Problem 83 - Introductory Algebra for College Students

Question

Perform the indicated operation. Where possible, reduce the answer to its lowest terms. $$\frac{11}{18}-\frac{2}{9}$$

Step-by-Step Solution

Answer

\(\frac{7}{18}\)

Step 1: Find a common denominator

In order to subtract fractions, they must have the same denominator. The denominators in these fractions, 18 and 9, have a common factor. Since \(18 = 9 \times 2\), we can already see the common denominator is 18. So the first fraction remains the same and the second fraction needs to be converted to have 18 as the denominator.

Step 2: Convert the second fraction

To convert the second fraction \(\frac{2}{9}\) to have 18 as the denominator, multiply both the numerator and the denominator by 2: \(\frac{2 \times 2}{9 \times 2} = \frac{4}{18}\)

Step 3: Subtract the fractions

Now, subtract the second fraction from the first: \(\frac{11}{18} - \frac{4}{18}\) equals \(\frac{11 - 4}{18} = \frac{7}{18}\)

Step 4: Check if the answer can be simplified

\(\frac{7}{18}\) is already in its simplest form. Both 7 and 18 do not share any other common factors apart from 1.