Basic Math Examples

$- \frac{1}{2} + \frac{2}{3} - \frac{3}{4} + n = 0$

Step 1

Simplify $- \frac{1}{2} + \frac{2}{3} - \frac{3}{4} + n$ .

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Step 1.1

To write $- \frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- \frac{1}{2} \cdot \frac{3}{3} + \frac{2}{3} - \frac{3}{4} + n = 0$

Step 1.2

To write $\frac{2}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{1}{2} \cdot \frac{3}{3} + \frac{2}{3} \cdot \frac{2}{2} - \frac{3}{4} + n = 0$

Step 1.3

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.3.1

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

$- \frac{3}{2 \cdot 3} + \frac{2}{3} \cdot \frac{2}{2} - \frac{3}{4} + n = 0$

Step 1.3.2

Multiply $2$ by $3$ .

$- \frac{3}{6} + \frac{2}{3} \cdot \frac{2}{2} - \frac{3}{4} + n = 0$

Step 1.3.3

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

$- \frac{3}{6} + \frac{2 \cdot 2}{3 \cdot 2} - \frac{3}{4} + n = 0$

Step 1.3.4

Multiply $3$ by $2$ .

$- \frac{3}{6} + \frac{2 \cdot 2}{6} - \frac{3}{4} + n = 0$

Step 1.4

Combine the numerators over the common denominator.

$\frac{- 3 + 2 \cdot 2}{6} - \frac{3}{4} + n = 0$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Multiply $2$ by $2$ .

$\frac{- 3 + 4}{6} - \frac{3}{4} + n = 0$

Step 1.5.2

Add $- 3$ and $4$ .

$\frac{1}{6} - \frac{3}{4} + n = 0$

Step 1.6

To write $\frac{1}{6}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{1}{6} \cdot \frac{2}{2} - \frac{3}{4} + n = 0$

Step 1.7

To write $- \frac{3}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{1}{6} \cdot \frac{2}{2} - \frac{3}{4} \cdot \frac{3}{3} + n = 0$

Step 1.8

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.8.1

Multiply $\frac{1}{6}$ by $\frac{2}{2}$ .

$\frac{2}{6 \cdot 2} - \frac{3}{4} \cdot \frac{3}{3} + n = 0$

Step 1.8.2

Multiply $6$ by $2$ .

$\frac{2}{12} - \frac{3}{4} \cdot \frac{3}{3} + n = 0$

Step 1.8.3

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

$\frac{2}{12} - \frac{3 \cdot 3}{4 \cdot 3} + n = 0$

Step 1.8.4

Multiply $4$ by $3$ .

$\frac{2}{12} - \frac{3 \cdot 3}{12} + n = 0$

Step 1.9

Combine the numerators over the common denominator.

$\frac{2 - 3 \cdot 3}{12} + n = 0$

Step 1.10

Simplify the numerator.

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Step 1.10.1

Multiply $- 3$ by $3$ .

$\frac{2 - 9}{12} + n = 0$

Step 1.10.2

Subtract $9$ from $2$ .

$\frac{- 7}{12} + n = 0$

Step 1.11

Move the negative in front of the fraction.

$- \frac{7}{12} + n = 0$

Step 2

Add $\frac{7}{12}$ to both sides of the equation.

$n = \frac{7}{12}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$n = \frac{7}{12}$

Decimal Form:

$n = 0.58\overline{3}$