Algebra Examples

$- \frac{2}{3} c - \frac{9}{5} + 14 c + \frac{3}{10}$

Step 1

Simplify each term.

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Step 1.1

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

$- \frac{c \cdot 2}{3} - \frac{9}{5} + 14 c + \frac{3}{10}$

Step 1.2

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

$- \frac{2 c}{3} - \frac{9}{5} + 14 c + \frac{3}{10}$

Step 2

To write $14 c$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- \frac{2 c}{3} + 14 c \cdot \frac{3}{3} - \frac{9}{5} + \frac{3}{10}$

Step 3

Combine $14 c$ and $\frac{3}{3}$ .

$- \frac{2 c}{3} + \frac{14 c \cdot 3}{3} - \frac{9}{5} + \frac{3}{10}$

Step 4

Combine the numerators over the common denominator.

$\frac{- 2 c + 14 c \cdot 3}{3} - \frac{9}{5} + \frac{3}{10}$

Step 5

Find the common denominator.

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Step 5.1

Multiply $\frac{- 2 c + 14 c \cdot 3}{3}$ by $\frac{10}{10}$ .

$\frac{- 2 c + 14 c \cdot 3}{3} \cdot \frac{10}{10} - \frac{9}{5} + \frac{3}{10}$

Step 5.2

Multiply $\frac{- 2 c + 14 c \cdot 3}{3}$ by $\frac{10}{10}$ .

$\frac{(- 2 c + 14 c \cdot 3) \cdot 10}{3 \cdot 10} - \frac{9}{5} + \frac{3}{10}$

Step 5.3

Multiply $\frac{9}{5}$ by $\frac{6}{6}$ .

$\frac{(- 2 c + 14 c \cdot 3) \cdot 10}{3 \cdot 10} - (\frac{9}{5} \cdot \frac{6}{6}) + \frac{3}{10}$

Step 5.4

Multiply $\frac{9}{5}$ by $\frac{6}{6}$ .

$\frac{(- 2 c + 14 c \cdot 3) \cdot 10}{3 \cdot 10} - \frac{9 \cdot 6}{5 \cdot 6} + \frac{3}{10}$

Step 5.5

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

$\frac{(- 2 c + 14 c \cdot 3) \cdot 10}{3 \cdot 10} - \frac{9 \cdot 6}{5 \cdot 6} + \frac{3}{10} \cdot \frac{3}{3}$

Step 5.6

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

$\frac{(- 2 c + 14 c \cdot 3) \cdot 10}{3 \cdot 10} - \frac{9 \cdot 6}{5 \cdot 6} + \frac{3 \cdot 3}{10 \cdot 3}$

Step 5.7

Multiply $3$ by $10$ .

$\frac{(- 2 c + 14 c \cdot 3) \cdot 10}{30} - \frac{9 \cdot 6}{5 \cdot 6} + \frac{3 \cdot 3}{10 \cdot 3}$

Step 5.8

Multiply $5$ by $6$ .

$\frac{(- 2 c + 14 c \cdot 3) \cdot 10}{30} - \frac{9 \cdot 6}{30} + \frac{3 \cdot 3}{10 \cdot 3}$

Step 5.9

Reorder the factors of $10 \cdot 3$ .

$\frac{(- 2 c + 14 c \cdot 3) \cdot 10}{30} - \frac{9 \cdot 6}{30} + \frac{3 \cdot 3}{3 \cdot 10}$

Step 5.10

Multiply $3$ by $10$ .

$\frac{(- 2 c + 14 c \cdot 3) \cdot 10}{30} - \frac{9 \cdot 6}{30} + \frac{3 \cdot 3}{30}$

Step 6

Combine the numerators over the common denominator.

$\frac{(- 2 c + 14 c \cdot 3) \cdot 10 - 9 \cdot 6 + 3 \cdot 3}{30}$

Step 7

Simplify each term.

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Step 7.1

Multiply $3$ by $14$ .

$\frac{(- 2 c + 42 c) \cdot 10 - 9 \cdot 6 + 3 \cdot 3}{30}$

Step 7.2

Add $- 2 c$ and $42 c$ .

$\frac{40 c \cdot 10 - 9 \cdot 6 + 3 \cdot 3}{30}$

Step 7.3

Multiply $10$ by $40$ .

$\frac{400 c - 9 \cdot 6 + 3 \cdot 3}{30}$

Step 7.4

Multiply $- 9$ by $6$ .

$\frac{400 c - 54 + 3 \cdot 3}{30}$

Step 7.5

Multiply $3$ by $3$ .

$\frac{400 c - 54 + 9}{30}$

Step 8

Reduce the expression by cancelling the common factors.

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Step 8.1

Add $- 54$ and $9$ .

$\frac{400 c - 45}{30}$

Step 8.2

Cancel the common factor of $400 c - 45$ and $30$ .

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Step 8.2.1

Factor $5$ out of $400 c$ .

$\frac{5 (80 c) - 45}{30}$

Step 8.2.2

Factor $5$ out of $- 45$ .

$\frac{5 (80 c) + 5 (- 9)}{30}$

Step 8.2.3

Factor $5$ out of $5 (80 c) + 5 (- 9)$ .

$\frac{5 (80 c - 9)}{30}$

Step 8.2.4

Cancel the common factors.

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Step 8.2.4.1

Factor $5$ out of $30$ .

$\frac{5 (80 c - 9)}{5 (6)}$

Step 8.2.4.2

Cancel the common factor.

$\frac{5 (80 c - 9)}{5 \cdot 6}$

Step 8.2.4.3

Rewrite the expression.

$\frac{80 c - 9}{6}$