Problem 89 - Introductory Algebra for College Students

Question

Perform the indicated operation. Where possible, reduce the answer to its lowest terms. $$3 \frac{3}{4}-2 \frac{1}{3}$$

Step-by-Step Solution

Answer

The solution to the problem is \(1 \frac{5}{12}\)

Step 1: Split each mixed number

Split each mixed number into its integer and fractional parts. So, we'll have:\[3 \frac{3}{4} = 3 + \frac{3}{4}\]and \[2 \frac{1}{3} = 2 + \frac{1}{3}\]

Step 2: Subtract the integers and fractions separately

Subtract the integer parts and the fractional parts separately. We have:\[\text{Integer parts: } 3 - 2 = 1\] \[\text{Fractional parts: } \frac{3}{4} - \frac{1}{3}\]To subtract the fractional parts, we need a common denominator. The least common denominator for 4 and 3 is 12. Convert \( \frac{3}{4} \) and \( \frac{1}{3} \) into similar fractions with denominator 12:\[\frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12}\] \[\frac{1}{3} = \frac{1 \times 4}{3 \times 4} = \frac{4}{12}\]Now subtract the two fractions:\[\frac{9}{12} - \frac{4}{12} = \frac{5}{12}\]

Step 3: Combine the results

Combine the results from the integer and the fraction parts to get the final answer. So, \[1 + \frac{5}{12} = 1 \frac{5}{12}\]