Basic Math Examples

$(6 + 121 \div (7 \cdot 3 - 5 \cdot 2 - 1 - 8 \div (- 8))) - 17$

Step 1

Find the common denominator.

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Step 1.1

To write $7 \cdot 3$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$6 + 121 \div (7 \cdot 3 \cdot \frac{8}{8} - 8 \div (- 8) - 5 \cdot 2 - 1) - 17$

Step 1.2

To write $- 8 \div (- 8)$ as a fraction with a common denominator, multiply by $\frac{- 1}{- 1}$ .

$6 + 121 \div (7 \cdot 3 \cdot \frac{8}{8} - 8 \div (- 8) \cdot \frac{- 1}{- 1} - 5 \cdot 2 - 1) - 17$

Step 1.3

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.3.1

Combine $7 \cdot 3$ and $\frac{8}{8}$ .

$6 + 121 \div (\frac{7 \cdot 3 \cdot 8}{8} - 8 \div (- 8) \cdot \frac{- 1}{- 1} - 5 \cdot 2 - 1) - 17$

Step 1.3.2

Multiply $8 \div (- 8)$ by $\frac{- 1}{- 1}$ .

$6 + 121 \div (\frac{7 \cdot 3 \cdot 8}{8} - \frac{8 \cdot - 1}{- 8 \cdot - 1} - 5 \cdot 2 - 1) - 17$

Step 1.3.3

Multiply $- 8$ by $- 1$ .

$6 + 121 \div (\frac{7 \cdot 3 \cdot 8}{8} - \frac{8 \cdot - 1}{8} - 5 \cdot 2 - 1) - 17$

Step 1.4

Combine the numerators over the common denominator.

$6 + 121 \div (\frac{7 \cdot 3 \cdot 8 - 8 \cdot - 1}{8} - 5 \cdot 2 - 1) - 17$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Multiply $7$ by $3$ .

$6 + 121 \div (\frac{21 \cdot 8 - 8 \cdot - 1}{8} - 5 \cdot 2 - 1) - 17$

Step 1.5.2

Multiply $21$ by $8$ .

$6 + 121 \div (\frac{168 - 8 \cdot - 1}{8} - 5 \cdot 2 - 1) - 17$

Step 1.5.3

Multiply $- 8$ by $- 1$ .

$6 + 121 \div (\frac{168 + 8}{8} - 5 \cdot 2 - 1) - 17$

Step 1.5.4

Add $168$ and $8$ .

$6 + 121 \div (\frac{176}{8} - 5 \cdot 2 - 1) - 17$

Step 1.6

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

$\frac{6}{1} + 121 \div (\frac{176}{8} - 5 \cdot 2 - 1) - 17$

Step 1.7

Multiply $\frac{6}{1}$ by $\frac{\frac{176}{8} - 5 \cdot 2 - 1}{\frac{176}{8} - 5 \cdot 2 - 1}$ .

$\frac{6}{1} \cdot \frac{\frac{176}{8} - 5 \cdot 2 - 1}{\frac{176}{8} - 5 \cdot 2 - 1} + 121 \div (\frac{176}{8} - 5 \cdot 2 - 1) - 17$

Step 1.8

Multiply $\frac{6}{1}$ by $\frac{\frac{176}{8} - 5 \cdot 2 - 1}{\frac{176}{8} - 5 \cdot 2 - 1}$ .

$\frac{6 (\frac{176}{8} - 5 \cdot 2 - 1)}{\frac{176}{8} - 5 \cdot 2 - 1} + 121 \div (\frac{176}{8} - 5 \cdot 2 - 1) - 17$

Step 1.9

Write $- 17$ as a fraction with denominator $1$ .

$\frac{6 (\frac{176}{8} - 5 \cdot 2 - 1)}{\frac{176}{8} - 5 \cdot 2 - 1} + 121 \div (\frac{176}{8} - 5 \cdot 2 - 1) + \frac{- 17}{1}$

Step 1.10

Multiply $\frac{- 17}{1}$ by $\frac{\frac{176}{8} - 5 \cdot 2 - 1}{\frac{176}{8} - 5 \cdot 2 - 1}$ .

