Which is greater 1/4 or 3/4
The Correct Answer and Explanation is:
To determine which fraction is greater between ( \frac{1}{4} ) and ( \frac{3}{4} ), we need to compare the two fractions. The fractions are both in terms of fourths, so they share the same denominator, making it easier to compare them directly.
Step 1: Understanding the Denominator
Both fractions have the denominator 4, which means they represent portions of a whole divided into 4 equal parts. In this case, the numerator indicates how many of those 4 parts are being considered.
- ( \frac{1}{4} ) means 1 part out of the 4 equal parts of a whole.
- ( \frac{3}{4} ) means 3 parts out of the 4 equal parts of a whole.
Step 2: Comparing the Numerators
Since the denominators are the same, the fraction with the larger numerator represents a larger portion of the whole.
- The numerator of ( \frac{1}{4} ) is 1.
- The numerator of ( \frac{3}{4} ) is 3.
Since 3 is greater than 1, we can conclude that ( \frac{3}{4} ) represents a larger portion of the whole than ( \frac{1}{4} ).
Step 3: Visualizing the Fractions
Another way to think about it is to visualize these fractions on a number line or as a whole divided into 4 equal parts. The fraction ( \frac{1}{4} ) is one quarter of the whole, while ( \frac{3}{4} ) is three quarters of the whole. Clearly, three parts out of four are more than one part out of four.
Step 4: Conclusion
Thus, ( \frac{3}{4} ) is greater than ( \frac{1}{4} ), because 3 out of 4 is a larger quantity than 1 out of 4. This is a straightforward comparison based on the principle that, when two fractions have the same denominator, the fraction with the larger numerator is always the larger fraction.
In summary, ( \frac{3}{4} ) is greater than ( \frac{1}{4} ), and this can be easily verified by comparing their numerators.