Which Fraction is the Smallest: 1/4, 3/4, 1/5, 1/6?
Understanding which among given fractions is the smallest can help in a variety of mathematical problems, particularly in comparing quantities. This article will explore the steps to determine the smallest fraction among 1/4, 3/4, 1/5, 1/6 using both visual and numerical methods.
Visual Comparison Using Common Denominators
The simplest method to compare fractions directly is to convert them to have a common denominator. Let's convert each fraction to a denominator of 60:
1/4 15/60 3/4 45/60 1/5 12/60 1/6 10/60By comparing these equivalent fractions, it's clear that 10/60 is the smallest, which translates to 1/6. This shows that the fraction with the largest denominator (when converted to a common denominator) is the smallest among the fractions.
Using Decimal Equivalents
Another straightforward method is to convert each fraction to its decimal equivalent:
1/4 0.25 3/4 0.75 1/5 0.2 1/6 ≈ 0.1667The decimal values make it simple to identify the smallest fraction as 0.1667, which corresponds to 1/6.
Understanding the Concept
The key concept to grasp is that the size of the fraction decreases as the denominator increases, assuming the numerators are the same. In this case:
1/4 (0.25) 1/5 (0.2) 1/6 (0.1667) 3/4 (0.75)It's clear that as the denominator increases (1/6 has the largest denominator), the fraction value decreases, making it the smallest.
Conclusion
In summary, among the given fractions 1/4, 3/4, 1/5, and 1/6, the smallest fraction is 1/6. This conclusion can be reached by either visual comparison using common denominators or by converting them to decimal equivalents.