How to Simplify Fractions Quickly and Easily?
Learn fast methods to simplify fractions using GCD and prime factorization for quick calculations.
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Simplifying fractions is quick if you follow these steps: Identify the greatest common divisor (GCD) of the numerator and denominator. Divide both by the GCD. For example, to simplify 8/12, the GCD is 4. Divide both parts by 4, resulting in 2/3. Another fast method is using prime factorization. Break down both numbers to their prime factors, cancel out common factors, and simplify to the lowest terms. These techniques provide a straightforward way to simplify fractions efficiently.
FAQs & Answers
- What is a fraction? A fraction is a mathematical expression representing the division of one quantity by another, typically written in the form 'a/b', where 'a' is the numerator and 'b' is the denominator.
- What is the greatest common divisor (GCD)? The greatest common divisor (GCD) is the largest number that divides two or more numbers without leaving a remainder. It is essential for simplifying fractions.
- How do I find the GCD of two numbers? To find the GCD of two numbers, you can list the factors of each number, or use the prime factorization method, or apply the Euclidean algorithm, which involves a series of division steps.
- Can all fractions be simplified? Yes, all fractions can be simplified to their lowest terms by dividing the numerator and denominator by their GCD.