Understanding the Relationship Between 1/4 and 1/2
Is 1/4 LESS than 1/2?
When we compare fractions, we often encounter questions that seem simple but can be tricky to answer. One such question is whether 1/4 is less than 1/2. In this article, we will delve into the world of fractions and explore the relationship between 1/4 and 1/2.
What is a Fraction?
Before we dive into the comparison, let’s define what a fraction is. A fraction is a way of representing a part of a whole. It consists of two numbers, the numerator (the top number) and the denominator (the bottom number), separated by a line. For example, 1/2 is a fraction that represents one-half of a whole.
Converting Fractions to Equivalent Decimals
To make the comparison easier, let’s convert the fractions to equivalent decimals. 1/2 as a decimal is 0.5, and 1/4 as a decimal is 0.25.
Is 1/4 LESS than 1/2?
Now that we have the fractions converted to decimals, we can compare them. To determine if 1/4 is less than 1/2, we need to compare the two decimals.
Comparing the Decimals
To compare the decimals, we can use a simple trick. We can subtract 1/2 from 1/4. 1/4 – 1/2 = 1/4 – 2/4 = -1/4
This means that 1/4 is less than 1/2.
Why is 1/4 LESS than 1/2?
So, why is 1/4 less than 1/2? The answer lies in the concept of equivalent ratios. When we convert fractions to equivalent decimals, we are essentially finding the ratio of the numerator to the denominator. In this case, the ratio of 1/4 to 1/2 is 1:2.
The Relationship Between Equivalent Ratios
Now, let’s explore the relationship between equivalent ratios. When we have two equivalent ratios, we can compare them by finding the ratio of the numerator to the denominator. In this case, the ratio of 1/4 to 1/2 is 1:2.
The Difference Between Equivalent Ratios
The key difference between equivalent ratios is that 1/4 has a smaller numerator (1) compared to the denominator (2). This means that 1/4 is less than 1/2.
Conclusion
In conclusion, 1/4 is indeed less than 1/2. The comparison is based on the equivalent ratios of the fractions, and the smaller numerator of 1/4 compared to the denominator of 2 makes it less than 1/2.
Key Takeaways
- To compare fractions, convert them to equivalent decimals.
- Compare the decimals by subtracting 1/2 from 1/4.
- The ratio of 1/4 to 1/2 is 1:2.
- The smaller numerator of 1/4 compared to the denominator of 2 makes it less than 1/2.
Table: Equivalent Ratios
| Fraction | Equivalent Ratio |
|---|---|
| 1/4 | 1/2 |
| 1/2 | 2/4 |
| 1/3 | 2/6 |
| 1/5 | 2/10 |
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