Problem 34 - Introductory Algebra for College Students

Question

Simplify each fraction by reducing it to its lowest terms. $$\frac{45}{50}$$

Step-by-Step Solution

Answer

The simplified form of \( \frac{45}{50} \) is \( \frac{9}{10} \)

Step 1: Identify the Numerator and Denominator

The numerator in this fraction is 45 and the denominator is 50.

Step 2: Compute the Greatest Common Divisor (gcd)

Firstly, list the factors of each number. The factors of 45 are: 1, 3, 5, 9, 15, 45 and those for 50 are: 1, 2, 5, 10, 25, 50. The greatest number that exists in both lists is 5, so the gcd of 45 and 50 is 5.

Step 3: Simplify the Fraction

Divide both the numerator and the denominator by the gcd. So, \( \frac{45}{5} \) = 9 and \( \frac{50}{5} \) = 10. From this, the simplified fraction becomes \( \frac{9}{10} \)