Basic Math Examples

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

Step 1

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

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Step 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 1.2

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

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Step 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 1.2.2

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

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

Step 1.2.3

Combine the numerators over the common denominator.

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

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $3$ by $3$ .

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

Step 1.2.4.2

Add $9$ and $2$ .

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

Step 2

Find the common denominator.

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Step 2.1

Multiply $\frac{12}{5}$ by $\frac{3}{3}$ .

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

Step 2.2

Multiply $\frac{12}{5}$ by $\frac{3}{3}$ .

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

Step 2.3

Write $| - \frac{13}{6} |$ as a fraction with denominator $1$ .

$- \frac{12 \cdot 3}{5 \cdot 3} + \frac{| - \frac{13}{6} |}{1} - \frac{11}{3}$

Step 2.4

Multiply $\frac{| - \frac{13}{6} |}{1}$ by $\frac{15}{15}$ .

$- \frac{12 \cdot 3}{5 \cdot 3} + \frac{| - \frac{13}{6} |}{1} \cdot \frac{15}{15} - \frac{11}{3}$

Step 2.5

Multiply $\frac{| - \frac{13}{6} |}{1}$ by $\frac{15}{15}$ .

$- \frac{12 \cdot 3}{5 \cdot 3} + \frac{| - \frac{13}{6} | \cdot 15}{15} - \frac{11}{3}$

Step 2.6

Multiply $\frac{11}{3}$ by $\frac{5}{5}$ .

$- \frac{12 \cdot 3}{5 \cdot 3} + \frac{| - \frac{13}{6} | \cdot 15}{15} - (\frac{11}{3} \cdot \frac{5}{5})$

Step 2.7

Multiply $\frac{11}{3}$ by $\frac{5}{5}$ .

$- \frac{12 \cdot 3}{5 \cdot 3} + \frac{| - \frac{13}{6} | \cdot 15}{15} - \frac{11 \cdot 5}{3 \cdot 5}$

Step 2.8

Reorder the factors of $5 \cdot 3$ .

$- \frac{12 \cdot 3}{3 \cdot 5} + \frac{| - \frac{13}{6} | \cdot 15}{15} - \frac{11 \cdot 5}{3 \cdot 5}$

Step 2.9

Multiply $3$ by $5$ .

$- \frac{12 \cdot 3}{15} + \frac{| - \frac{13}{6} | \cdot 15}{15} - \frac{11 \cdot 5}{3 \cdot 5}$

Step 2.10

Multiply $3$ by $5$ .

$- \frac{12 \cdot 3}{15} + \frac{| - \frac{13}{6} | \cdot 15}{15} - \frac{11 \cdot 5}{15}$

Step 3

Combine the numerators over the common denominator.

$\frac{- 12 \cdot 3 + | - \frac{13}{6} | \cdot 15 - 11 \cdot 5}{15}$

Step 4

Simplify each term.

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Step 4.1

Multiply $- 12$ by $3$ .

$\frac{- 36 + | - \frac{13}{6} | \cdot 15 - 11 \cdot 5}{15}$

Step 4.2

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

$\frac{- 36 + \frac{13}{6} \cdot 15 - 11 \cdot 5}{15}$

Step 4.3

Cancel the common factor of $3$ .

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Step 4.3.1

Factor $3$ out of $6$ .

$\frac{- 36 + \frac{13}{3 (2)} \cdot 15 - 11 \cdot 5}{15}$

Step 4.3.2

Factor $3$ out of $15$ .

$\frac{- 36 + \frac{13}{3 \cdot 2} \cdot (3 \cdot 5) - 11 \cdot 5}{15}$

Step 4.3.3

Cancel the common factor.

$\frac{- 36 + \frac{13}{3 \cdot 2} \cdot (3 \cdot 5) - 11 \cdot 5}{15}$

Step 4.3.4

Rewrite the expression.

$\frac{- 36 + \frac{13}{2} \cdot 5 - 11 \cdot 5}{15}$

Step 4.4

Combine $\frac{13}{2}$ and $5$ .

