¿Qué es más grande 1/3 o 1/2?

David Girones

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.
A visual representation is the best way to know if 1/3 is bigger than 1/2

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.
Numeric Line Comparing 1/3 and 1/2

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