Calculus Examples

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

Step 1

Find the common denominator.

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Step 1.1

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

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

Step 1.2

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

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

Step 1.3

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

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

Step 1.4

Write $- 3$ as a fraction with denominator $1$ .

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

Step 1.5

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

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

Step 1.6

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

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

Step 2

Combine the numerators over the common denominator.

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

Step 3

Simplify the expression.

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Step 3.1

Multiply $- 3$ by $3$ .

$\frac{1 + 3 - 9}{3}$

Step 3.2

Add $1$ and $3$ .

$\frac{4 - 9}{3}$

Step 3.3

Subtract $9$ from $4$ .

$\frac{- 5}{3}$

Step 3.4

Move the negative in front of the fraction.

$- \frac{5}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$- \frac{5}{3}$

Decimal Form:

$- 1.\overline{6}$

Mixed Number Form:

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