Basic Math Examples

$n = (15.9 - 3) \div \cos (30) \cdot 1.5$

Step 1

Subtract $3$ from $15.9$ .

$n = 12.9 \div \cos (30) \cdot 1.5$

Step 2

The exact value of $\cos (30)$ is $\frac{\sqrt{3}}{2}$ .

$n = 12.9 \div \frac{\sqrt{3}}{2} \cdot 1.5$

Step 3

To divide by a fraction, multiply by its reciprocal.

$n = 12.9 \frac{2}{\sqrt{3}} \cdot 1.5$

Step 4

Multiply $\frac{2}{\sqrt{3}}$ by $\frac{\sqrt{3}}{\sqrt{3}}$ .

$n = 12.9 (\frac{2}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}}) \cdot 1.5$

Step 5

Combine and simplify the denominator.

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Step 5.1

Multiply $\frac{2}{\sqrt{3}}$ by $\frac{\sqrt{3}}{\sqrt{3}}$ .

$n = 12.9 \frac{2 \sqrt{3}}{\sqrt{3} \sqrt{3}} \cdot 1.5$

Step 5.2

Raise $\sqrt{3}$ to the power of $1$ .

$n = 12.9 \frac{2 \sqrt{3}}{{\sqrt{3}}^{1} \sqrt{3}} \cdot 1.5$

Step 5.3

Raise $\sqrt{3}$ to the power of $1$ .

$n = 12.9 \frac{2 \sqrt{3}}{{\sqrt{3}}^{1} {\sqrt{3}}^{1}} \cdot 1.5$

Step 5.4

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

$n = 12.9 \frac{2 \sqrt{3}}{{\sqrt{3}}^{1 + 1}} \cdot 1.5$

Step 5.5

Add $1$ and $1$ .

$n = 12.9 \frac{2 \sqrt{3}}{{\sqrt{3}}^{2}} \cdot 1.5$

Step 5.6

Rewrite ${\sqrt{3}}^{2}$ as $3$ .

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Step 5.6.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3}$ as $3^{\frac{1}{2}}$ .

$n = 12.9 \frac{2 \sqrt{3}}{{(3^{\frac{1}{2}})}^{2}} \cdot 1.5$

Step 5.6.2

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

$n = 12.9 \frac{2 \sqrt{3}}{3^{\frac{1}{2} \cdot 2}} \cdot 1.5$

Step 5.6.3

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

$n = 12.9 \frac{2 \sqrt{3}}{3^{\frac{2}{2}}} \cdot 1.5$

Step 5.6.4

Cancel the common factor of $2$ .

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Step 5.6.4.1

Cancel the common factor.

$n = 12.9 \frac{2 \sqrt{3}}{3^{\frac{2}{2}}} \cdot 1.5$

Step 5.6.4.2

Rewrite the expression.

$n = 12.9 \frac{2 \sqrt{3}}{3^{1}} \cdot 1.5$

Step 5.6.5

Evaluate the exponent.

$n = 12.9 \frac{2 \sqrt{3}}{3} \cdot 1.5$

Step 6

Multiply $12.9 \frac{2 \sqrt{3}}{3}$ .

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Step 6.1

Combine $12.9$ and $\frac{2 \sqrt{3}}{3}$ .

$n = \frac{12.9 (2 \sqrt{3})}{3} \cdot 1.5$

Step 6.2

Multiply $2$ by $12.9$ .

$n = \frac{25.8 \sqrt{3}}{3} \cdot 1.5$

Step 6.3

Multiply $25.8$ by $\sqrt{3}$ .

$n = \frac{44.68691083}{3} \cdot 1.5$

Step 7

Cancel the common factor of $1.5$ .

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Step 7.1

Factor $1.5$ out of $3$ .

$n = \frac{44.68691083}{1.5 (2)} \cdot 1.5$

Step 7.2

Cancel the common factor.

$n = \frac{44.68691083}{1.5 \cdot 2} \cdot 1.5$

Step 7.3

Rewrite the expression.

$n = \frac{44.68691083}{2}$

Step 8

Divide $44.68691083$ by $2$ .

$n = 22.34345541$