Basic Math Examples

$1 - 2 \cdot 9 - 4 + 5 \div 6 - 7 - 8 + \sqrt{9} + 10$

Step 1

Simplify each term.

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Step 1.1

Multiply $- 2$ by $9$ .

$1 - 18 - 4 + 5 \div 6 - 7 - 8 + \sqrt{9} + 10$

Step 1.2

Rewrite the division as a fraction.

$1 - 18 - 4 + \frac{5}{6} - 7 - 8 + \sqrt{9} + 10$

Step 1.3

Rewrite $9$ as $3^{2}$ .

$1 - 18 - 4 + \frac{5}{6} - 7 - 8 + \sqrt{3^{2}} + 10$

Step 1.4

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

$1 - 18 - 4 + \frac{5}{6} - 7 - 8 + 3 + 10$

Step 2

Find the common denominator.

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Step 2.1

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

$\frac{1}{1} - 18 - 4 + \frac{5}{6} - 7 - 8 + 3 + 10$

Step 2.2

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

$\frac{1}{1} \cdot \frac{6}{6} - 18 - 4 + \frac{5}{6} - 7 - 8 + 3 + 10$

Step 2.3

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

$\frac{6}{6} - 18 - 4 + \frac{5}{6} - 7 - 8 + 3 + 10$

Step 2.4

Write $- 18$ as a fraction with denominator $1$ .

$\frac{6}{6} + \frac{- 18}{1} - 4 + \frac{5}{6} - 7 - 8 + 3 + 10$

Step 2.5

Multiply $\frac{- 18}{1}$ by $\frac{6}{6}$ .

$\frac{6}{6} + \frac{- 18}{1} \cdot \frac{6}{6} - 4 + \frac{5}{6} - 7 - 8 + 3 + 10$

Step 2.6

Multiply $\frac{- 18}{1}$ by $\frac{6}{6}$ .

$\frac{6}{6} + \frac{- 18 \cdot 6}{6} - 4 + \frac{5}{6} - 7 - 8 + 3 + 10$

Step 2.7

Write $- 4$ as a fraction with denominator $1$ .

$\frac{6}{6} + \frac{- 18 \cdot 6}{6} + \frac{- 4}{1} + \frac{5}{6} - 7 - 8 + 3 + 10$

Step 2.8

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

$\frac{6}{6} + \frac{- 18 \cdot 6}{6} + \frac{- 4}{1} \cdot \frac{6}{6} + \frac{5}{6} - 7 - 8 + 3 + 10$

Step 2.9

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

$\frac{6}{6} + \frac{- 18 \cdot 6}{6} + \frac{- 4 \cdot 6}{6} + \frac{5}{6} - 7 - 8 + 3 + 10$

Step 2.10

Write $- 7$ as a fraction with denominator $1$ .

$\frac{6}{6} + \frac{- 18 \cdot 6}{6} + \frac{- 4 \cdot 6}{6} + \frac{5}{6} + \frac{- 7}{1} - 8 + 3 + 10$

Step 2.11

Multiply $\frac{- 7}{1}$ by $\frac{6}{6}$ .

$\frac{6}{6} + \frac{- 18 \cdot 6}{6} + \frac{- 4 \cdot 6}{6} + \frac{5}{6} + \frac{- 7}{1} \cdot \frac{6}{6} - 8 + 3 + 10$

Step 2.12

Multiply $\frac{- 7}{1}$ by $\frac{6}{6}$ .

$\frac{6}{6} + \frac{- 18 \cdot 6}{6} + \frac{- 4 \cdot 6}{6} + \frac{5}{6} + \frac{- 7 \cdot 6}{6} - 8 + 3 + 10$

Step 2.13

Write $- 8$ as a fraction with denominator $1$ .

$\frac{6}{6} + \frac{- 18 \cdot 6}{6} + \frac{- 4 \cdot 6}{6} + \frac{5}{6} + \frac{- 7 \cdot 6}{6} + \frac{- 8}{1} + 3 + 10$

Step 2.14

Multiply $\frac{- 8}{1}$ by $\frac{6}{6}$ .

$\frac{6}{6} + \frac{- 18 \cdot 6}{6} + \frac{- 4 \cdot 6}{6} + \frac{5}{6} + \frac{- 7 \cdot 6}{6} + \frac{- 8}{1} \cdot \frac{6}{6} + 3 + 10$

Step 2.15

Multiply $\frac{- 8}{1}$ by $\frac{6}{6}$ .

$\frac{6}{6} + \frac{- 18 \cdot 6}{6} + \frac{- 4 \cdot 6}{6} + \frac{5}{6} + \frac{- 7 \cdot 6}{6} + \frac{- 8 \cdot 6}{6} + 3 + 10$

Step 2.16

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

$\frac{6}{6} + \frac{- 18 \cdot 6}{6} + \frac{- 4 \cdot 6}{6} + \frac{5}{6} + \frac{- 7 \cdot 6}{6} + \frac{- 8 \cdot 6}{6} + \frac{3}{1} + 10$

Step 2.17

Multiply $\frac{3}{1}$ by $\frac{6}{6}$ .