$\frac{6 (\frac{176}{8} - 5 \cdot 2 - 1)}{\frac{176}{8} - 5 \cdot 2 - 1} + 121 \div (\frac{176}{8} - 5 \cdot 2 - 1) + \frac{- 17}{1} \cdot \frac{\frac{176}{8} - 5 \cdot 2 - 1}{\frac{176}{8} - 5 \cdot 2 - 1}$

Step 1.11

Multiply $\frac{- 17}{1}$ by $\frac{\frac{176}{8} - 5 \cdot 2 - 1}{\frac{176}{8} - 5 \cdot 2 - 1}$ .

$\frac{6 (\frac{176}{8} - 5 \cdot 2 - 1)}{\frac{176}{8} - 5 \cdot 2 - 1} + 121 \div (\frac{176}{8} - 5 \cdot 2 - 1) + \frac{- 17 (\frac{176}{8} - 5 \cdot 2 - 1)}{\frac{176}{8} - 5 \cdot 2 - 1}$

Step 2

Simplify terms.

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Step 2.1

Combine the numerators over the common denominator.

$\frac{6 (\frac{176}{8} - 5 \cdot 2 - 1) + 121 - 17 (\frac{176}{8} - 5 \cdot 2 - 1)}{\frac{176}{8} - 1 - 5 \cdot 2}$

Step 2.2

Simplify each term.

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Step 2.2.1

Find the common denominator.

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Step 2.2.1.1

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

$\frac{6 (\frac{176}{8} + \frac{- 5 \cdot 2}{1} - 1) + 121 - 17 (\frac{176}{8} - 5 \cdot 2 - 1)}{\frac{176}{8} - 1 - 5 \cdot 2}$

Step 2.2.1.2

Multiply $\frac{- 5 \cdot 2}{1}$ by $\frac{8}{8}$ .

$\frac{6 (\frac{176}{8} + \frac{- 5 \cdot 2}{1} \cdot \frac{8}{8} - 1) + 121 - 17 (\frac{176}{8} - 5 \cdot 2 - 1)}{\frac{176}{8} - 1 - 5 \cdot 2}$

Step 2.2.1.3

Multiply $\frac{- 5 \cdot 2}{1}$ by $\frac{8}{8}$ .

$\frac{6 (\frac{176}{8} + \frac{- 5 \cdot 2 \cdot 8}{8} - 1) + 121 - 17 (\frac{176}{8} - 5 \cdot 2 - 1)}{\frac{176}{8} - 1 - 5 \cdot 2}$

Step 2.2.1.4

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

$\frac{6 (\frac{176}{8} + \frac{- 5 \cdot 2 \cdot 8}{8} + \frac{- 1}{1}) + 121 - 17 (\frac{176}{8} - 5 \cdot 2 - 1)}{\frac{176}{8} - 1 - 5 \cdot 2}$

Step 2.2.1.5

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

$\frac{6 (\frac{176}{8} + \frac{- 5 \cdot 2 \cdot 8}{8} + \frac{- 1}{1} \cdot \frac{8}{8}) + 121 - 17 (\frac{176}{8} - 5 \cdot 2 - 1)}{\frac{176}{8} - 1 - 5 \cdot 2}$

Step 2.2.1.6

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

$\frac{6 (\frac{176}{8} + \frac{- 5 \cdot 2 \cdot 8}{8} + \frac{- 1 \cdot 8}{8}) + 121 - 17 (\frac{176}{8} - 5 \cdot 2 - 1)}{\frac{176}{8} - 1 - 5 \cdot 2}$

Step 2.2.2

Combine the numerators over the common denominator.

$\frac{6 \frac{176 - 5 \cdot 2 \cdot 8 - 1 \cdot 8}{8} + 121 - 17 (\frac{176}{8} - 5 \cdot 2 - 1)}{\frac{176}{8} - 1 - 5 \cdot 2}$

Step 2.2.3

Simplify each term.

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Step 2.2.3.1

Multiply $- 5 \cdot 2 \cdot 8$ .

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Step 2.2.3.1.1

Multiply $- 5$ by $2$ .

$\frac{6 \frac{176 - 10 \cdot 8 - 1 \cdot 8}{8} + 121 - 17 (\frac{176}{8} - 5 \cdot 2 - 1)}{\frac{176}{8} - 1 - 5 \cdot 2}$

Step 2.2.3.1.2

Multiply $- 10$ by $8$ .

