Simplify the fraction 99/100
The Correct Answer and Explanation is:
The fraction ( \frac{99}{100} ) is already in its simplest form.
Explanation
To determine whether a fraction like ( \frac{99}{100} ) can be simplified further, we start by examining its numerator (99) and denominator (100) to see if they have any common factors other than 1. Simplifying a fraction means dividing both the numerator and denominator by their greatest common divisor (GCD), which is the largest integer that divides both numbers without leaving a remainder. In this case, the numerator is 99, and the denominator is 100.
- Prime Factorization: Breaking down 99 and 100 into their prime factors can help us check for common factors.
- 99: The prime factors of 99 are 3 and 11. We can express this as ( 99 = 3^2 \times 11 ).
- 100: The prime factors of 100 are 2 and 5. This can be expressed as ( 100 = 2^2 \times 5^2 ). Since 99 is only divisible by 3 and 11, and 100 is only divisible by 2 and 5, 99 and 100 have no common prime factors. This means their GCD is 1.
- Checking for Simplification: With a GCD of 1, we know that dividing both 99 and 100 by 1 would still leave us with 99 and 100, respectively. Therefore, no further simplification is possible, as there are no larger numbers that can divide both values evenly.
- Conclusion: Since the fraction is already in its lowest terms, ( \frac{99}{100} ) cannot be simplified further. It represents a proper fraction because the numerator (99) is less than the denominator (100), which makes it equivalent to 0.99 in decimal form.
In summary, ( \frac{99}{100} ) is already simplified because 99 and 100 share no common divisors other than 1, and therefore it is in its simplest form.