Identify the greatest common divisor (GCD) of the numerator and the denominator. In this case, find the GCD of 100 and 140.
Divide both the numerator and the denominator by their GCD to simplify the fraction.
Write the simplified fraction using the results from the division.
Verify that the fraction is in its lowest terms by checking that the numerator and denominator have no common factors other than 1.
Express the simplified fraction as the final answer.
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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 100/140 involves dividing both numbers by their GCD, which is 20, resulting in the fraction 5/7.