Algebra Examples

$- \frac{2}{3} p + \frac{1}{5} - 1 + \frac{5}{6} p$

Step 1

Simplify each term.

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Step 1.1

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

$- \frac{p \cdot 2}{3} + \frac{1}{5} - 1 + \frac{5}{6} p$

Step 1.2

Move $2$ to the left of $p$ .

$- \frac{2 \cdot p}{3} + \frac{1}{5} - 1 + \frac{5}{6} p$

Step 1.3

Combine $\frac{5}{6}$ and $p$ .

$- \frac{2 p}{3} + \frac{1}{5} - 1 + \frac{5 p}{6}$

Step 2

To write $- \frac{2 p}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{2 p}{3} \cdot \frac{2}{2} + \frac{5 p}{6} + \frac{1}{5} - 1$

Step 3

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{2 p}{3}$ by $\frac{2}{2}$ .

$- \frac{2 p \cdot 2}{3 \cdot 2} + \frac{5 p}{6} + \frac{1}{5} - 1$

Step 3.2

Multiply $3$ by $2$ .

$- \frac{2 p \cdot 2}{6} + \frac{5 p}{6} + \frac{1}{5} - 1$

Step 4

Combine the numerators over the common denominator.

$\frac{- 2 p \cdot 2 + 5 p}{6} + \frac{1}{5} - 1$

Step 5

Find the common denominator.

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Step 5.1

Multiply $\frac{- 2 p \cdot 2 + 5 p}{6}$ by $\frac{5}{5}$ .

$\frac{- 2 p \cdot 2 + 5 p}{6} \cdot \frac{5}{5} + \frac{1}{5} - 1$

Step 5.2

Multiply $\frac{- 2 p \cdot 2 + 5 p}{6}$ by $\frac{5}{5}$ .

$\frac{(- 2 p \cdot 2 + 5 p) \cdot 5}{6 \cdot 5} + \frac{1}{5} - 1$

Step 5.3

Multiply $\frac{1}{5}$ by $\frac{6}{6}$ .

$\frac{(- 2 p \cdot 2 + 5 p) \cdot 5}{6 \cdot 5} + \frac{1}{5} \cdot \frac{6}{6} - 1$

Step 5.4

Multiply $\frac{1}{5}$ by $\frac{6}{6}$ .

$\frac{(- 2 p \cdot 2 + 5 p) \cdot 5}{6 \cdot 5} + \frac{6}{5 \cdot 6} - 1$

Step 5.5

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

$\frac{(- 2 p \cdot 2 + 5 p) \cdot 5}{6 \cdot 5} + \frac{6}{5 \cdot 6} + \frac{- 1}{1}$

Step 5.6

Multiply $\frac{- 1}{1}$ by $\frac{30}{30}$ .

$\frac{(- 2 p \cdot 2 + 5 p) \cdot 5}{6 \cdot 5} + \frac{6}{5 \cdot 6} + \frac{- 1}{1} \cdot \frac{30}{30}$

Step 5.7

Multiply $\frac{- 1}{1}$ by $\frac{30}{30}$ .

$\frac{(- 2 p \cdot 2 + 5 p) \cdot 5}{6 \cdot 5} + \frac{6}{5 \cdot 6} + \frac{- 1 \cdot 30}{30}$

Step 5.8

Reorder the factors of $6 \cdot 5$ .

$\frac{(- 2 p \cdot 2 + 5 p) \cdot 5}{5 \cdot 6} + \frac{6}{5 \cdot 6} + \frac{- 1 \cdot 30}{30}$

Step 5.9

Multiply $5$ by $6$ .

$\frac{(- 2 p \cdot 2 + 5 p) \cdot 5}{30} + \frac{6}{5 \cdot 6} + \frac{- 1 \cdot 30}{30}$

Step 5.10

Multiply $5$ by $6$ .

$\frac{(- 2 p \cdot 2 + 5 p) \cdot 5}{30} + \frac{6}{30} + \frac{- 1 \cdot 30}{30}$

Step 6

Combine the numerators over the common denominator.

$\frac{(- 2 p \cdot 2 + 5 p) \cdot 5 + 6 - 1 \cdot 30}{30}$

Step 7

Simplify each term.

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Step 7.1

Multiply $2$ by $- 2$ .

$\frac{(- 4 p + 5 p) \cdot 5 + 6 - 1 \cdot 30}{30}$

Step 7.2

Add $- 4 p$ and $5 p$ .

$\frac{p \cdot 5 + 6 - 1 \cdot 30}{30}$

Step 7.3

Move $5$ to the left of $p$ .

$\frac{5 \cdot p + 6 - 1 \cdot 30}{30}$

Step 7.4

Multiply $- 1$ by $30$ .

$\frac{5 p + 6 - 30}{30}$

Step 8

Subtract $30$ from $6$ .

$\frac{5 p - 24}{30}$