Basic Math Examples

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

Step 1

Combine the numerators over the common denominator.

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

Step 2

Subtract $1$ from $3$ .

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

Step 3

Find the common denominator.

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Step 3.1

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

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

Step 3.2

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

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

Step 3.3

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

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

Step 3.4

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

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

Step 3.5

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

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

Step 3.6

Multiply $2$ by $2$ .

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

Step 4

Combine the numerators over the common denominator.

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

Step 5

Simplify each term.

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Step 5.1

Multiply $- 1$ by $4$ .

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

Step 5.2

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

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Step 5.2.1

Multiply $2$ by $- 1$ .

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

Step 5.2.2

Combine $- 2$ and $\frac{1}{3}$ .

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

Step 5.3

Move the negative in front of the fraction.

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

Step 6

Find the common denominator.

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Step 6.1

Write $- 4$ as a fraction with denominator $1$ .

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

Step 6.2

Multiply $\frac{- 4}{1}$ by $\frac{3}{3}$ .

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

Step 6.3

Multiply $\frac{- 4}{1}$ by $\frac{3}{3}$ .

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

Step 6.4

Write $2$ as a fraction with denominator $1$ .

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

Step 6.5

Multiply $\frac{2}{1}$ by $\frac{3}{3}$ .

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

Step 6.6

Multiply $\frac{2}{1}$ by $\frac{3}{3}$ .

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

Step 7

Combine the numerators over the common denominator.

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

Step 8

Simplify each term.

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Step 8.1

Multiply $- 4$ by $3$ .

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

Step 8.2

Multiply $2$ by $3$ .

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

Step 9

Simplify the expression.

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Step 9.1

Add $- 12$ and $6$ .

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

Step 9.2

Subtract $2$ from $- 6$ .

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

Step 9.3

Move the negative in front of the fraction.

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

Step 10

Multiply the numerator by the reciprocal of the denominator.

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

Step 11

Cancel the common factor of $4$ .

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Step 11.1

Move the leading negative in $- \frac{8}{3}$ into the numerator.

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

Step 11.2

Factor $4$ out of $- 8$ .

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

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:

$- 0.\overline{6}$