Is 2/3 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 2/3 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 2/3 of the pizza, it means we have two of the three 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.
A visual representation is the best way to know if 2/3 is bigger than 3/4

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

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

Is 2/3 bigger than 3/4?

No, 2/3 is smaller than 3/4. 2/3 represents 0.66, 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 2/3 is bigger than 3/4

The least common multiple (LCM) of three and four is 12.

We convert 2/3 to 8/12 by multiplying both the numerator and denominator by 4:

  • 2/3 = 8/12

And we convert 3/4 to 9/12 by multiplying both numerator and denominator by 3:

  • 3/4 = 9/12

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

  • 8/12 represents 8 slices of a pie divided into 12 parts.
  • 9/12 represents 9 slices of the same pie divided into 12 parts.

Clearly, 9/12 is larger than 8/12, and consequently, 2/3 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 three equal parts since the denominator is 3.
  • Divide the second line into four parts since the denominator is 4.
  • 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 1/4 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
Numeric Line Comparing 2/3 and 3/4

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

Conclusion: Unveiling the Winner. Is 2/3 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 2/3. Therefore, 2/3 is not bigger than 3/4.

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