What are Like Fractions and Unlike Fractions with Examples and Steps to Solve
The concept of Like Fractions and Unlike Fractions plays a key role in mathematics and is widely applicable to both real-life situations and exam scenarios. Mastering these concepts is crucial for operations such as addition, subtraction, and comparison of fractions, which are essential not just in primary school but also in higher classes and competitive exams.
What Are Like Fractions and Unlike Fractions?
A like fraction is defined as any fraction that shares the same denominator with another. For example, 2/7, 5/7, and 9/7 are like fractions because their denominators are all 7. On the other hand, unlike fractions have different denominators. For example, 1/3 and 2/5 are unlike fractions because their denominators are not the same. You’ll find these concepts applied in areas such as fraction addition, subtraction, simplification, and comparison, both in maths homework and in daily life like sharing pizzas or measuring ingredients.
Difference Between Like and Unlike Fractions
| Aspect | Like Fractions | Unlike Fractions |
|---|---|---|
| Definition | Fractions with the same denominator | Fractions with different denominators |
| Examples | 3/8, 6/8, 11/8 | 1/4, 5/7, 2/9 |
| Addition/Subtraction | Direct—add/subtract numerators | Convert to like fractions first |
Why Convert Unlike Fractions to Like Fractions?
Adding or subtracting unlike fractions directly is not possible because the sizes of the parts (denominators) are different. To perform these operations, we must first make the denominators the same. This involves converting unlike fractions into like fractions using either the LCM (Least Common Multiple) method or cross-multiplication.
Steps: Converting Unlike Fractions to Like Fractions
- Find the Least Common Multiple (LCM) of all denominators.
E.g., for 2/3 and 5/4, LCM of 3 and 4 is 12. - Rewrite each fraction with the LCM as the new denominator.
2/3 = (2×4)/(3×4) = 8/12
5/4 = (5×3)/(4×3) = 15/12 - Now both fractions are like fractions: 8/12 and 15/12.
Worked Example: Addition of Unlike Fractions
Example: Add 1/5 and 2/3.
1. Find LCM of 5 and 3: 152. Convert the fractions:
1/5 = (1×3)/(5×3) = 3/15
2/3 = (2×5)/(3×5) = 10/15
3. Add: 3/15 + 10/15 = 13/15
Adding & Subtracting Like Fractions
With like fractions, simply add or subtract the numerators and keep the denominator the same.
Example: 4/9 + 2/9 = (4+2)/9 = 6/9
Subtraction Example: 7/8 – 3/8 = (7-3)/8 = 4/8
Classroom Tip: Quick Visual Cue
Scan the denominators. If they’re all identical, they're like fractions! If not, remember to convert before adding or subtracting. Vedantu’s teachers always advise students to circle denominators as a visual check in your notebook.
Speed Tricks & Shortcuts
When converting two unlike fractions, double-check if one denominator is a multiple of the other. If yes, just change one fraction instead of both! This saves time in exams. For example, with 3/4 and 5/8, since 8 is a multiple of 4:
1. Multiply numerator and denominator of 3/4 by 2 to get 6/8.2. Now add: 6/8 + 5/8 = 11/8.
Little tricks like this are covered in Vedantu’s live maths doubt sessions for quick revision.
Sample Questions: Try These Yourself
- Write any four like fractions using denominator 15.
- Convert 2/5 and 3/10 into like fractions.
- Add 1/6 and 1/3.
- Subtract 9/12 from 11/12.
- Identify and separate like and unlike fractions from: 4/7, 7/7, 2/9, 5/7
Frequent Errors and Misconceptions
- Adding fractions by only adding numerators and denominators (e.g., 1/2 + 1/3 = 2/5 — incorrect!)
- Forgetting to convert unlike fractions when solving addition or subtraction problems.
- Thinking all fractions with different numerators are unlike fractions (numerators don't matter, denominators do).
Relation to Other Concepts
Understanding like fractions and unlike fractions is essential before moving on to more advanced topics, such as Addition and Subtraction of Fractions, Equivalent Fractions, and LCM. Once you master these basics, even concepts like Comparing Fractions and Simplification become much easier.
Wrapping It All Up
We explored Like Fractions and Unlike Fractions — their definitions, differences, steps to convert, examples, and why they matter so much in problem-solving. Practicing these will help you avoid common errors and speed up your calculations. With Vedantu’s clear explanations and regular practice, you’ll be ready for all types of fraction questions in school and beyond.
FAQs on Understanding Like and Unlike Fractions in Mathematics
1. What are like fractions?
Like fractions are fractions that have the same denominator. This means the bottom numbers are identical, even if the numerators are different.
- Examples: 3/7, 5/7, and 1/7
- All have the same denominator: 7
- They are easy to add or subtract because only the numerators change
2. What are unlike fractions?
Unlike fractions are fractions that have different denominators. The bottom numbers are not the same, so they cannot be directly added or subtracted.
- Examples: 1/2 and 3/4
- Denominators are different: 2 and 4
- They must be converted to like fractions before performing operations
3. How do you add like fractions?
To add like fractions, add the numerators and keep the denominator the same. The denominator does not change.
- Example: 2/5 + 1/5
- Add numerators: 2 + 1 = 3
- Keep denominator: 5
- Final answer: 3/5
4. How do you subtract like fractions?
To subtract like fractions, subtract the numerators and keep the denominator the same. Only the top number changes.
- Example: 5/8 − 2/8
- Subtract numerators: 5 − 2 = 3
- Keep denominator: 8
- Final answer: 3/8
5. How do you add unlike fractions step by step?
To add unlike fractions, first find a common denominator, then add the numerators. This converts them into like fractions.
- Example: 1/3 + 1/4
- LCM of 3 and 4 is 12
- Convert: 1/3 = 4/12, 1/4 = 3/12
- Add: 4/12 + 3/12 = 7/12
6. What is the difference between like and unlike fractions?
The main difference is that like fractions have the same denominator, while unlike fractions have different denominators. This affects how they are added or subtracted.
- Like fractions: 2/9 and 5/9
- Unlike fractions: 2/9 and 3/5
- Unlike fractions require finding a common denominator before calculation
7. Why do we need a common denominator for unlike fractions?
We need a common denominator because fractions must represent equal-sized parts before adding or subtracting. Different denominators mean different part sizes.
- Example: 1/2 and 1/3 have different part sizes
- Convert to common denominator 6
- 1/2 = 3/6 and 1/3 = 2/6
- Now they can be added correctly
8. What is the formula for adding unlike fractions?
The formula for adding unlike fractions is a/b + c/d = (ad + bc) / bd. This works when denominators are different.
- Multiply crosswise: a × d and b × c
- Add the results in the numerator
- Multiply denominators for the new denominator
- Example: 1/2 + 1/3 = (1×3 + 1×2) / (2×3) = 5/6
9. Can you give an example of converting unlike fractions into like fractions?
To convert unlike fractions into like fractions, find the LCM of the denominators and rewrite each fraction with that common denominator.
- Example: 2/5 and 3/10
- LCM of 5 and 10 is 10
- 2/5 = 4/10
- Now the like fractions are 4/10 and 3/10
10. What are common mistakes when working with like and unlike fractions?
A common mistake is adding or subtracting denominators directly, which is incorrect in fraction operations.
- Wrong: 1/2 + 1/3 = 2/5
- Correct method: Find common denominator 6
- 1/2 = 3/6 and 1/3 = 2/6
- Correct answer: 5/6
