Problem 85 - Introductory Algebra for College Students

Question

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

Step-by-Step Solution

Answer

The difference between \(\frac{4}{3}\) and \(\frac{3}{4}\) is \(\frac{7}{12}\).

Step 1: Find a Common Denominator

Both 3 and 4 are prime numbers, so they have no common factors other than 1. Their least common multiple (and therefore their least common denominator) is their product, which is 12. So rewrite \(\frac{4}{3}\) as \(\frac{4}{3} \times \frac{4}{4} = \frac{16}{12}\) and \(\frac{3}{4}\) as \(\frac{3}{4} \times \frac{3}{3} = \frac{9}{12}\).

Step 2: Perform the Subtraction

Now that the fractions have the same denominator, you can subtract the numerators: \(\frac{16}{12} - \frac{9}{12} = \frac{16 - 9}{12} = \frac{7}{12}\).

Step 3: Simplify the Fraction

The fraction \(\frac{7}{12}\) cannot be simplified further because 7 is a prime number and 12 has no factors of 7.