Basic Math Examples

- 1 + \frac{3}{4} - \frac{1}{3} \div 2 - \frac{1}{4}

$- 1 + \frac{3}{4} - \frac{1}{3} \div 2 - \frac{1}{4}$

Step 1

Combine the numerators over the common denominator.

- 1 + \frac{3 - 1}{4} + \frac{- \frac{1}{3}}{2}

$- 1 + \frac{3 - 1}{4} + \frac{- \frac{1}{3}}{2}$

Step 2

Subtract

1

$1$ from

3

$3$ .

- 1 + \frac{2}{4} + \frac{- \frac{1}{3}}{2}

$- 1 + \frac{2}{4} + \frac{- \frac{1}{3}}{2}$

Step 3

Find the common denominator.

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Step 3.1

Write

- 1

$- 1$ as a fraction with denominator

1

$1$ .

\frac{- 1}{1} + \frac{2}{4} + \frac{- \frac{1}{3}}{2}

$\frac{- 1}{1} + \frac{2}{4} + \frac{- \frac{1}{3}}{2}$

Step 3.2

Multiply

\frac{- 1}{1}

$\frac{- 1}{1}$ by

\frac{4}{4}

$\frac{4}{4}$ .

\frac{- 1}{1} \cdot \frac{4}{4} + \frac{2}{4} + \frac{- \frac{1}{3}}{2}

$\frac{- 1}{1} \cdot \frac{4}{4} + \frac{2}{4} + \frac{- \frac{1}{3}}{2}$

Step 3.3

Multiply

\frac{- 1}{1}

$\frac{- 1}{1}$ by

\frac{4}{4}

$\frac{4}{4}$ .

\frac{- 1 \cdot 4}{4} + \frac{2}{4} + \frac{- \frac{1}{3}}{2}

$\frac{- 1 \cdot 4}{4} + \frac{2}{4} + \frac{- \frac{1}{3}}{2}$

Step 3.4

Multiply

\frac{- \frac{1}{3}}{2}

$\frac{- \frac{1}{3}}{2}$ by

\frac{2}{2}

$\frac{2}{2}$ .

\frac{- 1 \cdot 4}{4} + \frac{2}{4} + \frac{- \frac{1}{3}}{2} \cdot \frac{2}{2}

$\frac{- 1 \cdot 4}{4} + \frac{2}{4} + \frac{- \frac{1}{3}}{2} \cdot \frac{2}{2}$

Step 3.5

Multiply

\frac{- \frac{1}{3}}{2}

$\frac{- \frac{1}{3}}{2}$ by

\frac{2}{2}

$\frac{2}{2}$ .

\frac{- 1 \cdot 4}{4} + \frac{2}{4} + \frac{- \frac{1}{3} \cdot 2}{2 \cdot 2}

$\frac{- 1 \cdot 4}{4} + \frac{2}{4} + \frac{- \frac{1}{3} \cdot 2}{2 \cdot 2}$

Step 3.6

Multiply

2

$2$ by

2

$2$ .

\frac{- 1 \cdot 4}{4} + \frac{2}{4} + \frac{- \frac{1}{3} \cdot 2}{4}

$\frac{- 1 \cdot 4}{4} + \frac{2}{4} + \frac{- \frac{1}{3} \cdot 2}{4}$

\frac{- 1 \cdot 4}{4} + \frac{2}{4} + \frac{- \frac{1}{3} \cdot 2}{4}

$\frac{- 1 \cdot 4}{4} + \frac{2}{4} + \frac{- \frac{1}{3} \cdot 2}{4}$

Step 4

Combine the numerators over the common denominator.

\frac{- 1 \cdot 4 + 2 - \frac{1}{3} \cdot 2}{4}

$\frac{- 1 \cdot 4 + 2 - \frac{1}{3} \cdot 2}{4}$

Step 5

Simplify each term.

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Step 5.1

Multiply

- 1

$- 1$ by

4

$4$ .

\frac{- 4 + 2 - \frac{1}{3} \cdot 2}{4}

$\frac{- 4 + 2 - \frac{1}{3} \cdot 2}{4}$

Step 5.2

Multiply

- \frac{1}{3} \cdot 2

$- \frac{1}{3} \cdot 2$ .

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Step 5.2.1

Multiply

2

$2$ by

- 1

$- 1$ .

\frac{- 4 + 2 - 2 (\frac{1}{3})}{4}

$\frac{- 4 + 2 - 2 (\frac{1}{3})}{4}$

Step 5.2.2

Combine

- 2

$- 2$ and

\frac{1}{3}

$\frac{1}{3}$ .

\frac{- 4 + 2 + \frac{- 2}{3}}{4}

$\frac{- 4 + 2 + \frac{- 2}{3}}{4}$

\frac{- 4 + 2 + \frac{- 2}{3}}{4}

$\frac{- 4 + 2 + \frac{- 2}{3}}{4}$

Step 5.3

Move the negative in front of the fraction.

\frac{- 4 + 2 - \frac{2}{3}}{4}

$\frac{- 4 + 2 - \frac{2}{3}}{4}$

\frac{- 4 + 2 - \frac{2}{3}}{4}

$\frac{- 4 + 2 - \frac{2}{3}}{4}$

Step 6

Find the common denominator.

