Basic Math Examples

$6 + 3 - 2 - 6 \div 2 + 3^{2} + 10 - \sqrt{16} - (8 - 4) \cdot 2 + 5 \cdot 2 + 2^{5} \div 4 + 10$

Step 1

Find the common denominator.

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Step 1.1

Write $6$ as a fraction with denominator $1$ .

$\frac{6}{1} + 3 - 2 - 6 \div 2 + 3^{2} + 10 - \sqrt{16} - (8 - 4) \cdot 2 + 5 \cdot 2 + 2^{5} \div 4 + 10$

Step 1.2

Multiply $\frac{6}{1}$ by $\frac{4}{4}$ .

$\frac{6}{1} \cdot \frac{4}{4} + 3 - 2 - 6 \div 2 + 3^{2} + 10 - \sqrt{16} - (8 - 4) \cdot 2 + 5 \cdot 2 + 2^{5} \div 4 + 10$

Step 1.3

Multiply $\frac{6}{1}$ by $\frac{4}{4}$ .

$\frac{6 \cdot 4}{4} + 3 - 2 - 6 \div 2 + 3^{2} + 10 - \sqrt{16} - (8 - 4) \cdot 2 + 5 \cdot 2 + 2^{5} \div 4 + 10$

Step 1.4

Write $3$ as a fraction with denominator $1$ .

$\frac{6 \cdot 4}{4} + \frac{3}{1} - 2 - 6 \div 2 + 3^{2} + 10 - \sqrt{16} - (8 - 4) \cdot 2 + 5 \cdot 2 + 2^{5} \div 4 + 10$

Step 1.5

Multiply $\frac{3}{1}$ by $\frac{4}{4}$ .

$\frac{6 \cdot 4}{4} + \frac{3}{1} \cdot \frac{4}{4} - 2 - 6 \div 2 + 3^{2} + 10 - \sqrt{16} - (8 - 4) \cdot 2 + 5 \cdot 2 + 2^{5} \div 4 + 10$

Step 1.6

Multiply $\frac{3}{1}$ by $\frac{4}{4}$ .

$\frac{6 \cdot 4}{4} + \frac{3 \cdot 4}{4} - 2 - 6 \div 2 + 3^{2} + 10 - \sqrt{16} - (8 - 4) \cdot 2 + 5 \cdot 2 + 2^{5} \div 4 + 10$

Step 1.7

Write $- 2$ as a fraction with denominator $1$ .

$\frac{6 \cdot 4}{4} + \frac{3 \cdot 4}{4} + \frac{- 2}{1} - 6 \div 2 + 3^{2} + 10 - \sqrt{16} - (8 - 4) \cdot 2 + 5 \cdot 2 + 2^{5} \div 4 + 10$

Step 1.8

Multiply $\frac{- 2}{1}$ by $\frac{4}{4}$ .

$\frac{6 \cdot 4}{4} + \frac{3 \cdot 4}{4} + \frac{- 2}{1} \cdot \frac{4}{4} - 6 \div 2 + 3^{2} + 10 - \sqrt{16} - (8 - 4) \cdot 2 + 5 \cdot 2 + 2^{5} \div 4 + 10$

Step 1.9

Multiply $\frac{- 2}{1}$ by $\frac{4}{4}$ .

$\frac{6 \cdot 4}{4} + \frac{3 \cdot 4}{4} + \frac{- 2 \cdot 4}{4} - 6 \div 2 + 3^{2} + 10 - \sqrt{16} - (8 - 4) \cdot 2 + 5 \cdot 2 + 2^{5} \div 4 + 10$

Step 1.10

Multiply $6 \div 2$ by $\frac{2}{2}$ .

$\frac{6 \cdot 4}{4} + \frac{3 \cdot 4}{4} + \frac{- 2 \cdot 4}{4} - (6 \div 2 \cdot \frac{2}{2}) + 3^{2} + 10 - \sqrt{16} - (8 - 4) \cdot 2 + 5 \cdot 2 + 2^{5} \div 4 + 10$

Step 1.11

Multiply $6 \div 2$ by $\frac{2}{2}$ .

$\frac{6 \cdot 4}{4} + \frac{3 \cdot 4}{4} + \frac{- 2 \cdot 4}{4} - \frac{6 \cdot 2}{2 \cdot 2} + 3^{2} + 10 - \sqrt{16} - (8 - 4) \cdot 2 + 5 \cdot 2 + 2^{5} \div 4 + 10$

Step 1.12

Write $3^{2}$ as a fraction with denominator $1$ .

