Basic Math Examples

$\frac{3 - (3) + 1}{1 - (- 3) - 3} + (- 3 + 8 - 4 - 3)$

Step 1

Remove parentheses.

$\frac{3 - (3) + 1}{1 - (- 3) - 3} - 3 + 8 - 4 - 3$

Step 2

Multiply $- 1$ by $3$ .

$\frac{3 - 3 + 1}{1 - (- 3) - 3} - 3 + 8 - 4 - 3$

Step 3

Subtract $3$ from $3$ .

$\frac{0 + 1}{1 - (- 3) - 3} - 3 + 8 - 4 - 3$

Step 4

Add $0$ and $1$ .

$\frac{1}{1 - (- 3) - 3} - 3 + 8 - 4 - 3$

Step 5

Find the common denominator.

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Step 5.1

Subtract $3$ from $1$ .

$\frac{1}{- 2 - (- 3)} - 3 + 8 - 4 - 3$

Step 5.2

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

$\frac{1}{- 2 - (- 3)} + \frac{- 3}{1} + 8 - 4 - 3$

Step 5.3

Multiply $\frac{- 3}{1}$ by $\frac{- 2 - - 3}{- 2 - - 3}$ .

$\frac{1}{- 2 - (- 3)} + \frac{- 3}{1} \cdot \frac{- 2 - - 3}{- 2 - - 3} + 8 - 4 - 3$

Step 5.4

Multiply $\frac{- 3}{1}$ by $\frac{- 2 - - 3}{- 2 - - 3}$ .

$\frac{1}{- 2 - (- 3)} + \frac{- 3 (- 2 - - 3)}{- 2 - - 3} + 8 - 4 - 3$

Step 5.5

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

$\frac{1}{- 2 - (- 3)} + \frac{- 3 (- 2 - - 3)}{- 2 - - 3} + \frac{8}{1} - 4 - 3$

Step 5.6

Multiply $\frac{8}{1}$ by $\frac{- 2 - - 3}{- 2 - - 3}$ .

$\frac{1}{- 2 - (- 3)} + \frac{- 3 (- 2 - - 3)}{- 2 - - 3} + \frac{8}{1} \cdot \frac{- 2 - - 3}{- 2 - - 3} - 4 - 3$

Step 5.7

Multiply $\frac{8}{1}$ by $\frac{- 2 - - 3}{- 2 - - 3}$ .

$\frac{1}{- 2 - (- 3)} + \frac{- 3 (- 2 - - 3)}{- 2 - - 3} + \frac{8 (- 2 - - 3)}{- 2 - - 3} - 4 - 3$

Step 5.8

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

$\frac{1}{- 2 - (- 3)} + \frac{- 3 (- 2 - - 3)}{- 2 - - 3} + \frac{8 (- 2 - - 3)}{- 2 - - 3} + \frac{- 4}{1} - 3$

Step 5.9

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

$\frac{1}{- 2 - (- 3)} + \frac{- 3 (- 2 - - 3)}{- 2 - - 3} + \frac{8 (- 2 - - 3)}{- 2 - - 3} + \frac{- 4}{1} \cdot \frac{- 2 - - 3}{- 2 - - 3} - 3$

Step 5.10

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

$\frac{1}{- 2 - (- 3)} + \frac{- 3 (- 2 - - 3)}{- 2 - - 3} + \frac{8 (- 2 - - 3)}{- 2 - - 3} + \frac{- 4 (- 2 - - 3)}{- 2 - - 3} - 3$

Step 5.11

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

$\frac{1}{- 2 - (- 3)} + \frac{- 3 (- 2 - - 3)}{- 2 - - 3} + \frac{8 (- 2 - - 3)}{- 2 - - 3} + \frac{- 4 (- 2 - - 3)}{- 2 - - 3} + \frac{- 3}{1}$

Step 5.12

Multiply $\frac{- 3}{1}$ by $\frac{- 2 - - 3}{- 2 - - 3}$ .

$\frac{1}{- 2 - (- 3)} + \frac{- 3 (- 2 - - 3)}{- 2 - - 3} + \frac{8 (- 2 - - 3)}{- 2 - - 3} + \frac{- 4 (- 2 - - 3)}{- 2 - - 3} + \frac{- 3}{1} \cdot \frac{- 2 - - 3}{- 2 - - 3}$

Step 5.13

Multiply $\frac{- 3}{1}$ by $\frac{- 2 - - 3}{- 2 - - 3}$ .

