Basic Math Examples

$(\frac{1}{1} - \frac{5}{3}) \cdot \frac{3}{4} + \frac{1}{2} - \sqrt{\frac{1}{25}}$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Divide $1$ by $1$ .

$(1 - \frac{5}{3}) \cdot \frac{3}{4} + \frac{1}{2} - \sqrt{\frac{1}{25}}$

Step 1.2

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

$(\frac{3}{3} - \frac{5}{3}) \cdot \frac{3}{4} + \frac{1}{2} - \sqrt{\frac{1}{25}}$

Step 1.3

Combine the numerators over the common denominator.

$\frac{3 - 5}{3} \cdot \frac{3}{4} + \frac{1}{2} - \sqrt{\frac{1}{25}}$

Step 1.4

Subtract $5$ from $3$ .

$\frac{- 2}{3} \cdot \frac{3}{4} + \frac{1}{2} - \sqrt{\frac{1}{25}}$

Step 1.5

Cancel the common factor of $2$ .

Tap for more steps...

Step 1.5.1

Factor $2$ out of $- 2$ .

$\frac{2 (- 1)}{3} \cdot \frac{3}{4} + \frac{1}{2} - \sqrt{\frac{1}{25}}$

Step 1.5.2

Factor $2$ out of $4$ .

$\frac{2 \cdot - 1}{3} \cdot \frac{3}{2 \cdot 2} + \frac{1}{2} - \sqrt{\frac{1}{25}}$

Step 1.5.3

Cancel the common factor.

$\frac{2 \cdot - 1}{3} \cdot \frac{3}{2 \cdot 2} + \frac{1}{2} - \sqrt{\frac{1}{25}}$

Step 1.5.4

Rewrite the expression.

$\frac{- 1}{3} \cdot \frac{3}{2} + \frac{1}{2} - \sqrt{\frac{1}{25}}$

Step 1.6

Cancel the common factor of $3$ .

Tap for more steps...

Step 1.6.1

Cancel the common factor.

$\frac{- 1}{3} \cdot \frac{3}{2} + \frac{1}{2} - \sqrt{\frac{1}{25}}$

Step 1.6.2

Rewrite the expression.

$- 1 \cdot \frac{1}{2} + \frac{1}{2} - \sqrt{\frac{1}{25}}$

Step 1.7

Rewrite $- 1 (\frac{1}{2})$ as $- (\frac{1}{2})$ .

$- (\frac{1}{2}) + \frac{1}{2} - \sqrt{\frac{1}{25}}$

Step 1.8

Rewrite $\sqrt{\frac{1}{25}}$ as $\frac{\sqrt{1}}{\sqrt{25}}$ .

$- \frac{1}{2} + \frac{1}{2} - \frac{\sqrt{1}}{\sqrt{25}}$

Step 1.9

Any root of $1$ is $1$ .

$- \frac{1}{2} + \frac{1}{2} - \frac{1}{\sqrt{25}}$

Step 1.10

Simplify the denominator.

Tap for more steps...

Step 1.10.1

Rewrite $25$ as $5^{2}$ .

$- \frac{1}{2} + \frac{1}{2} - \frac{1}{\sqrt{5^{2}}}$

Step 1.10.2

Pull terms out from under the radical, assuming positive real numbers.

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

Step 2

Combine fractions.

Tap for more steps...

Step 2.1

Combine the numerators over the common denominator.

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

Step 2.2

Add $- 1$ and $1$ .

$\frac{0}{2} + \frac{- 1}{5}$

Step 3

Simplify each term.

Tap for more steps...

Step 3.1

Divide $0$ by $2$ .

$0 + \frac{- 1}{5}$

Step 3.2

Move the negative in front of the fraction.

$0 - \frac{1}{5}$

Step 4

Subtract $\frac{1}{5}$ from $0$ .

$- \frac{1}{5}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$- \frac{1}{5}$

Decimal Form:

$- 0.2$