Write the fraction 16/18 in simplest form.
The Correct Answer and Explanation is:
To simplify the fraction ( \frac{16}{18} ), we need to find the greatest common divisor (GCD) of the numerator (16) and the denominator (18). The GCD is the largest number that divides both numbers without leaving a remainder.
Step 1: Find the GCD of 16 and 18
First, we can list the factors of both numbers:
- Factors of 16: 1, 2, 4, 8, 16
- Factors of 18: 1, 2, 3, 6, 9, 18
From the lists, we can see that the common factors are 1 and 2. The greatest of these is 2. Thus, the GCD of 16 and 18 is 2.
Step 2: Divide both the numerator and the denominator by the GCD
Next, we divide both the numerator and the denominator of the fraction ( \frac{16}{18} ) by the GCD (2):
[
\frac{16 \div 2}{18 \div 2} = \frac{8}{9}
]
Step 3: Confirm that the fraction is in simplest form
To ensure that ( \frac{8}{9} ) is in its simplest form, we check whether there are any common factors between 8 and 9. The factors of 8 are 1, 2, 4, and 8, while the factors of 9 are 1, 3, and 9. The only common factor is 1, which indicates that ( \frac{8}{9} ) cannot be simplified further.
Conclusion
Therefore, the simplified form of the fraction ( \frac{16}{18} ) is ( \frac{8}{9} ). Simplifying fractions is an important skill in mathematics, as it allows for easier calculations and clearer communication of numerical relationships. It also emphasizes the concept of equivalent fractions, where different fractions can represent the same value, but in its simplest form, a fraction conveys the most direct representation of that value.