Compute $\frac{3}{4} - \frac{2}{3}$.

How we read your problem

Exact arithmetic with fractions (results kept in lowest terms).

Step-by-step solution

1. 1

   Rewrite both fractions with the least common denominator

   The LCD of 4 and 3 is 12.

   $$\frac{3}{4} - \frac{2}{3} = \frac{9}{12} - \frac{8}{12}$$
2. 2

   Subtract the numerators and keep the denominator

   $$\frac{9 - 8}{12} = \frac{1}{12}$$
3. 3

   Final answer in lowest terms

   $$\frac{1}{12}$$

Formulas used

• Addition

  $$\frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd}$$

• Multiplication

  $$\frac{a}{b} \times \frac{c}{d} = \frac{ac}{bd}$$

• Division

  $$\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}$$

Fractions are combined over a common denominator for addition and subtraction, multiplied straight across, and divided by multiplying by the reciprocal. The result is reduced by the greatest common factor.

Verification

• Decimal check: 1/12 ≈ 0.08333333333