Basic Math Examples

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

Step 1

Simplify each term.

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Step 1.1

Combine $48 \div 8$ and $5$ .

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

Step 1.2

Multiply $48$ by $5$ .

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

Step 1.3

Divide $240$ by $8$ .

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

Step 1.4

Simplify the numerator.

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Step 1.4.1

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

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

Step 1.4.2

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

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

Step 1.4.3

Combine the numerators over the common denominator.

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

Step 1.4.4

Simplify the numerator.

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Step 1.4.4.1

Multiply $- 2$ by $3$ .

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

Step 1.4.4.2

Subtract $6$ from $30$ .

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

Step 1.4.5

Divide $24$ by $3$ .

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

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:

$34 \frac{1}{2}$