$\frac{6 \cdot 4}{4} + \frac{3 \cdot 4}{4} + \frac{- 2 \cdot 4}{4} - \frac{6 \cdot 2}{2 \cdot 2} + \frac{3^{2}}{1} + 10 - \sqrt{16} - (8 - 4) \cdot 2 + 5 \cdot 2 + 2^{5} \div 4 + 10$

Step 1.13

Multiply $\frac{3^{2}}{1}$ by $\frac{4}{4}$ .

$\frac{6 \cdot 4}{4} + \frac{3 \cdot 4}{4} + \frac{- 2 \cdot 4}{4} - \frac{6 \cdot 2}{2 \cdot 2} + \frac{3^{2}}{1} \cdot \frac{4}{4} + 10 - \sqrt{16} - (8 - 4) \cdot 2 + 5 \cdot 2 + 2^{5} \div 4 + 10$

Step 1.14

Multiply $\frac{3^{2}}{1}$ by $\frac{4}{4}$ .

$\frac{6 \cdot 4}{4} + \frac{3 \cdot 4}{4} + \frac{- 2 \cdot 4}{4} - \frac{6 \cdot 2}{2 \cdot 2} + \frac{3^{2} \cdot 4}{4} + 10 - \sqrt{16} - (8 - 4) \cdot 2 + 5 \cdot 2 + 2^{5} \div 4 + 10$

Step 1.15

Write $10$ as a fraction with denominator $1$ .

$\frac{6 \cdot 4}{4} + \frac{3 \cdot 4}{4} + \frac{- 2 \cdot 4}{4} - \frac{6 \cdot 2}{2 \cdot 2} + \frac{3^{2} \cdot 4}{4} + \frac{10}{1} - \sqrt{16} - (8 - 4) \cdot 2 + 5 \cdot 2 + 2^{5} \div 4 + 10$

Step 1.16

Multiply $\frac{10}{1}$ by $\frac{4}{4}$ .

$\frac{6 \cdot 4}{4} + \frac{3 \cdot 4}{4} + \frac{- 2 \cdot 4}{4} - \frac{6 \cdot 2}{2 \cdot 2} + \frac{3^{2} \cdot 4}{4} + \frac{10}{1} \cdot \frac{4}{4} - \sqrt{16} - (8 - 4) \cdot 2 + 5 \cdot 2 + 2^{5} \div 4 + 10$

Step 1.17

Multiply $\frac{10}{1}$ by $\frac{4}{4}$ .

$\frac{6 \cdot 4}{4} + \frac{3 \cdot 4}{4} + \frac{- 2 \cdot 4}{4} - \frac{6 \cdot 2}{2 \cdot 2} + \frac{3^{2} \cdot 4}{4} + \frac{10 \cdot 4}{4} - \sqrt{16} - (8 - 4) \cdot 2 + 5 \cdot 2 + 2^{5} \div 4 + 10$

Step 1.18

Write $- \sqrt{16}$ as a fraction with denominator $1$ .

$\frac{6 \cdot 4}{4} + \frac{3 \cdot 4}{4} + \frac{- 2 \cdot 4}{4} - \frac{6 \cdot 2}{2 \cdot 2} + \frac{3^{2} \cdot 4}{4} + \frac{10 \cdot 4}{4} + \frac{- \sqrt{16}}{1} - (8 - 4) \cdot 2 + 5 \cdot 2 + 2^{5} \div 4 + 10$

Step 1.19

Multiply $\frac{- \sqrt{16}}{1}$ by $\frac{4}{4}$ .

$\frac{6 \cdot 4}{4} + \frac{3 \cdot 4}{4} + \frac{- 2 \cdot 4}{4} - \frac{6 \cdot 2}{2 \cdot 2} + \frac{3^{2} \cdot 4}{4} + \frac{10 \cdot 4}{4} + \frac{- \sqrt{16}}{1} \cdot \frac{4}{4} - (8 - 4) \cdot 2 + 5 \cdot 2 + 2^{5} \div 4 + 10$

Step 1.20

Multiply $\frac{- \sqrt{16}}{1}$ by $\frac{4}{4}$ .

$\frac{6 \cdot 4}{4} + \frac{3 \cdot 4}{4} + \frac{- 2 \cdot 4}{4} - \frac{6 \cdot 2}{2 \cdot 2} + \frac{3^{2} \cdot 4}{4} + \frac{10 \cdot 4}{4} + \frac{- \sqrt{16} \cdot 4}{4} - (8 - 4) \cdot 2 + 5 \cdot 2 + 2^{5} \div 4 + 10$

Step 1.21

Write $- (8 - 4) \cdot 2$ as a fraction with denominator $1$ .

$\frac{6 \cdot 4}{4} + \frac{3 \cdot 4}{4} + \frac{- 2 \cdot 4}{4} - \frac{6 \cdot 2}{2 \cdot 2} + \frac{3^{2} \cdot 4}{4} + \frac{10 \cdot 4}{4} + \frac{- \sqrt{16} \cdot 4}{4} + \frac{- (8 - 4) \cdot 2}{1} + 5 \cdot 2 + 2^{5} \div 4 + 10$

Step 1.22

Multiply $\frac{- (8 - 4) \cdot 2}{1}$ by $\frac{4}{4}$ .