$\frac{6 \frac{176 - 80 - 1 \cdot 8}{8} + 121 - 17 (\frac{176}{8} - 5 \cdot 2 - 1)}{\frac{176}{8} - 1 - 5 \cdot 2}$

Step 2.2.3.2

Multiply $- 1$ by $8$ .

$\frac{6 \frac{176 - 80 - 8}{8} + 121 - 17 (\frac{176}{8} - 5 \cdot 2 - 1)}{\frac{176}{8} - 1 - 5 \cdot 2}$

Step 2.2.4

Subtract $80$ from $176$ .

$\frac{6 \frac{96 - 8}{8} + 121 - 17 (\frac{176}{8} - 5 \cdot 2 - 1)}{\frac{176}{8} - 1 - 5 \cdot 2}$

Step 2.2.5

Subtract $8$ from $96$ .

$\frac{6 (\frac{88}{8}) + 121 - 17 (\frac{176}{8} - 5 \cdot 2 - 1)}{\frac{176}{8} - 1 - 5 \cdot 2}$

Step 2.2.6

Cancel the common factor of $2$ .

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Step 2.2.6.1

Factor $2$ out of $6$ .

$\frac{2 (3) \frac{88}{8} + 121 - 17 (\frac{176}{8} - 5 \cdot 2 - 1)}{\frac{176}{8} - 1 - 5 \cdot 2}$

Step 2.2.6.2

Factor $2$ out of $8$ .

$\frac{2 \cdot 3 \frac{88}{2 \cdot 4} + 121 - 17 (\frac{176}{8} - 5 \cdot 2 - 1)}{\frac{176}{8} - 1 - 5 \cdot 2}$

Step 2.2.6.3

Cancel the common factor.

$\frac{2 \cdot 3 \frac{88}{2 \cdot 4} + 121 - 17 (\frac{176}{8} - 5 \cdot 2 - 1)}{\frac{176}{8} - 1 - 5 \cdot 2}$

Step 2.2.6.4

Rewrite the expression.

$\frac{3 (\frac{88}{4}) + 121 - 17 (\frac{176}{8} - 5 \cdot 2 - 1)}{\frac{176}{8} - 1 - 5 \cdot 2}$

Step 2.2.7

Combine $3$ and $\frac{88}{4}$ .

$\frac{\frac{3 \cdot 88}{4} + 121 - 17 (\frac{176}{8} - 5 \cdot 2 - 1)}{\frac{176}{8} - 1 - 5 \cdot 2}$

Step 2.2.8

Multiply $3$ by $88$ .

$\frac{\frac{264}{4} + 121 - 17 (\frac{176}{8} - 5 \cdot 2 - 1)}{\frac{176}{8} - 1 - 5 \cdot 2}$

Step 2.2.9

Divide $264$ by $4$ .

$\frac{66 + 121 - 17 (\frac{176}{8} - 5 \cdot 2 - 1)}{\frac{176}{8} - 1 - 5 \cdot 2}$

Step 2.2.10

Find the common denominator.

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Step 2.2.10.1

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

$\frac{66 + 121 - 17 (\frac{176}{8} + \frac{- 5 \cdot 2}{1} - 1)}{\frac{176}{8} - 1 - 5 \cdot 2}$

Step 2.2.10.2

Multiply $\frac{- 5 \cdot 2}{1}$ by $\frac{8}{8}$ .

$\frac{66 + 121 - 17 (\frac{176}{8} + \frac{- 5 \cdot 2}{1} \cdot \frac{8}{8} - 1)}{\frac{176}{8} - 1 - 5 \cdot 2}$

Step 2.2.10.3

Multiply $\frac{- 5 \cdot 2}{1}$ by $\frac{8}{8}$ .

