Pre-Algebra Examples

$- \frac{12}{5} + | - \frac{13}{6} | - 3 \frac{2}{3}$

Step 1

Simplify and reorder the polynomial.

Tap for more steps...

Step 1.1

Convert $3 \frac{2}{3}$ to an improper fraction.

Tap for more steps...

Step 1.1.1

A mixed number is an addition of its whole and fractional parts.

$- \frac{12}{5} + | - \frac{13}{6} | - (3 + \frac{2}{3})$

Step 1.1.2

Add $3$ and $\frac{2}{3}$ .

Tap for more steps...

Step 1.1.2.1

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

$- \frac{12}{5} + | - \frac{13}{6} | - (3 \cdot \frac{3}{3} + \frac{2}{3})$

Step 1.1.2.2

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

$- \frac{12}{5} + | - \frac{13}{6} | - (\frac{3 \cdot 3}{3} + \frac{2}{3})$

Step 1.1.2.3

Combine the numerators over the common denominator.

$- \frac{12}{5} + | - \frac{13}{6} | - \frac{3 \cdot 3 + 2}{3}$

Step 1.1.2.4

Simplify the numerator.

Tap for more steps...

Step 1.1.2.4.1

Multiply $3$ by $3$ .

$- \frac{12}{5} + | - \frac{13}{6} | - \frac{9 + 2}{3}$

Step 1.1.2.4.2

Add $9$ and $2$ .

$- \frac{12}{5} + | - \frac{13}{6} | - \frac{11}{3}$

Step 1.2

$- \frac{13}{6}$ is approximately $- 2.1\overline{6}$ which is negative so negate $- \frac{13}{6}$ and remove the absolute value

$- \frac{12}{5} + \frac{13}{6} - \frac{11}{3}$

Step 1.3

Find the common denominator.

Tap for more steps...

Step 1.3.1

Multiply $\frac{12}{5}$ by $\frac{6}{6}$ .

$- (\frac{12}{5} \cdot \frac{6}{6}) + \frac{13}{6} - \frac{11}{3}$

Step 1.3.2

Multiply $\frac{12}{5}$ by $\frac{6}{6}$ .

$- \frac{12 \cdot 6}{5 \cdot 6} + \frac{13}{6} - \frac{11}{3}$

Step 1.3.3

Multiply $\frac{13}{6}$ by $\frac{5}{5}$ .

$- \frac{12 \cdot 6}{5 \cdot 6} + \frac{13}{6} \cdot \frac{5}{5} - \frac{11}{3}$

Step 1.3.4

Multiply $\frac{13}{6}$ by $\frac{5}{5}$ .

$- \frac{12 \cdot 6}{5 \cdot 6} + \frac{13 \cdot 5}{6 \cdot 5} - \frac{11}{3}$

Step 1.3.5

Multiply $\frac{11}{3}$ by $\frac{10}{10}$ .

$- \frac{12 \cdot 6}{5 \cdot 6} + \frac{13 \cdot 5}{6 \cdot 5} - (\frac{11}{3} \cdot \frac{10}{10})$

Step 1.3.6

Multiply $\frac{11}{3}$ by $\frac{10}{10}$ .

$- \frac{12 \cdot 6}{5 \cdot 6} + \frac{13 \cdot 5}{6 \cdot 5} - \frac{11 \cdot 10}{3 \cdot 10}$

Step 1.3.7

Multiply $5$ by $6$ .

$- \frac{12 \cdot 6}{30} + \frac{13 \cdot 5}{6 \cdot 5} - \frac{11 \cdot 10}{3 \cdot 10}$

Step 1.3.8

Reorder the factors of $6 \cdot 5$ .

$- \frac{12 \cdot 6}{30} + \frac{13 \cdot 5}{5 \cdot 6} - \frac{11 \cdot 10}{3 \cdot 10}$

Step 1.3.9

Multiply $5$ by $6$ .

$- \frac{12 \cdot 6}{30} + \frac{13 \cdot 5}{30} - \frac{11 \cdot 10}{3 \cdot 10}$

Step 1.3.10

Multiply $3$ by $10$ .

$- \frac{12 \cdot 6}{30} + \frac{13 \cdot 5}{30} - \frac{11 \cdot 10}{30}$

Step 1.4

Combine the numerators over the common denominator.

$\frac{- 12 \cdot 6 + 13 \cdot 5 - 11 \cdot 10}{30}$

Step 1.5

Simplify each term.

Tap for more steps...

Step 1.5.1

Multiply $- 12$ by $6$ .

$\frac{- 72 + 13 \cdot 5 - 11 \cdot 10}{30}$

Step 1.5.2

Multiply $13$ by $5$ .

$\frac{- 72 + 65 - 11 \cdot 10}{30}$

Step 1.5.3

Multiply $- 11$ by $10$ .

$\frac{- 72 + 65 - 110}{30}$

Step 1.6

Reduce the expression by cancelling the common factors.

Tap for more steps...

Step 1.6.1

Add $- 72$ and $65$ .

$\frac{- 7 - 110}{30}$

Step 1.6.2

Subtract $110$ from $- 7$ .

$\frac{- 117}{30}$

Step 1.6.3

Cancel the common factor of $- 117$ and $30$ .

Tap for more steps...

Step 1.6.3.1

Factor $3$ out of $- 117$ .

$\frac{3 (- 39)}{30}$

Step 1.6.3.2

Cancel the common factors.

Tap for more steps...

Step 1.6.3.2.1

Factor $3$ out of $30$ .

$\frac{3 \cdot - 39}{3 \cdot 10}$

Step 1.6.3.2.2

Cancel the common factor.

$\frac{3 \cdot - 39}{3 \cdot 10}$

Step 1.6.3.2.3

Rewrite the expression.

$\frac{- 39}{10}$

Step 1.6.4

Move the negative in front of the fraction.

$- \frac{39}{10}$

Step 2

The expression is constant, which means it can be rewritten with a factor of $x^{0}$ . The degree is the largest exponent on the variable.

$0$