Identify the greatest common divisor (GCD) of the numerator and the denominator. In this case, find the GCD of 18 and 90.
List the factors of 18: 1, 2, 3, 6, 9, 18.
List the factors of 90: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90.
Determine the largest common factor from the lists: 18.
Divide both the numerator and the denominator by their GCD (18) to simplify the fraction.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Lowest Terms
A fraction is in lowest terms when the numerator and denominator have no common factors other than 1. This means that the fraction cannot be simplified further. To express a fraction in lowest terms, you divide both the numerator and the denominator by their greatest common divisor (GCD).
The greatest common divisor is the largest positive integer that divides two or more integers without leaving a remainder. Finding the GCD is essential for simplifying fractions, as it helps identify the common factors between the numerator and denominator. Methods to find the GCD include listing factors, using the Euclidean algorithm, or prime factorization.
Simplifying fractions involves reducing them to their lowest terms by eliminating common factors from the numerator and denominator. This process makes fractions easier to work with and understand. For example, simplifying 18/90 involves dividing both numbers by their GCD, which is 18, resulting in the simplified fraction 1/5.