Question

Perform the indicated operation. Write all results in lowest terms. $$\frac{1}{2}-\frac{1}{3}-\frac{1}{4}$$

Short answer

Question: Subtract the following fractions and express the result in the lowest terms: $$\frac{1}{2}-\frac{1}{3}-\frac{1}{4}$$ Answer: $$\frac{-1}{12}$$

Step-by-step solution

Find a common denominator

In order to perform the subtraction, each fraction needs to have the same denominator. The common denominator should be the least common multiple (LCM) of the denominators. The LCM of 2, 3, and 4 is 12, so we will make each fraction have a denominator of 12.

Convert each fraction to an equivalent fraction with a denominator of 12

Multiply the numerator and denominator of each fraction by an appropriate value so that the denominator becomes 12. $$\frac{1}{2} \times \frac{6}{6} = \frac{6}{12}$$ $$\frac{1}{3} \times \frac{4}{4} = \frac{4}{12}$$ $$\frac{1}{4} \times \frac{3}{3} = \frac{3}{12}$$

Perform the subtraction with the new fractions

Now that all the fractions have a common denominator, subtract them one by one. $$\frac{6}{12}-\frac{4}{12}-\frac{3}{12}$$

Simplify the resulting fraction

Combine the fractions and simplify the result. $$\frac{6-4-3}{12} = \frac{-1}{12}$$

Final Answer

The result of the subtraction is: $$\frac{1}{2}-\frac{1}{3}-\frac{1}{4} = \frac{-1}{12}$$