Basic Math Examples

$- 6 - (- 3 + \frac{12}{6} - | 7 - \frac{- 4 + 20}{4} |)$

Step 1

Simplify each term.

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Step 1.1

Find the common denominator.

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Step 1.1.1

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

$- 6 - (\frac{- 3}{1} + \frac{12}{6} - | 7 - \frac{- 4 + 20}{4} |)$

Step 1.1.2

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

$- 6 - (\frac{- 3}{1} \cdot \frac{6}{6} + \frac{12}{6} - | 7 - \frac{- 4 + 20}{4} |)$

Step 1.1.3

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

$- 6 - (\frac{- 3 \cdot 6}{6} + \frac{12}{6} - | 7 - \frac{- 4 + 20}{4} |)$

Step 1.1.4

Write $- | 7 - \frac{- 4 + 20}{4} |$ as a fraction with denominator $1$ .

$- 6 - (\frac{- 3 \cdot 6}{6} + \frac{12}{6} + \frac{- | 7 - \frac{- 4 + 20}{4} |}{1})$

Step 1.1.5

Multiply $\frac{- | 7 - \frac{- 4 + 20}{4} |}{1}$ by $\frac{6}{6}$ .

$- 6 - (\frac{- 3 \cdot 6}{6} + \frac{12}{6} + \frac{- | 7 - \frac{- 4 + 20}{4} |}{1} \cdot \frac{6}{6})$

Step 1.1.6

Multiply $\frac{- | 7 - \frac{- 4 + 20}{4} |}{1}$ by $\frac{6}{6}$ .

$- 6 - (\frac{- 3 \cdot 6}{6} + \frac{12}{6} + \frac{- | 7 - \frac{- 4 + 20}{4} | \cdot 6}{6})$

Step 1.2

Combine the numerators over the common denominator.

$- 6 - \frac{- 3 \cdot 6 + 12 - | 7 - \frac{- 4 + 20}{4} | \cdot 6}{6}$

Step 1.3

Simplify each term.

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Step 1.3.1

Multiply $- 3$ by $6$ .

$- 6 - \frac{- 18 + 12 - | 7 - \frac{- 4 + 20}{4} | \cdot 6}{6}$

Step 1.3.2

Simplify each term.

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Step 1.3.2.1

Cancel the common factor of $- 4 + 20$ and $4$ .

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Step 1.3.2.1.1

Factor $4$ out of $- 4$ .

$- 6 - \frac{- 18 + 12 - | 7 - \frac{4 \cdot - 1 + 20}{4} | \cdot 6}{6}$

Step 1.3.2.1.2

Factor $4$ out of $20$ .

$- 6 - \frac{- 18 + 12 - | 7 - \frac{4 \cdot - 1 + 4 \cdot 5}{4} | \cdot 6}{6}$

Step 1.3.2.1.3

Factor $4$ out of $4 \cdot - 1 + 4 \cdot 5$ .

$- 6 - \frac{- 18 + 12 - | 7 - \frac{4 \cdot (- 1 + 5)}{4} | \cdot 6}{6}$

Step 1.3.2.1.4

Cancel the common factors.

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Step 1.3.2.1.4.1

Factor $4$ out of $4$ .

$- 6 - \frac{- 18 + 12 - | 7 - \frac{4 \cdot (- 1 + 5)}{4 (1)} | \cdot 6}{6}$

Step 1.3.2.1.4.2

Cancel the common factor.

$- 6 - \frac{- 18 + 12 - | 7 - \frac{4 \cdot (- 1 + 5)}{4 \cdot 1} | \cdot 6}{6}$

Step 1.3.2.1.4.3

Rewrite the expression.

$- 6 - \frac{- 18 + 12 - | 7 - \frac{- 1 + 5}{1} | \cdot 6}{6}$

Step 1.3.2.1.4.4

Divide $- 1 + 5$ by $1$ .

$- 6 - \frac{- 18 + 12 - | 7 - (- 1 + 5) | \cdot 6}{6}$

Step 1.3.2.2

Add $- 1$ and $5$ .

$- 6 - \frac{- 18 + 12 - | 7 - 1 \cdot 4 | \cdot 6}{6}$

Step 1.3.2.3

Multiply $- 1$ by $4$ .

$- 6 - \frac{- 18 + 12 - | 7 - 4 | \cdot 6}{6}$

Step 1.3.3

Subtract $4$ from $7$ .

$- 6 - \frac{- 18 + 12 - | 3 | \cdot 6}{6}$

Step 1.3.4

The absolute value is the distance between a number and zero. The distance between $0$ and $3$ is $3$ .

$- 6 - \frac{- 18 + 12 - 1 \cdot 3 \cdot 6}{6}$

Step 1.3.5

Multiply $- 1 \cdot 3 \cdot 6$ .

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Step 1.3.5.1

Multiply $- 1$ by $3$ .

$- 6 - \frac{- 18 + 12 - 3 \cdot 6}{6}$

Step 1.3.5.2

Multiply $- 3$ by $6$ .

$- 6 - \frac{- 18 + 12 - 18}{6}$

Step 1.4

Add $- 18$ and $12$ .

$- 6 - \frac{- 6 - 18}{6}$

Step 1.5

Subtract $18$ from $- 6$ .

$- 6 - \frac{- 24}{6}$

Step 1.6

Divide $- 24$ by $6$ .

$- 6 - - 4$

Step 1.7

Multiply $- 1$ by $- 4$ .

$- 6 + 4$

Step 2

Add $- 6$ and $4$ .

$- 2$