Basic Math Examples

$- \frac{1}{3} + 2 - 1 \frac{5}{6}$

Step 1

Convert $1 \frac{5}{6}$ to an improper fraction.

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Step 1.1

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

$- \frac{1}{3} + 2 - (1 + \frac{5}{6})$

Step 1.2

Add $1$ and $\frac{5}{6}$ .

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Step 1.2.1

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

$- \frac{1}{3} + 2 - (\frac{6}{6} + \frac{5}{6})$

Step 1.2.2

Combine the numerators over the common denominator.

$- \frac{1}{3} + 2 - \frac{6 + 5}{6}$

Step 1.2.3

Add $6$ and $5$ .

$- \frac{1}{3} + 2 - \frac{11}{6}$

Step 2

Find the common denominator.

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Step 2.1

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

$- (\frac{1}{3} \cdot \frac{2}{2}) + 2 - \frac{11}{6}$

Step 2.2

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

$- \frac{2}{3 \cdot 2} + 2 - \frac{11}{6}$

Step 2.3

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

$- \frac{2}{3 \cdot 2} + \frac{2}{1} - \frac{11}{6}$

Step 2.4

Multiply $\frac{2}{1}$ by $\frac{6}{6}$ .

$- \frac{2}{3 \cdot 2} + \frac{2}{1} \cdot \frac{6}{6} - \frac{11}{6}$

Step 2.5

Multiply $\frac{2}{1}$ by $\frac{6}{6}$ .

$- \frac{2}{3 \cdot 2} + \frac{2 \cdot 6}{6} - \frac{11}{6}$

Step 2.6

Reorder the factors of $3 \cdot 2$ .

$- \frac{2}{2 \cdot 3} + \frac{2 \cdot 6}{6} - \frac{11}{6}$

Step 2.7

Multiply $2$ by $3$ .

$- \frac{2}{6} + \frac{2 \cdot 6}{6} - \frac{11}{6}$

Step 3

Combine the numerators over the common denominator.

$\frac{- 2 + 2 \cdot 6 - 11}{6}$

Step 4

Simplify the expression.

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Step 4.1

Multiply $2$ by $6$ .

$\frac{- 2 + 12 - 11}{6}$

Step 4.2

Add $- 2$ and $12$ .

$\frac{10 - 11}{6}$

Step 4.3

Subtract $11$ from $10$ .

$\frac{- 1}{6}$

Step 4.4

Move the negative in front of the fraction.

$- \frac{1}{6}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$- \frac{1}{6}$

Decimal Form:

$- 0.1\overline{6}$