Basic Math Examples

$\frac{3}{4} - \frac{5}{4} + (\frac{5}{6} - \frac{7}{12}) + 8$

Step 1

Remove parentheses.

$\frac{3}{4} - \frac{5}{4} + \frac{5}{6} - \frac{7}{12} + 8$

Step 2

Combine the numerators over the common denominator.

$8 + \frac{3 - 5}{4} + \frac{5}{6} + \frac{- 7}{12}$

Step 3

Subtract $5$ from $3$ .

$8 + \frac{- 2}{4} + \frac{5}{6} + \frac{- 7}{12}$

Step 4

Find the common denominator.

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Step 4.1

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

$\frac{8}{1} + \frac{- 2}{4} + \frac{5}{6} + \frac{- 7}{12}$

Step 4.2

Multiply $\frac{8}{1}$ by $\frac{12}{12}$ .

$\frac{8}{1} \cdot \frac{12}{12} + \frac{- 2}{4} + \frac{5}{6} + \frac{- 7}{12}$

Step 4.3

Multiply $\frac{8}{1}$ by $\frac{12}{12}$ .

$\frac{8 \cdot 12}{12} + \frac{- 2}{4} + \frac{5}{6} + \frac{- 7}{12}$

Step 4.4

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

$\frac{8 \cdot 12}{12} + \frac{- 2}{4} \cdot \frac{3}{3} + \frac{5}{6} + \frac{- 7}{12}$

Step 4.5

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

$\frac{8 \cdot 12}{12} + \frac{- 2 \cdot 3}{4 \cdot 3} + \frac{5}{6} + \frac{- 7}{12}$

Step 4.6

Multiply $\frac{5}{6}$ by $\frac{2}{2}$ .

$\frac{8 \cdot 12}{12} + \frac{- 2 \cdot 3}{4 \cdot 3} + \frac{5}{6} \cdot \frac{2}{2} + \frac{- 7}{12}$

Step 4.7

Multiply $\frac{5}{6}$ by $\frac{2}{2}$ .

$\frac{8 \cdot 12}{12} + \frac{- 2 \cdot 3}{4 \cdot 3} + \frac{5 \cdot 2}{6 \cdot 2} + \frac{- 7}{12}$

Step 4.8

Reorder the factors of $4 \cdot 3$ .

$\frac{8 \cdot 12}{12} + \frac{- 2 \cdot 3}{3 \cdot 4} + \frac{5 \cdot 2}{6 \cdot 2} + \frac{- 7}{12}$

Step 4.9

Multiply $3$ by $4$ .

$\frac{8 \cdot 12}{12} + \frac{- 2 \cdot 3}{12} + \frac{5 \cdot 2}{6 \cdot 2} + \frac{- 7}{12}$

Step 4.10

Reorder the factors of $6 \cdot 2$ .

$\frac{8 \cdot 12}{12} + \frac{- 2 \cdot 3}{12} + \frac{5 \cdot 2}{2 \cdot 6} + \frac{- 7}{12}$

Step 4.11

Multiply $2$ by $6$ .

$\frac{8 \cdot 12}{12} + \frac{- 2 \cdot 3}{12} + \frac{5 \cdot 2}{12} + \frac{- 7}{12}$

Step 5

Combine the numerators over the common denominator.

$\frac{8 \cdot 12 - 2 \cdot 3 + 5 \cdot 2 - 7}{12}$

Step 6

Simplify each term.

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Step 6.1

Multiply $8$ by $12$ .

$\frac{96 - 2 \cdot 3 + 5 \cdot 2 - 7}{12}$

Step 6.2

Multiply $- 2$ by $3$ .

$\frac{96 - 6 + 5 \cdot 2 - 7}{12}$

Step 6.3

Multiply $5$ by $2$ .

$\frac{96 - 6 + 10 - 7}{12}$

Step 7

Reduce the expression by cancelling the common factors.

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Step 7.1

Subtract $6$ from $96$ .

$\frac{90 + 10 - 7}{12}$

Step 7.2

Simplify by adding and subtracting.

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Step 7.2.1

Add $90$ and $10$ .

$\frac{100 - 7}{12}$

Step 7.2.2

Subtract $7$ from $100$ .

$\frac{93}{12}$

Step 7.3

Cancel the common factor of $93$ and $12$ .

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Step 7.3.1

Factor $3$ out of $93$ .

$\frac{3 (31)}{12}$

Step 7.3.2

Cancel the common factors.

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Step 7.3.2.1

Factor $3$ out of $12$ .

$\frac{3 \cdot 31}{3 \cdot 4}$

Step 7.3.2.2

Cancel the common factor.

$\frac{3 \cdot 31}{3 \cdot 4}$

Step 7.3.2.3

Rewrite the expression.

$\frac{31}{4}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{31}{4}$

Decimal Form:

$7.75$

Mixed Number Form:

$7 \frac{3}{4}$