Simplify the fraction to lowest terms. \frac{14}{17
The Correct Answer and Explanation is:
Correct Answer:
1417\frac{14}{17}1714 is already in its lowest terms.
Explanation
A fraction is simplified or reduced to lowest terms when the numerator and denominator share no common factors other than 1. To simplify a fraction, one must determine the greatest common divisor (GCD) of the numerator and denominator. The GCD is the largest positive integer that divides both numbers evenly.
In this case, the numerator is 14, and the denominator is 17. Begin by listing the factors of each number:
- Factors of 14: 1, 2, 7, 14
- Factors of 17: 1, 17
After comparing the factor lists, the only number that appears in both is 1. This means the GCD of 14 and 17 is 1. Since there is no higher common factor between the numerator and the denominator, no further simplification is possible.
An important property of fractions involving prime numbers is relevant here. The number 17 is a prime number, which means it is divisible only by 1 and itself. Therefore, unless the numerator is a multiple of 17, the fraction will already be in simplest form. Because 14 is not a multiple of 17, no simplification can occur.
The fraction 1417\frac{14}{17}1714 also represents a rational number that cannot be expressed more simply without converting to a decimal. In decimal form, 1417≈0.8235\frac{14}{17} \approx 0.82351714≈0.8235, but this is only an approximation and does not serve as a simplified fraction.
Understanding simplification of fractions is fundamental in arithmetic and algebra, as it helps in comparing, adding, or subtracting fractions more efficiently. The simplest form offers clarity and reduces the potential for arithmetic errors in more complex mathematical procedures.
Thus, 1417\frac{14}{17}1714 remains the simplest and most reduced form of the fraction.
