12/27 as a simplified fraction
The Correct Answer and Explanation is :
To simplify the fraction 12/27, we need to find the greatest common divisor (GCD) of 12 and 27 and divide both the numerator and the denominator by that number.
Step 1: Find the GCD of 12 and 27
To find the GCD of 12 and 27, we can list the factors of both numbers:
- The factors of 12 are: 1, 2, 3, 4, 6, 12
- The factors of 27 are: 1, 3, 9, 27
The greatest common factor between these two lists is 3.
Step 2: Divide the numerator and the denominator by the GCD
Now that we know the GCD is 3, we divide both the numerator and denominator by 3:
[
\frac{12}{27} = \frac{12 \div 3}{27 \div 3} = \frac{4}{9}
]
Final Answer: 4/9
Thus, the simplified fraction of 12/27 is 4/9.
Explanation of the Process:
Fractions represent a division of two numbers: the numerator (top number) and the denominator (bottom number). Simplifying a fraction means reducing it to its simplest form, where the numerator and the denominator have no common factors other than 1. To do this, we identify the largest number that divides both the numerator and denominator without leaving a remainder. This is called the greatest common divisor (GCD).
By dividing both parts of the fraction by the GCD, we reduce the fraction to its simplest equivalent. In this case, since the GCD of 12 and 27 is 3, dividing both the numerator and denominator by 3 results in 4/9, which is the simplest form of the original fraction.
Simplifying fractions is important because it makes them easier to understand and work with. When fractions are in their simplest form, it’s easier to perform operations like addition, subtraction, multiplication, and division.