What fraction is less than 1/2
The Correct Answer and Explanation is:
To find a fraction that is less than ( \frac{1}{2} ), we can consider several examples. A straightforward fraction is ( \frac{1}{3} ). Let’s explore why ( \frac{1}{3} ) is less than ( \frac{1}{2} ) and how fractions compare in general.
Understanding Fraction Comparison
Fractions are composed of two parts: the numerator (the top number) and the denominator (the bottom number). The value of a fraction depends on the relationship between these two components. When comparing two fractions, it’s essential to have a common denominator to see which fraction is larger or smaller.
- Finding a Common Denominator: The denominators of ( \frac{1}{3} ) and ( \frac{1}{2} ) are 3 and 2, respectively. The least common multiple (LCM) of 3 and 2 is 6.
- Converting to a Common Denominator:
- To convert ( \frac{1}{3} ) to have a denominator of 6, we multiply both the numerator and the denominator by 2:
[
\frac{1 \times 2}{3 \times 2} = \frac{2}{6}
] - To convert ( \frac{1}{2} ) to have a denominator of 6, we multiply both the numerator and the denominator by 3:
[
\frac{1 \times 3}{2 \times 3} = \frac{3}{6}
]
- Comparison: Now, we can compare the two fractions:
[
\frac{2}{6} \text{ (which is } \frac{1}{3}) < \frac{3}{6} \text{ (which is } \frac{1}{2})
]
Since ( \frac{2}{6} ) is less than ( \frac{3}{6} ), we can conclude that ( \frac{1}{3} ) is indeed less than ( \frac{1}{2} ).
Conclusion
In conclusion, ( \frac{1}{3} ) is a valid example of a fraction that is less than ( \frac{1}{2} ). There are countless other fractions that also fulfill this criterion, such as ( \frac{1}{4}, \frac{2}{5}, ) and ( \frac{3}{8} ). The key takeaway is understanding how to compare fractions by using a common denominator to facilitate the comparison. This method can be applied universally for any fractions to determine their relative sizes.