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Step 6.1

Write

- 4

$- 4$ as a fraction with denominator

1

$1$ .

\frac{\frac{- 4}{1} + 2 - \frac{2}{3}}{4}

$\frac{\frac{- 4}{1} + 2 - \frac{2}{3}}{4}$

Step 6.2

Multiply

\frac{- 4}{1}

$\frac{- 4}{1}$ by

\frac{3}{3}

$\frac{3}{3}$ .

\frac{\frac{- 4}{1} \cdot \frac{3}{3} + 2 - \frac{2}{3}}{4}

$\frac{\frac{- 4}{1} \cdot \frac{3}{3} + 2 - \frac{2}{3}}{4}$

Step 6.3

Multiply

\frac{- 4}{1}

$\frac{- 4}{1}$ by

\frac{3}{3}

$\frac{3}{3}$ .

\frac{\frac{- 4 \cdot 3}{3} + 2 - \frac{2}{3}}{4}

$\frac{\frac{- 4 \cdot 3}{3} + 2 - \frac{2}{3}}{4}$

Step 6.4

Write

2

$2$ as a fraction with denominator

1

$1$ .

\frac{\frac{- 4 \cdot 3}{3} + \frac{2}{1} - \frac{2}{3}}{4}

$\frac{\frac{- 4 \cdot 3}{3} + \frac{2}{1} - \frac{2}{3}}{4}$

Step 6.5

Multiply

\frac{2}{1}

$\frac{2}{1}$ by

\frac{3}{3}

$\frac{3}{3}$ .

\frac{\frac{- 4 \cdot 3}{3} + \frac{2}{1} \cdot \frac{3}{3} - \frac{2}{3}}{4}

$\frac{\frac{- 4 \cdot 3}{3} + \frac{2}{1} \cdot \frac{3}{3} - \frac{2}{3}}{4}$

Step 6.6

Multiply

\frac{2}{1}

$\frac{2}{1}$ by

\frac{3}{3}

$\frac{3}{3}$ .

\frac{\frac{- 4 \cdot 3}{3} + \frac{2 \cdot 3}{3} - \frac{2}{3}}{4}

$\frac{\frac{- 4 \cdot 3}{3} + \frac{2 \cdot 3}{3} - \frac{2}{3}}{4}$

\frac{\frac{- 4 \cdot 3}{3} + \frac{2 \cdot 3}{3} - \frac{2}{3}}{4}

$\frac{\frac{- 4 \cdot 3}{3} + \frac{2 \cdot 3}{3} - \frac{2}{3}}{4}$

Step 7

Combine the numerators over the common denominator.

\frac{\frac{- 4 \cdot 3 + 2 \cdot 3 - 2}{3}}{4}

$\frac{\frac{- 4 \cdot 3 + 2 \cdot 3 - 2}{3}}{4}$

Step 8

Simplify each term.

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Step 8.1

Multiply

- 4

$- 4$ by

3

$3$ .

\frac{\frac{- 12 + 2 \cdot 3 - 2}{3}}{4}

$\frac{\frac{- 12 + 2 \cdot 3 - 2}{3}}{4}$

Step 8.2

Multiply

2

$2$ by

3

$3$ .

\frac{\frac{- 12 + 6 - 2}{3}}{4}

$\frac{\frac{- 12 + 6 - 2}{3}}{4}$

\frac{\frac{- 12 + 6 - 2}{3}}{4}

$\frac{\frac{- 12 + 6 - 2}{3}}{4}$

Step 9

Simplify the expression.

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Step 9.1

Add

- 12

$- 12$ and

6

$6$ .

\frac{\frac{- 6 - 2}{3}}{4}

$\frac{\frac{- 6 - 2}{3}}{4}$

Step 9.2

Subtract

2

$2$ from

- 6

$- 6$ .

\frac{\frac{- 8}{3}}{4}

$\frac{\frac{- 8}{3}}{4}$

Step 9.3

Move the negative in front of the fraction.

\frac{- \frac{8}{3}}{4}

$\frac{- \frac{8}{3}}{4}$

\frac{- \frac{8}{3}}{4}

$\frac{- \frac{8}{3}}{4}$

Step 10

Multiply the numerator by the reciprocal of the denominator.

- \frac{8}{3} \cdot \frac{1}{4}

$- \frac{8}{3} \cdot \frac{1}{4}$

Step 11

Cancel the common factor of

4

$4$ .

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Step 11.1

Move the leading negative in

- \frac{8}{3}

$- \frac{8}{3}$ into the numerator.

\frac{- 8}{3} \cdot \frac{1}{4}

$\frac{- 8}{3} \cdot \frac{1}{4}$

Step 11.2

Factor

4

$4$ out of

- 8

$- 8$ .

\frac{4 (- 2)}{3} \cdot \frac{1}{4}

$\frac{4 (- 2)}{3} \cdot \frac{1}{4}$

Step 11.3

Cancel the common factor.

$\frac{4 \cdot - 2}{3} \cdot \frac{1}{4}$

Step 11.4

Rewrite the expression.

$\frac{- 2}{3}$

Step 12

Move the negative in front of the fraction.

$- \frac{2}{3}$

Step 13

The result can be shown in multiple forms.

Exact Form:

$- \frac{2}{3}$

Decimal Form:

$- 0.\overline{6}$