Problem 84 - Introductory Algebra for College Students

Question

Perform the indicated operation. Where possible, reduce the answer to its lowest terms. $$\frac{17}{18}-\frac{4}{9}$$

Step-by-Step Solution

Answer

The answer is \(\frac{1}{2}\).

Step 1: Identify the Least Common Denominator (LCD)

First thing to do in subtracting fractions is to find the least common denominator which, in this case, is the least common multiple of 18 and 9. The smallest number that both 18 and 9 can go into is 18. So our common denominator here is 18.

Step 2: Rewrite the Fractions

The first fraction is already over 18, so no changes there. But the second fraction is over 9. To make it over 18 (common denominator), we need to multiply both its numerator and denominator by 2. Giving a fraction \(\frac{8}{18}\). So, the new expression becomes \(\frac{17}{18}-\frac{8}{18}\)

Step 3: Subtract the Fractions

Now that they have the same denominator, subtract the numerators. \(17 - 8 = 9\). So, we have \(\frac{9}{18}\)

Step 4: Reduce to Lowest Terms

Finally, we need to express our result in lowest terms by dividing both the numerator and the denominator by their greatest common divisor. The greatest common divisor of 9 and 18 is 9. So, \(\frac{9}{18} = \frac{9 ÷ 9}{18 ÷ 9} = \frac{1}{2}\)