Is 1/2 bigger than 3/4?

David Girones

Updated on:

Mathematics, a discipline that has existed for millennia, has played a pivotal role throughout history in explaining the world around us. However, it can also be a source of confusion when we encounter unfamiliar operations.

In today’s article, we’ll embark on a journey to compare two fractions and determine which one is bigger. Is 1/2 bigger than 3/4?

Fractions, one of the most fundamental mathematical concepts, serve as tools to represent parts of a whole. To effectively compare them, it’s helpful to visualize them as slices of a pizza or a pie.

Imagine a pizza divided into equal portions.

• If we have 1/2 of the pizza, it means we have one of the two slices.
• If we have 3/4 of the pizza, it means we have three out of the four slices into which the pizza has been divided.

At first glance, 3/4 of the pizza appears larger than 1/2.

While we’ll delve into more details later, to answer your question upfront:

Is 1/2 bigger than 3/4?

No, 1/2 is smaller than 3/4. 1/2 represents 0.5, while 3/4 represents 0.75.

To confirm this mathematically, we can employ two methods:

Method 1: Converting Fractions to a Common Denominator to determine if 1/2 is bigger than 3/4

The least common multiple (LCM) of 2 and 4 is 4.

We convert 1/2 to 2/4 by multiplying both the numerator and denominator by 2: 1/2 = 2/4.

Now, we can easily compare both fractions since they have a common denominator:

• 2/4 represents two slices of a pie divided into four parts.
• 3/4 represents three slices of the same pie divided into four parts.

Clearly, 3/4 is larger than 2/4, and consequently, 1/2 is smaller than 3/4.

2. Method 2: Representing Fractions on a Number Line

To represent fractions on a number line, follow these steps:

• Locate the 0 (zero) at one end of the line and mark equal intervals based on the denominator.
• Divide the first line into two equal parts since the denominator is 2.
• Divide the second line into four parts since the denominator is 4.
• On the first line:
• Mark 1/2 at the first point to the right of 0.
• On the second line:
• Mark 1/4 at the first point to the right of 0.
• Mark 2/4 at the second point to the right of 0.
• Mark 3/4 at the third point to the right of 0.

Observing the lines, we can clearly see that 3/4 lies further to the right than 1/2, confirming that 1/2 is not larger than 3/4.

Conclusion: Unveiling the Winner. Is 1/2 bigger than 3/4?

Both the pizza slice visualization and the conversion to a common denominator or representation on a number line help us grasp and compare the value of fractions, revealing that 3/4 is indeed larger than 1/2. Therefore, 1/2 is not bigger than 3/4.