$\frac{- 36 + \frac{13 \cdot 5}{2} - 11 \cdot 5}{15}$

Step 4.5

Multiply $13$ by $5$ .

$\frac{- 36 + \frac{65}{2} - 11 \cdot 5}{15}$

Step 4.6

Multiply $- 11$ by $5$ .

$\frac{- 36 + \frac{65}{2} - 55}{15}$

Step 5

Find the common denominator.

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Step 5.1

Write $- 36$ as a fraction with denominator $1$ .

$\frac{\frac{- 36}{1} + \frac{65}{2} - 55}{15}$

Step 5.2

Multiply $\frac{- 36}{1}$ by $\frac{2}{2}$ .

$\frac{\frac{- 36}{1} \cdot \frac{2}{2} + \frac{65}{2} - 55}{15}$

Step 5.3

Multiply $\frac{- 36}{1}$ by $\frac{2}{2}$ .

$\frac{\frac{- 36 \cdot 2}{2} + \frac{65}{2} - 55}{15}$

Step 5.4

Write $- 55$ as a fraction with denominator $1$ .

$\frac{\frac{- 36 \cdot 2}{2} + \frac{65}{2} + \frac{- 55}{1}}{15}$

Step 5.5

Multiply $\frac{- 55}{1}$ by $\frac{2}{2}$ .

$\frac{\frac{- 36 \cdot 2}{2} + \frac{65}{2} + \frac{- 55}{1} \cdot \frac{2}{2}}{15}$

Step 5.6

Multiply $\frac{- 55}{1}$ by $\frac{2}{2}$ .

$\frac{\frac{- 36 \cdot 2}{2} + \frac{65}{2} + \frac{- 55 \cdot 2}{2}}{15}$

Step 6

Combine the numerators over the common denominator.

$\frac{\frac{- 36 \cdot 2 + 65 - 55 \cdot 2}{2}}{15}$

Step 7

Simplify each term.

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Step 7.1

Multiply $- 36$ by $2$ .

$\frac{\frac{- 72 + 65 - 55 \cdot 2}{2}}{15}$

Step 7.2

Multiply $- 55$ by $2$ .

$\frac{\frac{- 72 + 65 - 110}{2}}{15}$

Step 8

Simplify the expression.

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Step 8.1

Add $- 72$ and $65$ .

$\frac{\frac{- 7 - 110}{2}}{15}$

Step 8.2

Subtract $110$ from $- 7$ .

$\frac{\frac{- 117}{2}}{15}$

Step 8.3

Move the negative in front of the fraction.

$\frac{- \frac{117}{2}}{15}$

Step 9

Multiply the numerator by the reciprocal of the denominator.

$- \frac{117}{2} \cdot \frac{1}{15}$

Step 10

Cancel the common factor of $3$ .

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Step 10.1

Move the leading negative in $- \frac{117}{2}$ into the numerator.

$\frac{- 117}{2} \cdot \frac{1}{15}$

Step 10.2

Factor $3$ out of $- 117$ .

$\frac{3 (- 39)}{2} \cdot \frac{1}{15}$

Step 10.3

Factor $3$ out of $15$ .

$\frac{3 \cdot - 39}{2} \cdot \frac{1}{3 \cdot 5}$

Step 10.4

Cancel the common factor.

$\frac{3 \cdot - 39}{2} \cdot \frac{1}{3 \cdot 5}$

Step 10.5

Rewrite the expression.

$\frac{- 39}{2} \cdot \frac{1}{5}$

Step 11

Multiply $\frac{- 39}{2}$ by $\frac{1}{5}$ .

$\frac{- 39}{2 \cdot 5}$

Step 12

Simplify the expression.

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Step 12.1

Multiply $2$ by $5$ .

$\frac{- 39}{10}$

Step 12.2

Move the negative in front of the fraction.

$- \frac{39}{10}$

Step 13

The result can be shown in multiple forms.

Exact Form:

$- \frac{39}{10}$

Decimal Form:

$- 3.9$

Mixed Number Form:

$- 3 \frac{9}{10}$