How to Find Equivalent Fractions Easily with Stepwise Method and Table
The concept of equivalent fractions plays a key role in mathematics and is widely applicable to both real-life situations and exam scenarios. Mastering equivalent fractions makes comparing, simplifying, and calculating fractions easy, whether in school homework, board exams, or daily life situations like dividing pizza or splitting a bill.
What Is Equivalent Fraction?
An equivalent fraction is defined as a fraction that looks different but represents the same value or proportion as another fraction. For example, 1/2, 2/4, and 4/8 are equivalent fractions because they all signify “half” of a whole. You’ll find this concept applied in areas such as simplifying fractions, comparing fractions, and operations with fractions.
Key Formula for Equivalent Fractions
Here’s the standard method to create or check equivalent fractions:
If \(\frac{a}{b}\) is any fraction, then multiplying or dividing both numerator and denominator by the same nonzero number \(n\):
\(\frac{a}{b} = \frac{a \times n}{b \times n}\) or \(\frac{a}{b} = \frac{a \div n}{b \div n}\).
Step-by-Step Illustration
- Start with a given fraction, for example, \( \frac{2}{3} \). Suppose we want to find an equivalent fraction.
- Multiply numerator and denominator by the same number, say 4: \( 2 \times 4 = 8 \); \( 3 \times 4 = 12 \)
- The equivalent fraction is \( \frac{8}{12} \).
- Check by simplifying \( \frac{8}{12} \): divide both by 4: \( \frac{2}{3} \).
Equivalent Fractions Table
| Fraction | First Equivalent | Second Equivalent | Third Equivalent |
|---|---|---|---|
| 1/2 | 2/4 | 3/6 | 4/8 |
| 1/3 | 2/6 | 3/9 | 4/12 |
| 2/5 | 4/10 | 6/15 | 8/20 |
| 3/4 | 6/8 | 9/12 | 12/16 |
Cross-Disciplinary Usage
Equivalent fractions are not only useful in Maths but also play an important role in Physics (measuring quantities), Computer Science (data representation), and daily logical reasoning. Students preparing for board exams, JEE or NEET will see its relevance in questions involving ratio, proportion, and simplification.
Speed Trick or Vedic Shortcut
Here's an easy trick: To quickly generate equivalent fractions, just pick any number and multiply both parts by it! For fraction simplification, find the greatest common factor (GCF) for the numerator and denominator and divide both by it. This helps instantly check if a fraction can be reduced or matched to another fraction during exams.
Example Trick: Is 8/12 equivalent to 2/3?
1. Divide numerator and denominator by 4: 8 ÷ 4 = 2, 12 ÷ 4 = 3.
2. Simplified form is 2/3.
3. So, yes—they are equivalent!
Vedantu’s live sessions and worksheets include such shortcuts to help students solve fraction problems faster.
Try These Yourself
- Write three equivalent fractions for 3/5.
- Are 10/30 and 1/3 equivalent?
- Find an equivalent fraction for 7/9 with a denominator of 27.
- Which of the following are equivalent: 4/12, 1/3, 2/6?
- Simplify 12/16 and state if it’s equivalent to 3/4.
Frequent Errors and Misunderstandings
- Multiplying or dividing only the numerator or only the denominator, instead of both.
- Believing that adding or subtracting will give equivalent fractions (it never does!).
- Forgetting to use the same nonzero number for both numerator and denominator.
- Not reducing fractions to their simplest form to check for equivalence.
Relation to Other Concepts
The idea of equivalent fractions connects closely with topics such as fraction comparison and simplification. Mastering this helps with adding, subtracting, and even converting fractions to decimals and percentages in future chapters.
Classroom Tip
A quick way to remember equivalent fractions is to draw fraction strips or use pie diagrams for visualization. If two pieces look the same size, the fractions are equivalent! Vedantu’s teachers often use these visuals in live classes to cement the idea for every learner.
We explored equivalent fractions—from definition, formula, examples, mistakes, and connections to other subjects. Continue practicing with Vedantu and try fraction worksheets to become more confident in identifying and creating equivalent fractions easily.
For further learning, also check out: Comparing Fractions, Addition and Subtraction of Fractions, Simplest Form of Fraction, and Fraction Worksheets.
FAQs on Equivalent Fractions: Definition, Examples, and Step-by-Step Methods
1. What are equivalent fractions?
Equivalent fractions are different fractions that represent the same value or proportion. They look different but are equal. For example, 1/2 is equivalent to 2/4, 3/6, and so on. All of these fractions represent one-half of a whole.
2. How do you find equivalent fractions?
To find equivalent fractions, multiply or divide both the numerator (top number) and the denominator (bottom number) by the same non-zero number. For example, to find an equivalent fraction for 2/3, multiply both the numerator and the denominator by 2: 2/3 x 2/2 = 4/6. 4/6 is an equivalent fraction to 2/3.
3. What are some examples of equivalent fractions?
Here are some examples: 1/2 = 2/4 = 3/6 = 4/8; 1/3 = 2/6 = 3/9 = 4/12; 2/5 = 4/10 = 6/15 = 8/20. Notice how multiplying or dividing the numerator and denominator by the same number results in an equivalent fraction.
4. Why are equivalent fractions important?
Equivalent fractions are crucial for: simplifying fractions to their lowest terms; comparing fractions with different denominators; adding and subtracting fractions; and solving various mathematical problems involving fractions.
5. How can I simplify a fraction?
To simplify a fraction, find the greatest common factor (GCF) of the numerator and denominator. Then, divide both the numerator and denominator by the GCF. For example, to simplify 6/9, the GCF of 6 and 9 is 3. Dividing both by 3 gives 2/3 which is the simplest form.
6. How do I compare fractions using equivalent fractions?
To compare fractions, find equivalent fractions with a common denominator. Then, compare the numerators. The fraction with the larger numerator is the greater fraction. For example, to compare 2/3 and 3/4, find a common denominator (12). 2/3 becomes 8/12 and 3/4 becomes 9/12. Since 9/12 > 8/12, 3/4 is greater than 2/3.
7. What is the equivalent fraction of 2/3?
There are infinitely many equivalent fractions to 2/3. Some examples include 4/6, 6/9, 8/12, and so on. These are obtained by multiplying both the numerator and denominator by the same whole number.
8. Can you show me how to add fractions using equivalent fractions?
To add fractions with different denominators, first find equivalent fractions with a common denominator. Then, add the numerators and keep the common denominator. For example, to add 1/2 + 1/4, find an equivalent fraction for 1/2 with a denominator of 4 (2/4). Now add: 2/4 + 1/4 = 3/4.
9. How can I use equivalent fractions to solve word problems?
Word problems often involve parts of a whole. By representing these parts as fractions and finding equivalent fractions with a common denominator, you can easily solve these problems by comparing the sizes of the parts or finding total amounts.
10. Are there any online tools to help with equivalent fractions?
Yes, many online calculators and interactive tools can help you find equivalent fractions, simplify fractions, and even visualize them using diagrams or fraction bars. A simple search for "equivalent fraction calculator" will yield many results.
11. What is the simplest form of a fraction?
The simplest form of a fraction is when the numerator and denominator have no common factors other than 1. This means the fraction cannot be reduced any further. For example, the simplest form of 6/12 is 1/2.
