When reducing the fraction what should you find First
When reducing a fraction, the first step is to find the greatest common divisor (GCD) of the numerator and denominator.
When reducing a fraction, the first thing you should find is the greatest common divisor (GCD) of the numerator and the denominator. The GCD is the largest number that can divide both the numerator and the denominator without leaving a remainder.
When reducing a fraction, the first thing you should find is the greatest common divisor (GCD) of the numerator and denominator. The GCD is the largest number that divides both the numerator and denominator without leaving a remainder.
To find the GCD, you can use various methods such as prime factorization or the Euclidean algorithm.
- Prime factorization: Find the prime factors of both the numerator and denominator, and then determine their common factors. Multiply these common factors together to find the GCD.
For example, let's say we have the fraction 12/24:
- The prime factorization of 12 is 2 x 2 x 3.
- The prime factorization of 24 is 2 x 2 x 2 x 3.
- The common factors are 2 x 2 x 3 = 12.
So, the GCD of 12 and 24 is 12.
- Euclidean algorithm: Divide the larger number by the smaller number and find the remainder. Then, divide the smaller number by this remainder. Repeat this process until the remainder is zero. The last non-zero remainder will be the GCD.
For example, let's say we have the fraction 18/24:
- Divide 24 by 18. The remainder is 6.
- Divide 18 by 6. The remainder is 0.
So, the GCD of 18 and 24 is 6.
After finding the GCD, you can then divide both the numerator and denominator by it to simplify the fraction further if possible. By dividing both numbers by their GCD, you ensure that the fraction is in its simplest form.