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

Find the common denominator.

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Step 2.1

Multiply $\frac{2 p}{3}$ by $\frac{10}{10}$ .

$- (\frac{2 p}{3} \cdot \frac{10}{10}) + \frac{1}{5} - 1 + \frac{5 p}{6}$

Step 2.2

Multiply $\frac{2 p}{3}$ by $\frac{10}{10}$ .

$- \frac{2 p \cdot 10}{3 \cdot 10} + \frac{1}{5} - 1 + \frac{5 p}{6}$

Step 2.3

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

$- \frac{2 p \cdot 10}{3 \cdot 10} + \frac{1}{5} \cdot \frac{6}{6} - 1 + \frac{5 p}{6}$

Step 2.4

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

$- \frac{2 p \cdot 10}{3 \cdot 10} + \frac{6}{5 \cdot 6} - 1 + \frac{5 p}{6}$

Step 2.5

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

$- \frac{2 p \cdot 10}{3 \cdot 10} + \frac{6}{5 \cdot 6} + \frac{- 1}{1} + \frac{5 p}{6}$

Step 2.6

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

$- \frac{2 p \cdot 10}{3 \cdot 10} + \frac{6}{5 \cdot 6} + \frac{- 1}{1} \cdot \frac{30}{30} + \frac{5 p}{6}$

Step 2.7

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

$- \frac{2 p \cdot 10}{3 \cdot 10} + \frac{6}{5 \cdot 6} + \frac{- 1 \cdot 30}{30} + \frac{5 p}{6}$

Step 2.8

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

$- \frac{2 p \cdot 10}{3 \cdot 10} + \frac{6}{5 \cdot 6} + \frac{- 1 \cdot 30}{30} + \frac{5 p}{6} \cdot \frac{5}{5}$

Step 2.9

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

$- \frac{2 p \cdot 10}{3 \cdot 10} + \frac{6}{5 \cdot 6} + \frac{- 1 \cdot 30}{30} + \frac{5 p \cdot 5}{6 \cdot 5}$

Step 2.10

Multiply $3$ by $10$ .

$- \frac{2 p \cdot 10}{30} + \frac{6}{5 \cdot 6} + \frac{- 1 \cdot 30}{30} + \frac{5 p \cdot 5}{6 \cdot 5}$

Step 2.11

Multiply $5$ by $6$ .

$- \frac{2 p \cdot 10}{30} + \frac{6}{30} + \frac{- 1 \cdot 30}{30} + \frac{5 p \cdot 5}{6 \cdot 5}$

Step 2.12

Reorder the factors of $6 \cdot 5$ .

$- \frac{2 p \cdot 10}{30} + \frac{6}{30} + \frac{- 1 \cdot 30}{30} + \frac{5 p \cdot 5}{5 \cdot 6}$

Step 2.13

Multiply $5$ by $6$ .

$- \frac{2 p \cdot 10}{30} + \frac{6}{30} + \frac{- 1 \cdot 30}{30} + \frac{5 p \cdot 5}{30}$

Step 3

Combine the numerators over the common denominator.

$\frac{- 2 p \cdot 10 + 6 - 1 \cdot 30 + 5 p \cdot 5}{30}$

Step 4

Simplify each term.

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Step 4.1

Multiply $10$ by $- 2$ .

$\frac{- 20 p + 6 - 1 \cdot 30 + 5 p \cdot 5}{30}$

Step 4.2

Multiply $- 1$ by $30$ .

$\frac{- 20 p + 6 - 30 + 5 p \cdot 5}{30}$

Step 4.3

Multiply $5$ by $5$ .

$\frac{- 20 p + 6 - 30 + 25 p}{30}$

Step 5

Simplify by adding terms.

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Step 5.1

Add $- 20 p$ and $25 p$ .

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

Step 5.2

Subtract $30$ from $6$ .

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