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 1/3 bigger than 1/2?**

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

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

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

### Is 1/3 bigger than 1/2?

No, 1/3 is smaller than 1/2. 1/3 represents 0.33, while 1/2 represents 0.50.

To confirm this mathematically, we can employ two methods:

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

The least common multiple (LCM) of one and two is 6.

We convert 1/3 to 2/6 by multiplying both the numerator and denominator by 2:

- 1/3 = 2/6

And we convert 1/2 to 3/6 by multiplying both numerator and denominator by 3:

- 1/2 = 3/6

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

- 2/6 represents
**2 slices**of a pie divided into 6 parts. - 3/6 represents
**3 slices**of the same pie divided into 6 parts.

Clearly, 3/6 is larger than 2/6, and consequently, **1/3 is smaller than 1/2**.

## 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 one equal parts since the denominator is 3.
- Divide the second line into two parts since the denominator is 2.
- On the first line:
- Mark 1/3 at the first point to the right of 0.
- Mark 2/3 at the second point to the right of 0

- On the second line:
- Mark 1/2 at the first point to the right of 0.

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

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

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 **1/2 is indeed larger than 1/3**. Therefore, 1/3 is not bigger than 1/2.

### Other fractions compared

Photo by Ben Mack