$\frac{1}{- 2 - (- 3)} + \frac{- 3 (- 2 - - 3)}{- 2 - - 3} + \frac{8 (- 2 - - 3)}{- 2 - - 3} + \frac{- 4 (- 2 - - 3)}{- 2 - - 3} + \frac{- 3 (- 2 - - 3)}{- 2 - - 3}$

Step 5.14

Reorder terms.

$\frac{1}{- 2 - (- 3)} + \frac{- 3 (- 2 - - 3)}{- 2 - 3 \cdot - 1} + \frac{8 (- 2 - - 3)}{- 2 - - 3} + \frac{- 4 (- 2 - - 3)}{- 2 - - 3} + \frac{- 3 (- 2 - - 3)}{- 2 - - 3}$

Step 5.15

Multiply $- 3$ by $- 1$ .

$\frac{1}{- 2 - (- 3)} + \frac{- 3 (- 2 - - 3)}{- 2 + 3} + \frac{8 (- 2 - - 3)}{- 2 - - 3} + \frac{- 4 (- 2 - - 3)}{- 2 - - 3} + \frac{- 3 (- 2 - - 3)}{- 2 - - 3}$

Step 5.16

Reorder terms.

$\frac{1}{- 2 - (- 3)} + \frac{- 3 (- 2 - - 3)}{- 2 + 3} + \frac{8 (- 2 - - 3)}{- 2 - 3 \cdot - 1} + \frac{- 4 (- 2 - - 3)}{- 2 - - 3} + \frac{- 3 (- 2 - - 3)}{- 2 - - 3}$

Step 5.17

Multiply $- 3$ by $- 1$ .

$\frac{1}{- 2 - (- 3)} + \frac{- 3 (- 2 - - 3)}{- 2 + 3} + \frac{8 (- 2 - - 3)}{- 2 + 3} + \frac{- 4 (- 2 - - 3)}{- 2 - - 3} + \frac{- 3 (- 2 - - 3)}{- 2 - - 3}$

Step 5.18

Reorder terms.

$\frac{1}{- 2 - (- 3)} + \frac{- 3 (- 2 - - 3)}{- 2 + 3} + \frac{8 (- 2 - - 3)}{- 2 + 3} + \frac{- 4 (- 2 - - 3)}{- 2 - 3 \cdot - 1} + \frac{- 3 (- 2 - - 3)}{- 2 - - 3}$

Step 5.19

Multiply $- 3$ by $- 1$ .

$\frac{1}{- 2 - (- 3)} + \frac{- 3 (- 2 - - 3)}{- 2 + 3} + \frac{8 (- 2 - - 3)}{- 2 + 3} + \frac{- 4 (- 2 - - 3)}{- 2 + 3} + \frac{- 3 (- 2 - - 3)}{- 2 - - 3}$

Step 5.20

Reorder terms.

$\frac{1}{- 2 - (- 3)} + \frac{- 3 (- 2 - - 3)}{- 2 + 3} + \frac{8 (- 2 - - 3)}{- 2 + 3} + \frac{- 4 (- 2 - - 3)}{- 2 + 3} + \frac{- 3 (- 2 - - 3)}{- 2 - 3 \cdot - 1}$

Step 5.21

Multiply $- 3$ by $- 1$ .

$\frac{1}{- 2 - (- 3)} + \frac{- 3 (- 2 - - 3)}{- 2 + 3} + \frac{8 (- 2 - - 3)}{- 2 + 3} + \frac{- 4 (- 2 - - 3)}{- 2 + 3} + \frac{- 3 (- 2 - - 3)}{- 2 + 3}$

Step 6

Combine the numerators over the common denominator.

$\frac{1}{- 2 - 3 \cdot - 1} + \frac{- 3 (- 2 - - 3) + 8 (- 2 - - 3) - 4 (- 2 - - 3) - 3 (- 2 - - 3)}{- 2 + 3}$

Step 7

Simplify each term.

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Step 7.1

Multiply $- 1$ by $- 3$ .

