Basic Math Examples

92 - {(48 \div 8 \cdot 5 \div 3 - 2)}^{2} \div 16 \div 4 \cdot 5 \div 2 \cdot 7 - 4 \cdot 20 \div \sqrt{4}

$92 - {(48 \div 8 \cdot 5 \div 3 - 2)}^{2} \div 16 \div 4 \cdot 5 \div 2 \cdot 7 - 4 \cdot 20 \div \sqrt{4}$

Step 1

Simplify each term.

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Step 1.1

Combine

48 \div 8

$48 \div 8$ and

5

$5$ .

92 - {(\frac{48 \cdot 5}{8} \div 3 - 2)}^{2} \div 16 \div 4 \cdot 5 \div 2 \cdot 7 - 4 \cdot 20 \div \sqrt{4}

$92 - {(\frac{48 \cdot 5}{8} \div 3 - 2)}^{2} \div 16 \div 4 \cdot 5 \div 2 \cdot 7 - 4 \cdot 20 \div \sqrt{4}$

Step 1.2

Multiply

48

$48$ by

5

$5$ .

92 - {(\frac{240}{8} \div 3 - 2)}^{2} \div 16 \div 4 \cdot 5 \div 2 \cdot 7 - 4 \cdot 20 \div \sqrt{4}

$92 - {(\frac{240}{8} \div 3 - 2)}^{2} \div 16 \div 4 \cdot 5 \div 2 \cdot 7 - 4 \cdot 20 \div \sqrt{4}$

Step 1.3

Divide

240

$240$ by

8

$8$ .

92 - {(30 \div 3 - 2)}^{2} \div 16 \div 4 \cdot 5 \div 2 \cdot 7 - 4 \cdot 20 \div \sqrt{4}

$92 - {(30 \div 3 - 2)}^{2} \div 16 \div 4 \cdot 5 \div 2 \cdot 7 - 4 \cdot 20 \div \sqrt{4}$

Step 1.4

Simplify the numerator.

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Step 1.4.1

To write

- 2

$- 2$ as a fraction with a common denominator, multiply by

\frac{3}{3}

$\frac{3}{3}$ .

92 - {(30 \div 3 - 2 \cdot \frac{3}{3})}^{2} \div 16 \div 4 \cdot 5 \div 2 \cdot 7 - 4 \cdot 20 \div \sqrt{4}

$92 - {(30 \div 3 - 2 \cdot \frac{3}{3})}^{2} \div 16 \div 4 \cdot 5 \div 2 \cdot 7 - 4 \cdot 20 \div \sqrt{4}$

Step 1.4.2

Combine

- 2

$- 2$ and

\frac{3}{3}

$\frac{3}{3}$ .

92 - {(30 \div 3 + \frac{- 2 \cdot 3}{3})}^{2} \div 16 \div 4 \cdot 5 \div 2 \cdot 7 - 4 \cdot 20 \div \sqrt{4}

$92 - {(30 \div 3 + \frac{- 2 \cdot 3}{3})}^{2} \div 16 \div 4 \cdot 5 \div 2 \cdot 7 - 4 \cdot 20 \div \sqrt{4}$

Step 1.4.3

Combine the numerators over the common denominator.

92 - {((30 - 2 \cdot 3) \div 3)}^{2} \div 16 \div 4 \cdot 5 \div 2 \cdot 7 - 4 \cdot 20 \div \sqrt{4}

$92 - {((30 - 2 \cdot 3) \div 3)}^{2} \div 16 \div 4 \cdot 5 \div 2 \cdot 7 - 4 \cdot 20 \div \sqrt{4}$

Step 1.4.4

Simplify the numerator.

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Step 1.4.4.1

Multiply

- 2

$- 2$ by

3

$3$ .

92 - {((30 - 6) \div 3)}^{2} \div 16 \div 4 \cdot 5 \div 2 \cdot 7 - 4 \cdot 20 \div \sqrt{4}

$92 - {((30 - 6) \div 3)}^{2} \div 16 \div 4 \cdot 5 \div 2 \cdot 7 - 4 \cdot 20 \div \sqrt{4}$

Step 1.4.4.2

Subtract

6

$6$ from

30

$30$ .

92 - {(24 \div 3)}^{2} \div 16 \div 4 \cdot 5 \div 2 \cdot 7 - 4 \cdot 20 \div \sqrt{4}

$92 - {(24 \div 3)}^{2} \div 16 \div 4 \cdot 5 \div 2 \cdot 7 - 4 \cdot 20 \div \sqrt{4}$

92 - {(24 \div 3)}^{2} \div 16 \div 4 \cdot 5 \div 2 \cdot 7 - 4 \cdot 20 \div \sqrt{4}

$92 - {(24 \div 3)}^{2} \div 16 \div 4 \cdot 5 \div 2 \cdot 7 - 4 \cdot 20 \div \sqrt{4}$

Step 1.4.5

Divide

24

$24$ by

3

$3$ .

