Write a fraction less than 1/4 that has a numerator of 1.
The Correct Answer and Explanation is :
A fraction less than ( \frac{1}{4} ) that has a numerator of 1 is ( \frac{1}{5} ).
Explanation:
To understand why ( \frac{1}{5} ) is less than ( \frac{1}{4} ), let’s first define what fractions represent. A fraction is a way of expressing a part of a whole, where the numerator represents the number of parts we have, and the denominator represents the total number of equal parts the whole is divided into.
In this case, ( \frac{1}{4} ) represents one part out of four equal parts, while ( \frac{1}{5} ) represents one part out of five equal parts. To compare fractions, we can use the concept of common denominators or simply visualize the sizes of the parts.
- Visualizing the fractions: Imagine a whole divided into 4 equal parts. Each part would represent ( \frac{1}{4} ) of the whole. Now, imagine dividing the same whole into 5 equal parts. Each part would represent ( \frac{1}{5} ), which is smaller than ( \frac{1}{4} ), because the whole is divided into more parts. Therefore, ( \frac{1}{5} ) is smaller than ( \frac{1}{4} ).
- Using common denominators: Another way to compare fractions is to find a common denominator. The least common denominator (LCD) of 4 and 5 is 20. So, we rewrite the fractions with this denominator:
- ( \frac{1}{4} = \frac{5}{20} )
- ( \frac{1}{5} = \frac{4}{20} )
Since ( \frac{4}{20} ) is less than ( \frac{5}{20} ), it confirms that ( \frac{1}{5} ) is smaller than ( \frac{1}{4} ).
Thus, ( \frac{1}{5} ) is a fraction with a numerator of 1 that is less than ( \frac{1}{4} ).