What Is Equivalent to 2/3 Fraction?

Fractions play a major role in mathematics and help represent parts of a whole. Understanding equivalent fractions makes solving math problems easier and improves calculation accuracy. In this article, we will learn what fractions are equivalent to 2/3, how to calculate them, and where they are used in real-life situations.

Understanding the Fraction 2/3

The fraction 2/3 means two parts out of three equal parts of a whole.

Breaking Down 2/3

• 2 (Numerator): Shows how many parts are selected or taken.
• 3 (Denominator): Shows the total number of equal parts.

For example, if a cake is divided into 3 equal slices and you eat 2 slices, you have eaten 2/3 of the cake.

What Are Equivalent Fractions?

Equivalent fractions are fractions that may look different but represent the same numerical value. These fractions are created when both the numerator and denominator are multiplied or divided by the same number.

Definition

Equivalent fractions are fractions that represent the same portion of a whole even if their numbers are different.

Examples of fractions equivalent to 2/3 include:

• 4/6
• 6/9
• 8/12

All of these fractions have the same value as 2/3.

Equivalent Fractions of 2/3

To find equivalent fractions of 2/3, multiply both the numerator and denominator by the same number.

Examples of Equivalent Fractions

Multiply By	Equivalent Fraction
2	4/6
3	6/9
4	8/12
5	10/15
6	12/18
7	14/21
8	16/24
9	18/27
10	20/30

Each of these fractions represents the same value as 2/3.

How to Find Equivalent Fractions of 2/3

Finding equivalent fractions follows a simple and reliable method.

Step-by-Step Method

Step 1: Start With the Original Fraction

Example: 2/3

Step 2: Select Any Whole Number

Choose any number such as 2, 3, 4, or more.

Step 3: Multiply Both Numerator and Denominator

Example:

Multiply by 2
2 × 2 = 4
3 × 2 = 6
Equivalent fraction = 4/6

Multiply by 5
2 × 5 = 10
3 × 5 = 15
Equivalent fraction = 10/15

This process can be repeated infinitely.

Why Are Equivalent Fractions Important?

Equivalent fractions are useful in many mathematical and practical applications.

Simplifying Fractions

Equivalent fractions help simplify complex fractions into smaller, easier forms.

Example:
12/18 can be simplified to 2/3 by dividing both numbers by 6.

Comparing Fractions

Equivalent fractions help compare fractions that have different denominators.

Example:
2/3 and 8/12
Since 2/3 = 8/12, both fractions are equal.

Performing Fraction Operations

Equivalent fractions help create common denominators while adding or subtracting fractions.

Example:
2/3 + 1/6

Convert 2/3 into 4/6
Now add:
4/6 + 1/6 = 5/6

Visual Representation of Equivalent Fractions of 2/3

Equivalent fractions can be understood easily with visual examples.

Imagine a chocolate bar divided into equal sections:

• Dividing into 3 parts and eating 2 parts means 2/3 is consumed.
• Dividing into 6 parts and eating 4 parts still equals 2/3.
• Dividing into 9 parts and eating 6 parts also equals 2/3.

The portion remains the same even if the total pieces increase.

Converting 2/3 into Decimal and Percentage

Fractions can also be expressed in decimal and percentage forms.

Decimal Form

To convert 2/3 into decimal:

2 ÷ 3 = 0.666… (Repeating)

Percentage Form

To convert into percentage:

0.666 × 100 = 66.67%

All equivalent fractions of 2/3 represent approximately 66.67% of a whole.

How to Check If Two Fractions Are Equivalent to 2/3

Cross multiplication is a simple way to verify equivalent fractions.

Example: Is 8/12 Equivalent to 2/3?

Step 1: Cross multiply
2 × 12 = 24
3 × 8 = 24

Step 2: Compare the results
Since both results are equal, 8/12 is equivalent to 2/3.

Common Mistakes While Finding Equivalent Fractions

Multiplying Only One Part

Always multiply both numerator and denominator.

Wrong:
2 × 2 / 3 = 4/3

Correct:
(2 × 2) / (3 × 2) = 4/6

Using Different Multipliers

Both numerator and denominator must be multiplied by the same number to maintain equality.

Real-Life Examples of 2/3 Equivalent Fractions

Equivalent fractions are widely used in everyday activities.

Cooking Measurements

If a recipe needs 2/3 cup of milk, you can use:

• 4/6 cup
• 6/9 cup
• 8/12 cup

All provide the same quantity.

Time Calculation

2/3 of an hour equals:

60 × 2/3 = 40 minutes

Academic Grading and Scores

If a student scores 2/3 of total marks, it equals approximately 66.67% marks.

Infinite Equivalent Fractions of 2/3

There are unlimited equivalent fractions for 2/3. Some examples include:

• 22/33
• 24/36
• 50/75
• 200/300

All these fractions represent the same value as 2/3.