92 - 8^{2} \div 16 \div 4 \cdot 5 \div 2 \cdot 7 - 4 \cdot 20 \div \sqrt{4}

$92 - 8^{2} \div 16 \div 4 \cdot 5 \div 2 \cdot 7 - 4 \cdot 20 \div \sqrt{4}$

Step 1.4.6

Raise

$8$ to the power of

$2$ .

$92 - 64 \div 16 \div 4 \cdot 5 \div 2 \cdot 7 - 4 \cdot 20 \div \sqrt{4}$

Step 1.5

Divide

$64$ by

$16$ .

$92 - 4 \div 4 \cdot 5 \div 2 \cdot 7 - 4 \cdot 20 \div \sqrt{4}$

Step 1.6

Combine

$4 \div 4$ and

$5$ .

$92 - \frac{4 \cdot 5}{4} \div 2 \cdot 7 - 4 \cdot 20 \div \sqrt{4}$

Step 1.7

Multiply

$4$ by

$5$ .

$92 - \frac{20}{4} \div 2 \cdot 7 - 4 \cdot 20 \div \sqrt{4}$

Step 1.8

Divide

$20$ by

$4$ .

$92 - 5 \div 2 \cdot 7 - 4 \cdot 20 \div \sqrt{4}$

Step 1.9

Rewrite the division as a fraction.

$92 - \frac{5}{2} \cdot 7 - 4 \cdot 20 \div \sqrt{4}$

Step 1.10

Multiply

$- \frac{5}{2} \cdot 7$ .

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Step 1.10.1

Multiply

$7$ by

$- 1$ .

$92 - 7 (\frac{5}{2}) - 4 \cdot 20 \div \sqrt{4}$

Step 1.10.2

Combine

$- 7$ and

$\frac{5}{2}$ .

$92 + \frac{- 7 \cdot 5}{2} - 4 \cdot 20 \div \sqrt{4}$

Step 1.10.3

Multiply

$- 7$ by

$5$ .

$92 + \frac{- 35}{2} - 4 \cdot 20 \div \sqrt{4}$

Step 1.11

Move the negative in front of the fraction.

$92 - \frac{35}{2} - 4 \cdot 20 \div \sqrt{4}$

Step 1.12

Rewrite the division as a fraction.

$92 - \frac{35}{2} - \frac{4 \cdot 20}{\sqrt{4}}$

Step 1.13

Multiply

$4$ by

$20$ .

$92 - \frac{35}{2} - \frac{80}{\sqrt{4}}$

Step 1.14

Simplify the denominator.

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Step 1.14.1

Rewrite

$4$ as

$2^{2}$ .

$92 - \frac{35}{2} - \frac{80}{\sqrt{2^{2}}}$

Step 1.14.2

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

$92 - \frac{35}{2} - \frac{80}{2}$

Step 1.15

Divide

$80$ by

$2$ .

$92 - \frac{35}{2} - 1 \cdot 40$

Step 1.16

Multiply

$- 1$ by

$40$ .

$92 - \frac{35}{2} - 40$

Step 2

Find the common denominator.

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Step 2.1

Write

$92$ as a fraction with denominator

$1$ .

$\frac{92}{1} - \frac{35}{2} - 40$

Step 2.2

Multiply

$\frac{92}{1}$ by

$\frac{2}{2}$ .

$\frac{92}{1} \cdot \frac{2}{2} - \frac{35}{2} - 40$

Step 2.3

Multiply

$\frac{92}{1}$ by

$\frac{2}{2}$ .

$\frac{92 \cdot 2}{2} - \frac{35}{2} - 40$

Step 2.4

Write

$- 40$ as a fraction with denominator

$1$ .

$\frac{92 \cdot 2}{2} - \frac{35}{2} + \frac{- 40}{1}$

Step 2.5

Multiply

$\frac{- 40}{1}$ by

$\frac{2}{2}$ .

$\frac{92 \cdot 2}{2} - \frac{35}{2} + \frac{- 40}{1} \cdot \frac{2}{2}$

Step 2.6

Multiply

$\frac{- 40}{1}$ by

$\frac{2}{2}$ .

$\frac{92 \cdot 2}{2} - \frac{35}{2} + \frac{- 40 \cdot 2}{2}$

Step 3

Combine the numerators over the common denominator.

$\frac{92 \cdot 2 - 35 - 40 \cdot 2}{2}$

Step 4

Simplify each term.

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Step 4.1

Multiply

$92$ by

$2$ .

$\frac{184 - 35 - 40 \cdot 2}{2}$

Step 4.2

Multiply

$- 40$ by

$2$ .

$\frac{184 - 35 - 80}{2}$

Step 5

Simplify by subtracting numbers.

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Step 5.1

Subtract

$35$ from

$184$ .

$\frac{149 - 80}{2}$

Step 5.2

Subtract

$80$ from

$149$ .

$\frac{69}{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{69}{2}$

Decimal Form:

$34.5$

Mixed Number Form:

$34 \frac{1}{2}$