Step 1.23

Multiply $\frac{- (8 - 4) \cdot 2}{1}$ by $\frac{4}{4}$ .

Step 1.24

Write $5 \cdot 2$ as a fraction with denominator $1$ .

Step 1.25

Multiply $\frac{5 \cdot 2}{1}$ by $\frac{4}{4}$ .

Step 1.26

Multiply $\frac{5 \cdot 2}{1}$ by $\frac{4}{4}$ .

Step 1.27

Write $10$ as a fraction with denominator $1$ .

Step 1.28

Multiply $\frac{10}{1}$ by $\frac{4}{4}$ .

Step 1.29

Multiply $\frac{10}{1}$ by $\frac{4}{4}$ .

Step 1.30

Multiply $2$ by $2$ .

$\frac{6 \cdot 4}{4} + \frac{3 \cdot 4}{4} + \frac{- 2 \cdot 4}{4} - \frac{6 \cdot 2}{4} + \frac{3^{2} \cdot 4}{4} + \frac{10 \cdot 4}{4} + \frac{- \sqrt{16} \cdot 4}{4} + \frac{- (8 - 4) \cdot 2 \cdot 4}{4} + \frac{5 \cdot 2 \cdot 4}{4} + 2^{5} \div 4 + \frac{10 \cdot 4}{4}$

Step 2

Combine the numerators over the common denominator.

$\frac{6 \cdot 4 + 3 \cdot 4 - 2 \cdot 4 - 6 \cdot 2 + 3^{2} \cdot 4 + 10 \cdot 4 - \sqrt{16} \cdot 4 - (8 - 4) \cdot 2 \cdot 4 + 5 \cdot 2 \cdot 4 + 2^{5} + 10 \cdot 4}{4}$

Step 3

Simplify each term.

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Step 3.1

Multiply $6$ by $4$ .

$\frac{24 + 3 \cdot 4 - 2 \cdot 4 - 6 \cdot 2 + 3^{2} \cdot 4 + 10 \cdot 4 - \sqrt{16} \cdot 4 - (8 - 4) \cdot 2 \cdot 4 + 5 \cdot 2 \cdot 4 + 2^{5} + 10 \cdot 4}{4}$

Step 3.2

Multiply $3$ by $4$ .

$\frac{24 + 12 - 2 \cdot 4 - 6 \cdot 2 + 3^{2} \cdot 4 + 10 \cdot 4 - \sqrt{16} \cdot 4 - (8 - 4) \cdot 2 \cdot 4 + 5 \cdot 2 \cdot 4 + 2^{5} + 10 \cdot 4}{4}$

Step 3.3

Multiply $- 2$ by $4$ .

$\frac{24 + 12 - 8 - 6 \cdot 2 + 3^{2} \cdot 4 + 10 \cdot 4 - \sqrt{16} \cdot 4 - (8 - 4) \cdot 2 \cdot 4 + 5 \cdot 2 \cdot 4 + 2^{5} + 10 \cdot 4}{4}$

Step 3.4

Multiply $- 6$ by $2$ .

$\frac{24 + 12 - 8 - 12 + 3^{2} \cdot 4 + 10 \cdot 4 - \sqrt{16} \cdot 4 - (8 - 4) \cdot 2 \cdot 4 + 5 \cdot 2 \cdot 4 + 2^{5} + 10 \cdot 4}{4}$

Step 3.5

Raise $3$ to the power of $2$ .

$\frac{24 + 12 - 8 - 12 + 9 \cdot 4 + 10 \cdot 4 - \sqrt{16} \cdot 4 - (8 - 4) \cdot 2 \cdot 4 + 5 \cdot 2 \cdot 4 + 2^{5} + 10 \cdot 4}{4}$

Step 3.6

Multiply $9$ by $4$ .

$\frac{24 + 12 - 8 - 12 + 36 + 10 \cdot 4 - \sqrt{16} \cdot 4 - (8 - 4) \cdot 2 \cdot 4 + 5 \cdot 2 \cdot 4 + 2^{5} + 10 \cdot 4}{4}$

Step 3.7

Multiply $10$ by $4$ .

$\frac{24 + 12 - 8 - 12 + 36 + 40 - \sqrt{16} \cdot 4 - (8 - 4) \cdot 2 \cdot 4 + 5 \cdot 2 \cdot 4 + 2^{5} + 10 \cdot 4}{4}$

Step 3.8

Rewrite $16$ as $4^{2}$ .

