Question

Find the difference. $$\frac{3}{4}-\frac{5}{12}$$

Short answer

The difference between \(\frac{3}{4}\) and \(\frac{5}{12}\) is \(\frac{1}{3}\).

Step-by-step solution

Find the Least Common Multiple (LCM)

The LCM is the smallest number that both 4 and 12 can divide into. Multiples of 4 are 4, 8, 12, 16, 20, ... and multiples of 12 are 12, 24, 36, .... The smallest multiple they share is 12.

Convert Fractions to Equivalent Fractions

With the LCM, convert each fraction to equivalent fractions that have this denominator. The first fraction is already \(\frac{3}{4}\). To make 4 into 12, multiply by 3, therefore also multiply 3 by 3. The first fraction becomes \(\frac{9}{12}\). The second fraction is already \(\frac{5}{12}\), so no changes needed.

Subtract Fractions

Now, subtract the equivalent fractions: \(\frac{9}{12} - \frac{5}{12} = \frac{9-5}{12} = \frac{4}{12}\)

Simplify the Fraction

The fraction \(\frac{4}{12}\) can be simplified as both 4 and 12 have common factors. They can both be divided by 4, so the simplified fraction is \(\frac{1}{3}\).