48/100 in simplest form
The Correct Answer and Explanation is :
To simplify the fraction ( \frac{48}{100} ), we need to find the greatest common divisor (GCD) of 48 and 100. The GCD is the largest number that divides both 48 and 100 without leaving a remainder. Once we find the GCD, we can divide both the numerator (48) and the denominator (100) by that number to simplify the fraction.
Step 1: Find the GCD of 48 and 100
First, let’s break down both 48 and 100 into their prime factors.
- Prime factorization of 48:
[
48 = 2^4 \times 3
] - Prime factorization of 100:
[
100 = 2^2 \times 5^2
]
The common prime factor between 48 and 100 is ( 2 ), and the smallest power of ( 2 ) in their factorizations is ( 2^2 = 4 ). Therefore, the GCD of 48 and 100 is 4.
Step 2: Divide both the numerator and the denominator by the GCD
Now, divide both the numerator (48) and the denominator (100) by the GCD (4):
[
\frac{48}{100} = \frac{48 \div 4}{100 \div 4} = \frac{12}{25}
]
Step 3: Check if the fraction is in simplest form
The fraction ( \frac{12}{25} ) is now in its simplest form because 12 and 25 have no common factors other than 1. The prime factorization of 12 is ( 2^2 \times 3 ), and the prime factorization of 25 is ( 5^2 ). Since there are no common prime factors, the fraction cannot be simplified further.
Final Answer:
The fraction ( \frac{48}{100} ) simplifies to ( \frac{12}{25} ).
Explanation:
Simplifying fractions is a process of reducing them to their simplest form by dividing both the numerator and denominator by their greatest common divisor (GCD). The GCD ensures that both numbers are divided as much as possible while maintaining the ratio between them. In this case, by dividing both 48 and 100 by 4, we get the simplest form of the fraction, ( \frac{12}{25} ).