Is 1/4 less than or greater than 1/8?
The Correct Answer and Explanation is:
To determine whether ( \frac{1}{4} ) is less than or greater than ( \frac{1}{8} ), we can use a few different methods. Let’s explore these in detail.
Method 1: Common Denominators
One effective way to compare fractions is to express them with a common denominator. The denominators in this case are 4 and 8. The least common denominator (LCD) of 4 and 8 is 8.
Now, we can convert ( \frac{1}{4} ) to a fraction with a denominator of 8:
[
\frac{1}{4} = \frac{1 \times 2}{4 \times 2} = \frac{2}{8}
]
Now we can directly compare the two fractions:
- ( \frac{2}{8} )
- ( \frac{1}{8} )
Since ( 2 ) is greater than ( 1 ), we find that:
[
\frac{2}{8} > \frac{1}{8}
]
Thus, ( \frac{1}{4} ) is greater than ( \frac{1}{8} ).
Method 2: Decimal Conversion
Another way to compare fractions is by converting them to decimals.
To convert ( \frac{1}{4} ):
[
\frac{1}{4} = 0.25
]
To convert ( \frac{1}{8} ):
[
\frac{1}{8} = 0.125
]
Now that both fractions are expressed as decimals, we can see:
[
0.25 > 0.125
]
This confirms that ( \frac{1}{4} ) is indeed greater than ( \frac{1}{8} ).
Conclusion
From both methods, we can confidently conclude that ( \frac{1}{4} ) is greater than ( \frac{1}{8} ). This comparison demonstrates the relationship between these two fractions, highlighting the importance of using common denominators or decimal conversions for clarity. Therefore, the answer is:
( \frac{1}{4} > \frac{1}{8} ).