What is the simplified form of the fraction below 8/48
The Correct Answer and Explanation is :
To simplify the fraction 8/48, we need to find the greatest common divisor (GCD) of the numerator (8) and the denominator (48). The GCD is the largest number that divides both numbers without leaving a remainder.
Step 1: Find the factors of 8 and 48.
- The factors of 8 are: 1, 2, 4, 8.
- The factors of 48 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.
The largest common factor between 8 and 48 is 8, so the GCD of 8 and 48 is 8.
Step 2: Divide both the numerator and the denominator by the GCD.
To simplify the fraction, divide both the numerator (8) and the denominator (48) by their GCD (8):
[
\frac{8}{48} = \frac{8 \div 8}{48 \div 8} = \frac{1}{6}
]
Thus, the simplified form of 8/48 is 1/6.
Step 3: Verify the result.
The fraction 1/6 is in its simplest form because the numerator (1) and the denominator (6) have no common divisors other than 1. Therefore, we cannot simplify it further.
Explanation:
Simplifying a fraction is an important skill in mathematics. It allows us to express fractions in their most efficient and understandable form. The process involves finding the GCD of the numerator and denominator, then dividing both numbers by the GCD. By doing so, we reduce the fraction to its lowest terms, making it easier to compare, perform arithmetic operations, or interpret. For example, 8/48 represents the same value as 1/6, but the latter is more compact and easier to work with.