$\frac{24 + 12 - 8 - 12 + 36 + 40 - \sqrt{4^{2}} \cdot 4 - (8 - 4) \cdot 2 \cdot 4 + 5 \cdot 2 \cdot 4 + 2^{5} + 10 \cdot 4}{4}$

Step 3.9

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

$\frac{24 + 12 - 8 - 12 + 36 + 40 - 1 \cdot 4 \cdot 4 - (8 - 4) \cdot 2 \cdot 4 + 5 \cdot 2 \cdot 4 + 2^{5} + 10 \cdot 4}{4}$

Step 3.10

Multiply $- 1 \cdot 4 \cdot 4$ .

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Step 3.10.1

Multiply $- 1$ by $4$ .

$\frac{24 + 12 - 8 - 12 + 36 + 40 - 4 \cdot 4 - (8 - 4) \cdot 2 \cdot 4 + 5 \cdot 2 \cdot 4 + 2^{5} + 10 \cdot 4}{4}$

Step 3.10.2

Multiply $- 4$ by $4$ .

$\frac{24 + 12 - 8 - 12 + 36 + 40 - 16 - (8 - 4) \cdot 2 \cdot 4 + 5 \cdot 2 \cdot 4 + 2^{5} + 10 \cdot 4}{4}$

Step 3.11

Subtract $4$ from $8$ .

$\frac{24 + 12 - 8 - 12 + 36 + 40 - 16 - 1 \cdot 4 \cdot 2 \cdot 4 + 5 \cdot 2 \cdot 4 + 2^{5} + 10 \cdot 4}{4}$

Step 3.12

Multiply $- 1 \cdot 4 \cdot 2 \cdot 4$ .

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Step 3.12.1

Multiply $- 1$ by $4$ .

$\frac{24 + 12 - 8 - 12 + 36 + 40 - 16 - 4 \cdot 2 \cdot 4 + 5 \cdot 2 \cdot 4 + 2^{5} + 10 \cdot 4}{4}$

Step 3.12.2

Multiply $- 4$ by $2$ .

$\frac{24 + 12 - 8 - 12 + 36 + 40 - 16 - 8 \cdot 4 + 5 \cdot 2 \cdot 4 + 2^{5} + 10 \cdot 4}{4}$

Step 3.12.3

Multiply $- 8$ by $4$ .

$\frac{24 + 12 - 8 - 12 + 36 + 40 - 16 - 32 + 5 \cdot 2 \cdot 4 + 2^{5} + 10 \cdot 4}{4}$

Step 3.13

Multiply $5 \cdot 2 \cdot 4$ .

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Step 3.13.1

Multiply $5$ by $2$ .

$\frac{24 + 12 - 8 - 12 + 36 + 40 - 16 - 32 + 10 \cdot 4 + 2^{5} + 10 \cdot 4}{4}$

Step 3.13.2

Multiply $10$ by $4$ .

$\frac{24 + 12 - 8 - 12 + 36 + 40 - 16 - 32 + 40 + 2^{5} + 10 \cdot 4}{4}$

Step 3.14

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

$\frac{24 + 12 - 8 - 12 + 36 + 40 - 16 - 32 + 40 + 32 + 10 \cdot 4}{4}$

Step 3.15

Multiply $10$ by $4$ .

$\frac{24 + 12 - 8 - 12 + 36 + 40 - 16 - 32 + 40 + 32 + 40}{4}$

Step 4

Simplify the expression.

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Step 4.1

Add $24$ and $12$ .

$\frac{36 - 8 - 12 + 36 + 40 - 16 - 32 + 40 + 32 + 40}{4}$

Step 4.2

Subtract $8$ from $36$ .

$\frac{28 - 12 + 36 + 40 - 16 - 32 + 40 + 32 + 40}{4}$

Step 4.3

Subtract $12$ from $28$ .

$\frac{16 + 36 + 40 - 16 - 32 + 40 + 32 + 40}{4}$

Step 4.4

Add $16$ and $36$ .

$\frac{52 + 40 - 16 - 32 + 40 + 32 + 40}{4}$

Step 4.5

Add $52$ and $40$ .

$\frac{92 - 16 - 32 + 40 + 32 + 40}{4}$

Step 4.6

Subtract $16$ from $92$ .

$\frac{76 - 32 + 40 + 32 + 40}{4}$

Step 4.7

Subtract $32$ from $76$ .

$\frac{44 + 40 + 32 + 40}{4}$

Step 4.8

Add $44$ and $40$ .

$\frac{84 + 32 + 40}{4}$

Step 4.9

Add $84$ and $32$ .

$\frac{116 + 40}{4}$

Step 4.10

Add $116$ and $40$ .

$\frac{156}{4}$

Step 4.11

Divide $156$ by $4$ .

$39$