Fractions represent a part of a whole, and sometimes you may need to find *equivalent fractions*. These are fractions that may look different but represent the same value. Let’s explore how to find the four equivalent fractions of 2/3 in a simple, step-by-step way.

## What Is an Equivalent Fraction?

An equivalent fraction is a fraction that has the same value as the original fraction but is written using different numbers. You create equivalent fractions by multiplying (or dividing) both the numerator (the top number) and the denominator (the bottom number) of a fraction by the same non-zero number. The result will still represent the same portion of the whole.

## How To Find Equivalent Fractions

Let’s start with 2/3. To find equivalent fractions, we multiply both 2 and 3 by the same number. Here’s how:

1. Multiply both the numerator and the denominator by **2: 2/3×2/2 = 4/6**

So, **4/6 is an equivalent fraction of 2/3.**

2. Multiply both the numerator and the denominator by 3: **2/3 × 3/3 = 6/9 **

So, **6/9 is another equivalent fraction of 2/3.**

3. Multiply both the numerator and the denominator by 4: **2/3 × 4/4 = 8/12 **

So, **8/12 is an equivalent fraction of 2/3.**

4. Multiply both the numerator and the denominator by 5: **2/3 × 5/5 = 10/15 **

So, **10/15 is also an equivalent fraction of 2/3.**

Hence, The four equivalent fractions of 2/3 are **4/6, 6/9, 8/12, and 10/15**.

You can use our free Equivalent Fractions Calculator to match the answer.

#### Why Do Equivalent Fractions Work?

The key idea behind equivalent fractions is that multiplying or dividing both the top and bottom of a fraction by the same number does not change the value of the fraction. For example, if you have 2/3 of a pizza, multiplying the top and bottom by 2 (to get 4/6) simply means you’re cutting the pizza into smaller pieces, but you still have the same amount of pizza.

#### Conclusion

The four equivalent fractions of 2/3 are 4/6, 6/9, 8/12, and 10/15. Finding equivalent fractions is a useful way to compare fractions, solve math problems, and understand the relationship between different numbers.