$\frac{6}{6} + \frac{- 18 \cdot 6}{6} + \frac{- 4 \cdot 6}{6} + \frac{5}{6} + \frac{- 7 \cdot 6}{6} + \frac{- 8 \cdot 6}{6} + \frac{3}{1} \cdot \frac{6}{6} + 10$

Step 2.18

Multiply $\frac{3}{1}$ by $\frac{6}{6}$ .

$\frac{6}{6} + \frac{- 18 \cdot 6}{6} + \frac{- 4 \cdot 6}{6} + \frac{5}{6} + \frac{- 7 \cdot 6}{6} + \frac{- 8 \cdot 6}{6} + \frac{3 \cdot 6}{6} + 10$

Step 2.19

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

$\frac{6}{6} + \frac{- 18 \cdot 6}{6} + \frac{- 4 \cdot 6}{6} + \frac{5}{6} + \frac{- 7 \cdot 6}{6} + \frac{- 8 \cdot 6}{6} + \frac{3 \cdot 6}{6} + \frac{10}{1}$

Step 2.20

Multiply $\frac{10}{1}$ by $\frac{6}{6}$ .

$\frac{6}{6} + \frac{- 18 \cdot 6}{6} + \frac{- 4 \cdot 6}{6} + \frac{5}{6} + \frac{- 7 \cdot 6}{6} + \frac{- 8 \cdot 6}{6} + \frac{3 \cdot 6}{6} + \frac{10}{1} \cdot \frac{6}{6}$

Step 2.21

Multiply $\frac{10}{1}$ by $\frac{6}{6}$ .

$\frac{6}{6} + \frac{- 18 \cdot 6}{6} + \frac{- 4 \cdot 6}{6} + \frac{5}{6} + \frac{- 7 \cdot 6}{6} + \frac{- 8 \cdot 6}{6} + \frac{3 \cdot 6}{6} + \frac{10 \cdot 6}{6}$

Step 3

Combine the numerators over the common denominator.

$\frac{6 - 18 \cdot 6 - 4 \cdot 6 + 5 - 7 \cdot 6 - 8 \cdot 6 + 3 \cdot 6 + 10 \cdot 6}{6}$

Step 4

Simplify each term.

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Step 4.1

Multiply $- 18$ by $6$ .

$\frac{6 - 108 - 4 \cdot 6 + 5 - 7 \cdot 6 - 8 \cdot 6 + 3 \cdot 6 + 10 \cdot 6}{6}$

Step 4.2

Multiply $- 4$ by $6$ .

$\frac{6 - 108 - 24 + 5 - 7 \cdot 6 - 8 \cdot 6 + 3 \cdot 6 + 10 \cdot 6}{6}$

Step 4.3

Multiply $- 7$ by $6$ .

$\frac{6 - 108 - 24 + 5 - 42 - 8 \cdot 6 + 3 \cdot 6 + 10 \cdot 6}{6}$

Step 4.4

Multiply $- 8$ by $6$ .

$\frac{6 - 108 - 24 + 5 - 42 - 48 + 3 \cdot 6 + 10 \cdot 6}{6}$

Step 4.5

Multiply $3$ by $6$ .

$\frac{6 - 108 - 24 + 5 - 42 - 48 + 18 + 10 \cdot 6}{6}$

Step 4.6

Multiply $10$ by $6$ .

$\frac{6 - 108 - 24 + 5 - 42 - 48 + 18 + 60}{6}$

Step 5

Simplify the expression.

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Step 5.1

Subtract $108$ from $6$ .

$\frac{- 102 - 24 + 5 - 42 - 48 + 18 + 60}{6}$

Step 5.2

Subtract $24$ from $- 102$ .

$\frac{- 126 + 5 - 42 - 48 + 18 + 60}{6}$

Step 5.3

Add $- 126$ and $5$ .

$\frac{- 121 - 42 - 48 + 18 + 60}{6}$

Step 5.4

Subtract $42$ from $- 121$ .

$\frac{- 163 - 48 + 18 + 60}{6}$

Step 5.5

Subtract $48$ from $- 163$ .

$\frac{- 211 + 18 + 60}{6}$

Step 5.6

Add $- 211$ and $18$ .

$\frac{- 193 + 60}{6}$

Step 5.7

Add $- 193$ and $60$ .

$\frac{- 133}{6}$

Step 5.8

Move the negative in front of the fraction.

$- \frac{133}{6}$

Step 6

The approximate value of $1 - 2 \cdot 9 - 4 + 5 \div 6 - 7 - 8 + \sqrt{9} + 10$ found by front end estimation.

$1 - 2 \cdot 9 - 4 + 5 \div 6 - 7 - 8 + \sqrt{9} + 10 \approx - \frac{133}{6}$