step 5.3

Multiply $\frac{9}{1}$ by $\frac{4}{4}$ .

$\frac{- 15 p - p \cdot 2}{4} + \frac{9 \cdot 4}{4} + 16$

Step 5.4

Write $16$ as a fraction with denominator $1$ .

$\frac{- 15 p - p \cdot 2}{4} + \frac{9 \cdot 4}{4} + \frac{16}{1}$

Step 5.5

Multiply $\frac{16}{1}$ by $\frac{4}{4}$ .

$\frac{- 15 p - p \cdot 2}{4} + \frac{9 \cdot 4}{4} + \frac{16}{1} \cdot \frac{4}{4}$

Step 5.6

Multiply $\frac{16}{1}$ by $\frac{4}{4}$ .

$\frac{- 15 p - p \cdot 2}{4} + \frac{9 \cdot 4}{4} + \frac{16 \cdot 4}{4}$

Step 6

Combine the numerators over the common denominator.

$\frac{- 15 p - p \cdot 2 + 9 \cdot 4 + 16 \cdot 4}{4}$

Step 7

Simplify each term.

Tap for more steps...

Step 7.1

Multiply $2$ by $- 1$ .

$\frac{- 15 p - 2 p + 9 \cdot 4 + 16 \cdot 4}{4}$

Step 7.2

Multiply $9$ by $4$ .

$\frac{- 15 p - 2 p + 36 + 16 \cdot 4}{4}$

Step 7.3

Multiply $16$ by $4$ .

$\frac{- 15 p - 2 p + 36 + 64}{4}$

Step 8

Simplify terms.

Tap for more steps...

Step 8.1

Subtract $2 p$ from $- 15 p$ .

$\frac{- 17 p + 36 + 64}{4}$

Step 8.2

Add $36$ and $64$ .

$\frac{- 17 p + 100}{4}$

Step 8.3

Factor $- 1$ out of $- 17 p$ .

$\frac{- (17 p) + 100}{4}$

Step 8.4

Rewrite $100$ as $- 1 (- 100)$ .

$\frac{- (17 p) - 1 (- 100)}{4}$

Step 8.5

Factor $- 1$ out of $- (17 p) - 1 (- 100)$ .

$\frac{- (17 p - 100)}{4}$

Step 8.6

Simplify the expression.

Tap for more steps...

Step 8.6.1

Rewrite $- (17 p - 100)$ as $- 1 (17 p - 100)$ .

$\frac{- 1 (17 p - 100)}{4}$

Step 8.6.2

Move the negative in front of the fraction.

$- \frac{17 p - 100}{4}$