Basic Math Examples

${(3 - \frac{1}{2})}^{- 2} - 0.02 \div \frac{1}{10} + \frac{\sqrt[3]{0} \cdot 7}{8} - 1$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

To write $3$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

${(3 \cdot \frac{2}{2} - \frac{1}{2})}^{- 2} - 0.02 \div \frac{1}{10} + \frac{\sqrt[3]{0} \cdot 7}{8} - 1$

Step 1.2

Combine $3$ and $\frac{2}{2}$ .

${(\frac{3 \cdot 2}{2} - \frac{1}{2})}^{- 2} - 0.02 \div \frac{1}{10} + \frac{\sqrt[3]{0} \cdot 7}{8} - 1$

Step 1.3

Combine the numerators over the common denominator.

${(\frac{3 \cdot 2 - 1}{2})}^{- 2} - 0.02 \div \frac{1}{10} + \frac{\sqrt[3]{0} \cdot 7}{8} - 1$

Step 1.4

Simplify the numerator.

Tap for more steps...

Step 1.4.1

Multiply $3$ by $2$ .

${(\frac{6 - 1}{2})}^{- 2} - 0.02 \div \frac{1}{10} + \frac{\sqrt[3]{0} \cdot 7}{8} - 1$

Step 1.4.2

Subtract $1$ from $6$ .

${(\frac{5}{2})}^{- 2} - 0.02 \div \frac{1}{10} + \frac{\sqrt[3]{0} \cdot 7}{8} - 1$

Step 1.5

Change the sign of the exponent by rewriting the base as its reciprocal.

${(\frac{2}{5})}^{2} - 0.02 \div \frac{1}{10} + \frac{\sqrt[3]{0} \cdot 7}{8} - 1$

Step 1.6

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

$\frac{2^{2}}{5^{2}} - 0.02 \div \frac{1}{10} + \frac{\sqrt[3]{0} \cdot 7}{8} - 1$

Step 1.7

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

$\frac{4}{5^{2}} - 0.02 \div \frac{1}{10} + \frac{\sqrt[3]{0} \cdot 7}{8} - 1$

Step 1.8

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

$\frac{4}{25} - 0.02 \div \frac{1}{10} + \frac{\sqrt[3]{0} \cdot 7}{8} - 1$

Step 1.9

To divide by a fraction, multiply by its reciprocal.

$\frac{4}{25} - (0.02 \cdot 10) + \frac{\sqrt[3]{0} \cdot 7}{8} - 1$

Step 1.10

Multiply $- (0.02 \cdot 10)$ .

Tap for more steps...

Step 1.10.1

Multiply $0.02$ by $10$ .

$\frac{4}{25} - 1 \cdot 0.2 + \frac{\sqrt[3]{0} \cdot 7}{8} - 1$

Step 1.10.2

Multiply $- 1$ by $0.2$ .

$\frac{4}{25} - 0.2 + \frac{\sqrt[3]{0} \cdot 7}{8} - 1$

Step 1.11

Simplify the numerator.

Tap for more steps...

Step 1.11.1

Rewrite $0$ as $0^{3}$ .

$\frac{4}{25} - 0.2 + \frac{\sqrt[3]{0^{3}} \cdot 7}{8} - 1$

Step 1.11.2

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

$\frac{4}{25} - 0.2 + \frac{0 \cdot 7}{8} - 1$

Step 1.12

Multiply $0$ by $7$ .

$\frac{4}{25} - 0.2 + \frac{0}{8} - 1$

Step 1.13

Divide $0$ by $8$ .

$\frac{4}{25} - 0.2 + 0 - 1$

Step 2

To write $- 0.2$ as a fraction with a common denominator, multiply by $\frac{25}{25}$ .

$\frac{4}{25} - 0.2 \cdot \frac{25}{25} + 0 - 1$

Step 3

Combine $- 0.2$ and $\frac{25}{25}$ .

$\frac{4}{25} + \frac{- 0.2 \cdot 25}{25} + 0 - 1$

Step 4

Combine the numerators over the common denominator.

$\frac{4 - 0.2 \cdot 25}{25} + 0 - 1$

Step 5

Simplify the numerator.

Tap for more steps...

Step 5.1

Multiply $- 0.2$ by $25$ .

$\frac{4 - 5}{25} + 0 - 1$

Step 5.2

Subtract $5$ from $4$ .

$\frac{- 1}{25} + 0 - 1$

Step 6

Simplify each term.

Tap for more steps...

Step 6.1

Cancel the common factor of $- 1$ and $25$ .

Tap for more steps...

Step 6.1.1

Rewrite $- 1$ as $1 (- 1)$ .

$\frac{1 (- 1)}{25} + 0 - 1$

Step 6.1.2

Cancel the common factors.

Tap for more steps...

Step 6.1.2.1

Rewrite $25$ as $1 (25)$ .

$\frac{1 \cdot - 1}{1 \cdot 25} + 0 - 1$

Step 6.1.2.2

Cancel the common factor.

$\frac{1 \cdot - 1}{1 \cdot 25} + 0 - 1$

Step 6.1.2.3

Rewrite the expression.

$\frac{- 1}{25} + 0 - 1$

Step 6.2

Move the negative in front of the fraction.

$- \frac{1}{25} + 0 - 1$

Step 7

Add $- \frac{1}{25}$ and $0$ .

$- \frac{1}{25} - 1$

Step 8

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{25}{25}$ .

$- \frac{1}{25} - 1 \cdot \frac{25}{25}$

Step 9

Combine $- 1$ and $\frac{25}{25}$ .

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

Step 10

Combine the numerators over the common denominator.

$\frac{- 1 - 1 \cdot 25}{25}$

Step 11

Simplify the numerator.

Tap for more steps...

Step 11.1

Multiply $- 1$ by $25$ .

$\frac{- 1 - 25}{25}$

Step 11.2

Subtract $25$ from $- 1$ .

$\frac{- 26}{25}$

Step 12

Move the negative in front of the fraction.

$- \frac{26}{25}$

Step 13

The result can be shown in multiple forms.

Exact Form:

$- \frac{26}{25}$

Decimal Form:

$- 1.04$

Mixed Number Form:

$- 1 \frac{1}{25}$