Simplify the fraction 12/18 to its simplest form.
The Correct Answer and Explanation is :
The fraction ( \frac{12}{18} ) can be simplified by finding the greatest common divisor (GCD) of 12 and 18, which is the largest number that divides both the numerator (12) and the denominator (18) without leaving a remainder.
Step-by-Step Simplification:
- Find the GCD of 12 and 18:
- Factors of 12: ( 1, 2, 3, 4, 6, 12 )
- Factors of 18: ( 1, 2, 3, 6, 9, 18 )
- The greatest common divisor of 12 and 18 is 6.
- Divide both the numerator and the denominator by their GCD (6):
- ( \frac{12 \div 6}{18 \div 6} = \frac{2}{3} )
Thus, the simplified form of ( \frac{12}{18} ) is ( \frac{2}{3} ).
Explanation:
Simplifying fractions is the process of reducing them to their lowest terms by dividing both the numerator (top number) and the denominator (bottom number) by their greatest common divisor. This does not change the value of the fraction; it only expresses the same ratio in simpler terms.
In this case, the fraction ( \frac{12}{18} ) means “12 parts out of 18 total parts.” To simplify, we determine that both 12 and 18 are divisible by 6, their greatest common factor. After dividing both numbers by 6, we get ( \frac{2}{3} ), which means “2 parts out of 3 total parts.”
Simplifying fractions helps make them easier to work with, whether for comparison, addition, subtraction, or other mathematical operations. This process ensures that the fraction is in its simplest and most understandable form, without changing the proportion or value it represents.