Write each fraction in lowest terms. 90/150

Verified step by step guidance

1. Identify the numerator and denominator of the fraction: numerator = 90, denominator = 150.
2. Find the greatest common divisor (GCD) of 90 and 150. The GCD is the largest number that divides both 90 and 150 without leaving a remainder.
3. Divide both the numerator and the denominator by the GCD to simplify the fraction.
4. Write the simplified fraction as \(\frac{\text{numerator} \div \text{GCD}}{\text{denominator} \div \text{GCD}}\).
5. Verify that the resulting fraction is in lowest terms by checking that the numerator and denominator have no common divisors other than 1.

Key Concepts

Greatest Common Divisor (GCD)

The Greatest Common Divisor is the largest positive integer that divides two numbers without leaving a remainder. Finding the GCD of the numerator and denominator helps simplify fractions by reducing them to their lowest terms.

Simplifying Fractions

Simplifying a fraction involves dividing both the numerator and denominator by their GCD to produce an equivalent fraction with the smallest possible whole numbers. This process makes fractions easier to understand and compare.

Prime Factorization

Prime factorization breaks down numbers into their prime number components. It is a useful method to find the GCD by identifying common prime factors between the numerator and denominator.