$\frac{1}{- 2 - 3 \cdot - 1} + \frac{- 3 (- 2 + 3) + 8 (- 2 - - 3) - 4 (- 2 - - 3) - 3 (- 2 - - 3)}{- 2 + 3}$

Step 7.2

Add $- 2$ and $3$ .

$\frac{1}{- 2 - 3 \cdot - 1} + \frac{- 3 \cdot 1 + 8 (- 2 - - 3) - 4 (- 2 - - 3) - 3 (- 2 - - 3)}{- 2 + 3}$

Step 7.3

Multiply $- 3$ by $1$ .

$\frac{1}{- 2 - 3 \cdot - 1} + \frac{- 3 + 8 (- 2 - - 3) - 4 (- 2 - - 3) - 3 (- 2 - - 3)}{- 2 + 3}$

Step 7.4

Multiply $- 1$ by $- 3$ .

$\frac{1}{- 2 - 3 \cdot - 1} + \frac{- 3 + 8 (- 2 + 3) - 4 (- 2 - - 3) - 3 (- 2 - - 3)}{- 2 + 3}$

Step 7.5

Add $- 2$ and $3$ .

$\frac{1}{- 2 - 3 \cdot - 1} + \frac{- 3 + 8 \cdot 1 - 4 (- 2 - - 3) - 3 (- 2 - - 3)}{- 2 + 3}$

Step 7.6

Multiply $8$ by $1$ .

$\frac{1}{- 2 - 3 \cdot - 1} + \frac{- 3 + 8 - 4 (- 2 - - 3) - 3 (- 2 - - 3)}{- 2 + 3}$

Step 7.7

Multiply $- 1$ by $- 3$ .

$\frac{1}{- 2 - 3 \cdot - 1} + \frac{- 3 + 8 - 4 (- 2 + 3) - 3 (- 2 - - 3)}{- 2 + 3}$

Step 7.8

Add $- 2$ and $3$ .

$\frac{1}{- 2 - 3 \cdot - 1} + \frac{- 3 + 8 - 4 \cdot 1 - 3 (- 2 - - 3)}{- 2 + 3}$

Step 7.9

Multiply $- 4$ by $1$ .

$\frac{1}{- 2 - 3 \cdot - 1} + \frac{- 3 + 8 - 4 - 3 (- 2 - - 3)}{- 2 + 3}$

Step 7.10

Multiply $- 1$ by $- 3$ .

$\frac{1}{- 2 - 3 \cdot - 1} + \frac{- 3 + 8 - 4 - 3 (- 2 + 3)}{- 2 + 3}$

Step 7.11

Add $- 2$ and $3$ .

$\frac{1}{- 2 - 3 \cdot - 1} + \frac{- 3 + 8 - 4 - 3 \cdot 1}{- 2 + 3}$

Step 7.12

Multiply $- 3$ by $1$ .

$\frac{1}{- 2 - 3 \cdot - 1} + \frac{- 3 + 8 - 4 - 3}{- 2 + 3}$

Step 8

Simplify by adding and subtracting.

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Step 8.1

Add $- 3$ and $8$ .

$\frac{1}{- 2 - 3 \cdot - 1} + \frac{5 - 4 - 3}{- 2 + 3}$

Step 8.2

Subtract $4$ from $5$ .

$\frac{1}{- 2 - 3 \cdot - 1} + \frac{1 - 3}{- 2 + 3}$

Step 8.3

Subtract $3$ from $1$ .

$\frac{1}{- 2 - 3 \cdot - 1} + \frac{- 2}{- 2 + 3}$

Step 9

Simplify each term.

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Step 9.1

Simplify the denominator.

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Step 9.1.1

Multiply $- 3$ by $- 1$ .

$\frac{1}{- 2 + 3} + \frac{- 2}{- 2 + 3}$

Step 9.1.2

Add $- 2$ and $3$ .

$\frac{1}{1} + \frac{- 2}{- 2 + 3}$

Step 9.2

Divide $1$ by $1$ .

$1 + \frac{- 2}{- 2 + 3}$

Step 9.3

Add $- 2$ and $3$ .

$1 + \frac{- 2}{1}$

Step 9.4

Divide $- 2$ by $1$ .

$1 - 2$

Step 10

Subtract $2$ from $1$ .

$- 1$