Write each fraction in lowest terms. 100/140

Verified step by step guidance

1. Identify the numerator and denominator of the fraction: numerator = 100, denominator = 140.
2. Find the greatest common divisor (GCD) of 100 and 140. This is the largest number that divides both 100 and 140 without leaving a remainder.
3. To find the GCD, list the factors of 100 and 140 or use the Euclidean algorithm.
4. Divide both the numerator and the denominator by the GCD to simplify the fraction.
5. Write the simplified fraction with the new numerator and denominator after division.

Key Concepts

Greatest Common Divisor (GCD)

The Greatest Common Divisor of two numbers is the largest number that divides both without leaving a remainder. Finding the GCD is essential for simplifying fractions because it helps identify the factor by which both numerator and denominator can be divided to reduce the fraction to its lowest terms.

Simplifying Fractions

Simplifying a fraction involves dividing the numerator and denominator by their GCD to express the fraction in its simplest form. This process ensures the fraction is easier to understand and work with, as it has no common factors other than 1.

Prime Factorization

Prime factorization breaks down numbers into their prime number components. This method helps in finding the GCD by identifying common prime factors between the numerator and denominator, facilitating the simplification of fractions.