Problem 87 - Introductory Algebra for College Students

Question

Perform the indicated operation. Where possible, reduce the answer to its lowest terms. $$\frac{7}{10}-\frac{3}{16}$$

Step-by-Step Solution

Answer

\(\frac{41}{80}\)

Step 1: Find a common denominator

The first step is to find a common denominator so the fractions can be subtracted. The least common denominator for 10 and 16 is 80. Therefore, the fractions will be converted as follows: \(\frac{7}{10} = \frac{7 \times 8}{10 \times 8} = \frac{56}{80}\) and \(\frac{3}{16} = \frac{3 \times 5}{16 \times 5} = \frac{15}{80}\)

Step 2: Subtract fractions

Since they now have the same denominator, the fractions can be subtracted directly: \(\frac{56}{80} - \frac{15}{80} = \frac{41}{80}\

Step 3: Simplify the fraction

The last step is to simplify the result to lowest terms, which means finding the greatest common factor of the numerator and denominator and dividing both by it. The greatest common factor of 41 and 80 is 1, so the fraction is already in its simplest form: \(\frac{41}{80}\)