Basic Math Examples

$\frac{47.4 - 50}{13.5} \div \sqrt{23}$

Step 1

Rewrite the division as a fraction.

$\frac{\frac{47.4 - 50}{13.5}}{\sqrt{23}}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$\frac{47.4 - 50}{13.5} \cdot \frac{1}{\sqrt{23}}$

Step 3

Subtract $50$ from $47.4$ .

$\frac{- 2.6}{13.5} \cdot \frac{1}{\sqrt{23}}$

Step 4

Divide $- 2.6$ by $13.5$ .

$- 0.1\overline{925} \frac{1}{\sqrt{23}}$

Step 5

Multiply $\frac{1}{\sqrt{23}}$ by $\frac{\sqrt{23}}{\sqrt{23}}$ .

$- 0.1\overline{925} (\frac{1}{\sqrt{23}} \cdot \frac{\sqrt{23}}{\sqrt{23}})$

Step 6

Combine and simplify the denominator.

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Step 6.1

Multiply $\frac{1}{\sqrt{23}}$ by $\frac{\sqrt{23}}{\sqrt{23}}$ .

$- 0.1\overline{925} \frac{\sqrt{23}}{\sqrt{23} \sqrt{23}}$

Step 6.2

Raise $\sqrt{23}$ to the power of $1$ .

$- 0.1\overline{925} \frac{\sqrt{23}}{{\sqrt{23}}^{1} \sqrt{23}}$

Step 6.3

Raise $\sqrt{23}$ to the power of $1$ .

$- 0.1\overline{925} \frac{\sqrt{23}}{{\sqrt{23}}^{1} {\sqrt{23}}^{1}}$

Step 6.4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$- 0.1\overline{925} \frac{\sqrt{23}}{{\sqrt{23}}^{1 + 1}}$

Step 6.5

Add $1$ and $1$ .

$- 0.1\overline{925} \frac{\sqrt{23}}{{\sqrt{23}}^{2}}$

Step 6.6

Rewrite ${\sqrt{23}}^{2}$ as $23$ .

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Step 6.6.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{23}$ as $23^{\frac{1}{2}}$ .

$- 0.1\overline{925} \frac{\sqrt{23}}{{(23^{\frac{1}{2}})}^{2}}$

Step 6.6.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$- 0.1\overline{925} \frac{\sqrt{23}}{23^{\frac{1}{2} \cdot 2}}$

Step 6.6.3

Combine $\frac{1}{2}$ and $2$ .

$- 0.1\overline{925} \frac{\sqrt{23}}{23^{\frac{2}{2}}}$

Step 6.6.4

Cancel the common factor of $2$ .

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Step 6.6.4.1

Cancel the common factor.

$- 0.1\overline{925} \frac{\sqrt{23}}{23^{\frac{2}{2}}}$

Step 6.6.4.2

Rewrite the expression.

$- 0.1\overline{925} \frac{\sqrt{23}}{23^{1}}$

Step 6.6.5

Evaluate the exponent.

$- 0.1\overline{925} \frac{\sqrt{23}}{23}$

Step 7

Multiply $- 0.1\overline{925} \frac{\sqrt{23}}{23}$ .

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Step 7.1

Combine $- 0.1\overline{925}$ and $\frac{\sqrt{23}}{23}$ .

$\frac{- 0.1\overline{925} \sqrt{23}}{23}$

Step 7.2

Multiply $- 0.1\overline{925}$ by $\sqrt{23}$ .

$\frac{- 0.92364162}{23}$

Step 8

Divide $- 0.92364162$ by $23$ .

$- 0.04015833$