Basic Math Examples

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

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

Step 1

Convert

3 \frac{2}{3}

$3 \frac{2}{3}$ 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})

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

Step 1.2

Add

3

$3$ and

\frac{2}{3}

$\frac{2}{3}$ .

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Step 1.2.1

To write

3

$3$ as a fraction with a common denominator, multiply by

\frac{3}{3}

$\frac{3}{3}$ .

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

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

Step 1.2.2

Combine

3

$3$ and

\frac{3}{3}

$\frac{3}{3}$ .

- \frac{12}{5} + ∣ ∣ ∣ - \frac{13}{6} ∣ ∣ ∣ - (\frac{3 \cdot 3}{3} + \frac{2}{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}

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

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

3

$3$ by

3

$3$ .

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

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

Step 1.2.4.2

Add

9

$9$ and

2

$2$ .

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

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

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

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

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

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

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

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

Step 2

Find the common denominator.

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Step 2.1

Multiply

\frac{12}{5}

$\frac{12}{5}$ by

\frac{3}{3}

$\frac{3}{3}$ .

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

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

Step 2.2

Multiply

\frac{12}{5}

$\frac{12}{5}$ by

\frac{3}{3}

$\frac{3}{3}$ .

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

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

Step 2.3

Write

∣ ∣ ∣ - \frac{13}{6} ∣ ∣ ∣

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

1

$1$ .

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

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

Step 2.4

Multiply

\frac{∣ ∣ - \frac{13}{6} ∣ ∣}{1}

$\frac{| - \frac{13}{6} |}{1}$ by

\frac{15}{15}

$\frac{15}{15}$ .

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

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

Step 2.5

Multiply

\frac{∣ ∣ - \frac{13}{6} ∣ ∣}{1}

$\frac{| - \frac{13}{6} |}{1}$ by

\frac{15}{15}

$\frac{15}{15}$ .

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

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

Step 2.6

Multiply

\frac{11}{3}

$\frac{11}{3}$ by

\frac{5}{5}

$\frac{5}{5}$ .

- \frac{12 \cdot 3}{5 \cdot 3} + \frac{∣ ∣ - \frac{13}{6} ∣ ∣ \cdot 15}{15} - (\frac{11}{3} \cdot \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}

$\frac{11}{3}$ by

\frac{5}{5}

$\frac{5}{5}$ .

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

$5 \cdot 3$ .

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

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

Step 2.9

Multiply

3

$3$ by

5

$5$ .

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

$3$ by

5

$5$ .

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

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

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

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

Step 3

Combine the numerators over the common denominator.

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

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

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:

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