Basic Math Examples

$\frac{1}{3} - (\frac{1}{2} + 1) + \frac{3}{4} - \frac{3}{5}$

Step 1

Find the common denominator.

Tap for more steps...

Step 1.1

Multiply $\frac{1}{3}$ by $\frac{20}{20}$ .

$\frac{1}{3} \cdot \frac{20}{20} - (\frac{1}{2} + 1) + \frac{3}{4} - \frac{3}{5}$

Step 1.2

Multiply $\frac{1}{3}$ by $\frac{20}{20}$ .

$\frac{20}{3 \cdot 20} - (\frac{1}{2} + 1) + \frac{3}{4} - \frac{3}{5}$

Step 1.3

Write $- (\frac{1}{2} + 1)$ as a fraction with denominator $1$ .

$\frac{20}{3 \cdot 20} + \frac{- (\frac{1}{2} + 1)}{1} + \frac{3}{4} - \frac{3}{5}$

Step 1.4

Multiply $\frac{- (\frac{1}{2} + 1)}{1}$ by $\frac{60}{60}$ .

$\frac{20}{3 \cdot 20} + \frac{- (\frac{1}{2} + 1)}{1} \cdot \frac{60}{60} + \frac{3}{4} - \frac{3}{5}$

Step 1.5

Multiply $\frac{- (\frac{1}{2} + 1)}{1}$ by $\frac{60}{60}$ .

$\frac{20}{3 \cdot 20} + \frac{- (\frac{1}{2} + 1) \cdot 60}{60} + \frac{3}{4} - \frac{3}{5}$

Step 1.6

Multiply $\frac{3}{4}$ by $\frac{15}{15}$ .

$\frac{20}{3 \cdot 20} + \frac{- (\frac{1}{2} + 1) \cdot 60}{60} + \frac{3}{4} \cdot \frac{15}{15} - \frac{3}{5}$

Step 1.7

Multiply $\frac{3}{4}$ by $\frac{15}{15}$ .

$\frac{20}{3 \cdot 20} + \frac{- (\frac{1}{2} + 1) \cdot 60}{60} + \frac{3 \cdot 15}{4 \cdot 15} - \frac{3}{5}$

Step 1.8

Multiply $\frac{3}{5}$ by $\frac{12}{12}$ .

$\frac{20}{3 \cdot 20} + \frac{- (\frac{1}{2} + 1) \cdot 60}{60} + \frac{3 \cdot 15}{4 \cdot 15} - (\frac{3}{5} \cdot \frac{12}{12})$

Step 1.9

Multiply $\frac{3}{5}$ by $\frac{12}{12}$ .

$\frac{20}{3 \cdot 20} + \frac{- (\frac{1}{2} + 1) \cdot 60}{60} + \frac{3 \cdot 15}{4 \cdot 15} - \frac{3 \cdot 12}{5 \cdot 12}$

Step 1.10

Multiply $3$ by $20$ .

$\frac{20}{60} + \frac{- (\frac{1}{2} + 1) \cdot 60}{60} + \frac{3 \cdot 15}{4 \cdot 15} - \frac{3 \cdot 12}{5 \cdot 12}$

Step 1.11

Multiply $4$ by $15$ .

$\frac{20}{60} + \frac{- (\frac{1}{2} + 1) \cdot 60}{60} + \frac{3 \cdot 15}{60} - \frac{3 \cdot 12}{5 \cdot 12}$

Step 1.12

Multiply $5$ by $12$ .

$\frac{20}{60} + \frac{- (\frac{1}{2} + 1) \cdot 60}{60} + \frac{3 \cdot 15}{60} - \frac{3 \cdot 12}{60}$

Step 2

Combine the numerators over the common denominator.

$\frac{20 - (\frac{1}{2} + 1) \cdot 60 + 3 \cdot 15 - 3 \cdot 12}{60}$

Step 3

Simplify each term.

Tap for more steps...

Step 3.1

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

$\frac{20 - (\frac{1}{2} + \frac{2}{2}) \cdot 60 + 3 \cdot 15 - 3 \cdot 12}{60}$

Step 3.2

Combine the numerators over the common denominator.

$\frac{20 - \frac{1 + 2}{2} \cdot 60 + 3 \cdot 15 - 3 \cdot 12}{60}$

Step 3.3

Add $1$ and $2$ .

$\frac{20 - \frac{3}{2} \cdot 60 + 3 \cdot 15 - 3 \cdot 12}{60}$

Step 3.4

Cancel the common factor of $2$ .

Tap for more steps...

Step 3.4.1

Move the leading negative in $- \frac{3}{2}$ into the numerator.

$\frac{20 + \frac{- 3}{2} \cdot 60 + 3 \cdot 15 - 3 \cdot 12}{60}$

Step 3.4.2

Factor $2$ out of $60$ .

$\frac{20 + \frac{- 3}{2} \cdot (2 (30)) + 3 \cdot 15 - 3 \cdot 12}{60}$

Step 3.4.3

Cancel the common factor.

$\frac{20 + \frac{- 3}{2} \cdot (2 \cdot 30) + 3 \cdot 15 - 3 \cdot 12}{60}$

Step 3.4.4

Rewrite the expression.

$\frac{20 - 3 \cdot 30 + 3 \cdot 15 - 3 \cdot 12}{60}$

Step 3.5

Multiply $- 3$ by $30$ .

$\frac{20 - 90 + 3 \cdot 15 - 3 \cdot 12}{60}$

Step 3.6

Multiply $3$ by $15$ .

$\frac{20 - 90 + 45 - 3 \cdot 12}{60}$

Step 3.7

Multiply $- 3$ by $12$ .

$\frac{20 - 90 + 45 - 36}{60}$

Step 4

Simplify the expression.

Tap for more steps...

Step 4.1

Subtract $90$ from $20$ .

$\frac{- 70 + 45 - 36}{60}$

Step 4.2

Add $- 70$ and $45$ .

$\frac{- 25 - 36}{60}$

Step 4.3

Subtract $36$ from $- 25$ .

$\frac{- 61}{60}$

Step 4.4

Move the negative in front of the fraction.

$- \frac{61}{60}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$- \frac{61}{60}$

Decimal Form:

$- 1.01\overline{6}$

Mixed Number Form:

$- 1 \frac{1}{60}$