$\frac{66 + 121 - 17 (\frac{176}{8} + \frac{- 5 \cdot 2 \cdot 8}{8} - 1)}{\frac{176}{8} - 1 - 5 \cdot 2}$

Step 2.2.10.4

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

$\frac{66 + 121 - 17 (\frac{176}{8} + \frac{- 5 \cdot 2 \cdot 8}{8} + \frac{- 1}{1})}{\frac{176}{8} - 1 - 5 \cdot 2}$

Step 2.2.10.5

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

$\frac{66 + 121 - 17 (\frac{176}{8} + \frac{- 5 \cdot 2 \cdot 8}{8} + \frac{- 1}{1} \cdot \frac{8}{8})}{\frac{176}{8} - 1 - 5 \cdot 2}$

Step 2.2.10.6

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

$\frac{66 + 121 - 17 (\frac{176}{8} + \frac{- 5 \cdot 2 \cdot 8}{8} + \frac{- 1 \cdot 8}{8})}{\frac{176}{8} - 1 - 5 \cdot 2}$

Step 2.2.11

Combine the numerators over the common denominator.

$\frac{66 + 121 - 17 \frac{176 - 5 \cdot 2 \cdot 8 - 1 \cdot 8}{8}}{\frac{176}{8} - 1 - 5 \cdot 2}$

Step 2.2.12

Simplify each term.

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Step 2.2.12.1

Multiply $- 5 \cdot 2 \cdot 8$ .

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Step 2.2.12.1.1

Multiply $- 5$ by $2$ .

$\frac{66 + 121 - 17 \frac{176 - 10 \cdot 8 - 1 \cdot 8}{8}}{\frac{176}{8} - 1 - 5 \cdot 2}$

Step 2.2.12.1.2

Multiply $- 10$ by $8$ .

$\frac{66 + 121 - 17 \frac{176 - 80 - 1 \cdot 8}{8}}{\frac{176}{8} - 1 - 5 \cdot 2}$

Step 2.2.12.2

Multiply $- 1$ by $8$ .

$\frac{66 + 121 - 17 \frac{176 - 80 - 8}{8}}{\frac{176}{8} - 1 - 5 \cdot 2}$

Step 2.2.13

Subtract $80$ from $176$ .

$\frac{66 + 121 - 17 \frac{96 - 8}{8}}{\frac{176}{8} - 1 - 5 \cdot 2}$

Step 2.2.14

Subtract $8$ from $96$ .

$\frac{66 + 121 - 17 (\frac{88}{8})}{\frac{176}{8} - 1 - 5 \cdot 2}$

Step 2.2.15

Divide $88$ by $8$ .

$\frac{66 + 121 - 17 \cdot 11}{\frac{176}{8} - 1 - 5 \cdot 2}$

Step 2.2.16

Multiply $- 17$ by $11$ .

$\frac{66 + 121 - 187}{\frac{176}{8} - 1 - 5 \cdot 2}$

Step 2.3

Reduce the expression by cancelling the common factors.

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Step 2.3.1

Add $66$ and $121$ .

$\frac{187 - 187}{\frac{176}{8} - 1 - 5 \cdot 2}$

Step 2.3.2

Subtract $187$ from $187$ .

$\frac{0}{\frac{176}{8} - 1 - 5 \cdot 2}$

Step 2.3.3

Cancel the common factor of $176$ and $8$ .

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Step 2.3.3.1

Factor $8$ out of $176$ .

$\frac{0}{\frac{8 \cdot 22}{8} - 1 - 5 \cdot 2}$

Step 2.3.3.2

Cancel the common factors.

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Step 2.3.3.2.1

Factor $8$ out of $8$ .

$\frac{0}{\frac{8 \cdot 22}{8 (1)} - 1 - 5 \cdot 2}$

Step 2.3.3.2.2

Cancel the common factor.

$\frac{0}{\frac{8 \cdot 22}{8 \cdot 1} - 1 - 5 \cdot 2}$

Step 2.3.3.2.3

Rewrite the expression.

$\frac{0}{\frac{22}{1} - 1 - 5 \cdot 2}$

Step 2.3.3.2.4

Divide $22$ by $1$ .

$\frac{0}{22 - 1 - 5 \cdot 2}$

Step 3

Simplify the denominator.

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Step 3.1

Multiply $- 5$ by $2$ .

$\frac{0}{22 - 1 - 10}$

Step 3.2

Subtract $1$ from $22$ .

$\frac{0}{21 - 10}$

Step 3.3

Subtract $10$ from $21$ .

$\frac{0}{11}$

Step 4

Divide $0$ by $11$ .

$0$