How to Convert Unlike Fractions to Like Fractions (Step-by-Step Guide)
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 Like Fractions and Unlike Fractions: Definitions, Examples & Key Differences
1. What are like fractions in Maths?
Like fractions are fractions that share the same denominator. This means the bottom number (the denominator) is identical in all the fractions. For example, 1/4, 3/4, and 5/4 are like fractions because they all have a denominator of 4. The numerators (top numbers) can be different.
2. What are unlike fractions?
Unlike fractions are fractions with different denominators. The bottom number (denominator) is unique to each fraction. For instance, 1/2, 2/3, and 5/6 are unlike fractions as their denominators (2, 3, and 6) are all different.
3. What is the main difference between like and unlike fractions?
The key difference lies in their denominators. Like fractions have the same denominator, while unlike fractions have different denominators. This distinction is crucial when performing addition and subtraction; like fractions can be directly added or subtracted, unlike fractions require conversion to like fractions first.
4. How do you add unlike fractions?
To add unlike fractions, you must first convert them into like fractions. Follow these steps:
• Find the Least Common Multiple (LCM) of the denominators.
• Convert each fraction to an equivalent fraction with the LCM as the new denominator.
• Add the numerators of the like fractions.
• Simplify the resulting fraction, if necessary. For example, to add 1/2 and 1/3, the LCM is 6. Converting, we get 3/6 + 2/6 = 5/6.
5. How do you subtract unlike fractions?
Subtracting unlike fractions is similar to addition. First, find the LCM of the denominators and convert the fractions into like fractions. Then, subtract the numerators and simplify the result. For example, to subtract 2/3 from 5/6, the LCM is 6. This gives us 5/6 - 4/6 = 1/6.
6. How do you convert unlike fractions to like fractions?
To convert unlike fractions to like fractions, find the LCM of the denominators. Then, multiply the numerator and denominator of each fraction by the number that makes the denominator equal to the LCM. This creates equivalent fractions with a common denominator, transforming them into like fractions.
7. Why do we convert unlike fractions to like fractions?
We convert unlike fractions to like fractions because we can only directly add or subtract fractions when they have the same denominator. Converting allows for straightforward calculations without changing the value of the fractions.
8. Can you give 5 examples of like and unlike fractions?
Like Fractions: 2/5, 4/5, 7/5, 1/5, 9/5
Unlike Fractions: 1/2, 2/3, 3/4, 5/6, 7/8
9. What are some common mistakes students make when working with unlike fractions?
Common mistakes include forgetting to find the LCM before adding or subtracting, incorrectly converting fractions to like fractions, and not simplifying the final answer. Carefully following the steps and double-checking work helps avoid these errors.
10. How can visual aids help in understanding like and unlike fractions?
Visual aids like diagrams (circles divided into parts), number lines, and fraction bars can help visualize the concept of fractions and their denominators, clarifying the difference between like and unlike fractions. These visual representations can make abstract concepts more concrete and easier to grasp.
11. Are there real-life word problems involving like and unlike fractions?
Yes! Many real-world scenarios involve fractions. For example, sharing pizzas, measuring ingredients in cooking, or calculating distances on a map can all involve adding or subtracting like and unlike fractions. Practicing word problems helps apply the concept to everyday situations.
12. How can I check my answers when adding or subtracting fractions?
To check your answers, you can use a calculator or estimate the answer. Estimating involves rounding fractions to nearby whole numbers or common fractions. For instance, 2/3 is roughly equal to 0.67. By making approximations, you will have a rough answer and can check if your solution is reasonably accurate. Another way is to double-check that you found the LCM correctly and converted each fraction accurately to its equivalent with the common denominator before carrying out the addition or subtraction.
