Basic Math Examples

${(\frac{1}{5} - \frac{3}{5})}^{2} - (\frac{1}{2} - \frac{2}{5}) + \sqrt{\frac{1}{9}}$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Combine the numerators over the common denominator.

${(\frac{1 - 3}{5})}^{2} - (\frac{1}{2} - \frac{2}{5}) + \sqrt{\frac{1}{9}}$

Step 1.2

Subtract $3$ from $1$ .

${(\frac{- 2}{5})}^{2} - (\frac{1}{2} - \frac{2}{5}) + \sqrt{\frac{1}{9}}$

Step 1.3

Move the negative in front of the fraction.

${(- \frac{2}{5})}^{2} - (\frac{1}{2} - \frac{2}{5}) + \sqrt{\frac{1}{9}}$

Step 1.4

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Tap for more steps...

Step 1.4.1

Apply the product rule to $- \frac{2}{5}$ .

${(- 1)}^{2} {(\frac{2}{5})}^{2} - (\frac{1}{2} - \frac{2}{5}) + \sqrt{\frac{1}{9}}$

Step 1.4.2

Apply the product rule to $\frac{2}{5}$ .

${(- 1)}^{2} \frac{2^{2}}{5^{2}} - (\frac{1}{2} - \frac{2}{5}) + \sqrt{\frac{1}{9}}$

Step 1.5

Raise $- 1$ to the power of $2$ .

$1 \frac{2^{2}}{5^{2}} - (\frac{1}{2} - \frac{2}{5}) + \sqrt{\frac{1}{9}}$

Step 1.6

Multiply $\frac{2^{2}}{5^{2}}$ by $1$ .

$\frac{2^{2}}{5^{2}} - (\frac{1}{2} - \frac{2}{5}) + \sqrt{\frac{1}{9}}$

Step 1.7

Raise $2$ to the power of $2$ .

$\frac{4}{5^{2}} - (\frac{1}{2} - \frac{2}{5}) + \sqrt{\frac{1}{9}}$

Step 1.8

Raise $5$ to the power of $2$ .

$\frac{4}{25} - (\frac{1}{2} - \frac{2}{5}) + \sqrt{\frac{1}{9}}$

Step 1.9

To write $\frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{4}{25} - (\frac{1}{2} \cdot \frac{5}{5} - \frac{2}{5}) + \sqrt{\frac{1}{9}}$

Step 1.10

To write $- \frac{2}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{4}{25} - (\frac{1}{2} \cdot \frac{5}{5} - \frac{2}{5} \cdot \frac{2}{2}) + \sqrt{\frac{1}{9}}$

Step 1.11

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 1.11.1

Multiply $\frac{1}{2}$ by $\frac{5}{5}$ .

$\frac{4}{25} - (\frac{5}{2 \cdot 5} - \frac{2}{5} \cdot \frac{2}{2}) + \sqrt{\frac{1}{9}}$

Step 1.11.2

Multiply $2$ by $5$ .

$\frac{4}{25} - (\frac{5}{10} - \frac{2}{5} \cdot \frac{2}{2}) + \sqrt{\frac{1}{9}}$

Step 1.11.3

Multiply $\frac{2}{5}$ by $\frac{2}{2}$ .

$\frac{4}{25} - (\frac{5}{10} - \frac{2 \cdot 2}{5 \cdot 2}) + \sqrt{\frac{1}{9}}$

Step 1.11.4

Multiply $5$ by $2$ .

$\frac{4}{25} - (\frac{5}{10} - \frac{2 \cdot 2}{10}) + \sqrt{\frac{1}{9}}$

Step 1.12

Combine the numerators over the common denominator.

$\frac{4}{25} - \frac{5 - 2 \cdot 2}{10} + \sqrt{\frac{1}{9}}$

Step 1.13

Simplify the numerator.

Tap for more steps...

Step 1.13.1

Multiply $- 2$ by $2$ .

$\frac{4}{25} - \frac{5 - 4}{10} + \sqrt{\frac{1}{9}}$

Step 1.13.2

Subtract $4$ from $5$ .

$\frac{4}{25} - \frac{1}{10} + \sqrt{\frac{1}{9}}$

Step 1.14

Rewrite $\sqrt{\frac{1}{9}}$ as $\frac{\sqrt{1}}{\sqrt{9}}$ .

$\frac{4}{25} - \frac{1}{10} + \frac{\sqrt{1}}{\sqrt{9}}$

Step 1.15

Any root of $1$ is $1$ .

$\frac{4}{25} - \frac{1}{10} + \frac{1}{\sqrt{9}}$

Step 1.16

Simplify the denominator.

Tap for more steps...

Step 1.16.1

Rewrite $9$ as $3^{2}$ .

$\frac{4}{25} - \frac{1}{10} + \frac{1}{\sqrt{3^{2}}}$

Step 1.16.2

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

$\frac{4}{25} - \frac{1}{10} + \frac{1}{3}$

Step 2

Find the common denominator.

Tap for more steps...

Step 2.1

Multiply $\frac{4}{25}$ by $\frac{6}{6}$ .

$\frac{4}{25} \cdot \frac{6}{6} - \frac{1}{10} + \frac{1}{3}$

Step 2.2

Multiply $\frac{4}{25}$ by $\frac{6}{6}$ .

$\frac{4 \cdot 6}{25 \cdot 6} - \frac{1}{10} + \frac{1}{3}$

Step 2.3

Multiply $\frac{1}{10}$ by $\frac{15}{15}$ .

$\frac{4 \cdot 6}{25 \cdot 6} - (\frac{1}{10} \cdot \frac{15}{15}) + \frac{1}{3}$

Step 2.4

Multiply $\frac{1}{10}$ by $\frac{15}{15}$ .

$\frac{4 \cdot 6}{25 \cdot 6} - \frac{15}{10 \cdot 15} + \frac{1}{3}$

Step 2.5

Multiply $\frac{1}{3}$ by $\frac{50}{50}$ .

$\frac{4 \cdot 6}{25 \cdot 6} - \frac{15}{10 \cdot 15} + \frac{1}{3} \cdot \frac{50}{50}$

Step 2.6

Multiply $\frac{1}{3}$ by $\frac{50}{50}$ .

$\frac{4 \cdot 6}{25 \cdot 6} - \frac{15}{10 \cdot 15} + \frac{50}{3 \cdot 50}$

Step 2.7

Reorder the factors of $25 \cdot 6$ .

$\frac{4 \cdot 6}{6 \cdot 25} - \frac{15}{10 \cdot 15} + \frac{50}{3 \cdot 50}$

Step 2.8

Multiply $6$ by $25$ .

$\frac{4 \cdot 6}{150} - \frac{15}{10 \cdot 15} + \frac{50}{3 \cdot 50}$

Step 2.9

Multiply $10$ by $15$ .

$\frac{4 \cdot 6}{150} - \frac{15}{150} + \frac{50}{3 \cdot 50}$

Step 2.10

Multiply $3$ by $50$ .

$\frac{4 \cdot 6}{150} - \frac{15}{150} + \frac{50}{150}$

Step 3

Combine the numerators over the common denominator.

$\frac{4 \cdot 6 - 15 + 50}{150}$

Step 4

Simplify the expression.

Tap for more steps...

Step 4.1

Multiply $4$ by $6$ .

$\frac{24 - 15 + 50}{150}$

Step 4.2

Subtract $15$ from $24$ .

$\frac{9 + 50}{150}$

Step 4.3

Add $9$ and $50$ .

$\frac{59}{150}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{59}{150}$

Decimal Form:

$0.39\overline{3}$