Write the fraction in simplest form 5/5
The Correct Answer and Explanation is :
The correct answer is: ( \frac{1}{1} )
To simplify the fraction ( \frac{5}{5} ), we first need to understand what a fraction represents. A fraction consists of a numerator (the top number) and a denominator (the bottom number). In this case, both the numerator and the denominator are the same, which is 5.
Steps to Simplify the Fraction:
- Identifying the Greatest Common Divisor (GCD):
To simplify a fraction, we look for the greatest common divisor (GCD) of the numerator and the denominator. The GCD is the largest number that divides both numbers without leaving a remainder. For ( 5 ) and ( 5 ), the GCD is ( 5 ) itself. - Dividing Both the Numerator and Denominator by the GCD:
We simplify the fraction by dividing both the numerator and the denominator by their GCD:
[
\frac{5 \div 5}{5 \div 5} = \frac{1}{1}
] - Understanding the Simplified Fraction:
The fraction ( \frac{1}{1} ) represents a whole number. In mathematical terms, any fraction where the numerator is equal to the denominator is equal to 1. This is because you are essentially saying you have the same amount in the numerator as you do in the denominator, which equals one complete unit.
Conclusion:
Thus, the fraction ( \frac{5}{5} ) simplifies to ( \frac{1}{1} ), which is equivalent to 1. This result highlights an essential property of fractions: whenever the numerator and denominator are the same, the fraction simplifies to one. In summary, ( \frac{5}{5} ) in its simplest form is ( 1 ), emphasizing the fundamental concept that equal quantities yield a whole when compared. This concept is crucial in various mathematical applications, such as solving equations or performing arithmetic operations with fractions.