Addition of Fractions
Suppose you ate 1/4 of a pizza and your friend ate 2/4. How much pizza did you eat together? Since both fractions have the same denominator, you simply add the numerators: 1/4 + 2/4 = 3/4. You ate 3/4 of the pizza together.
But what if you ate 1/3 and your friend ate 1/4? The denominators are different, so you cannot add the numerators directly. You first need to make the denominators the same.
In Class 6 NCERT Maths, you will learn how to add like fractions (same denominator) and unlike fractions (different denominators).
What is Addition of Fractions - Grade 6 Maths (Fractions)?
Addition of like fractions:
a/c + b/c = (a + b)/c
Keep the denominator the same. Add only the numerators.
Addition of unlike fractions:
- Find the LCM of the denominators.
- Convert each fraction to an equivalent fraction with the LCM as denominator.
- Add the numerators. Keep the common denominator.
- Simplify the result if possible.
Addition of Fractions Formula
Formula for adding two fractions:
a/b + c/d = (a×d + c×b) / (b×d)
This is called the cross-multiplication method. It always works but may give a larger denominator. Using the LCM method gives a simpler answer.
Adding mixed numbers:
- Add the whole number parts separately.
- Add the fraction parts separately (using LCM if needed).
- If the fraction part is improper, convert and carry over to the whole number.
Types and Properties
Cases in addition of fractions:
- Like fractions: Just add numerators. Example: 2/7 + 3/7 = 5/7.
- Unlike fractions: Find LCM, convert, then add. Example: 1/3 + 1/4 = 4/12 + 3/12 = 7/12.
- Whole number + fraction: Write the whole number as a fraction. Example: 2 + 3/5 = 10/5 + 3/5 = 13/5 = 2 3/5.
- Mixed numbers: Add whole parts and fraction parts separately.
Solved Examples
Example 1: Adding Like Fractions
Problem: Add 2/9 + 5/9.
Solution:
Same denominator (9). Add numerators: 2 + 5 = 7.
2/9 + 5/9 = 7/9.
Answer: 7/9
Example 2: Adding Unlike Fractions
Problem: Add 1/3 + 1/4.
Solution:
Step 1: LCM of 3 and 4 = 12.
Step 2: 1/3 = 4/12 and 1/4 = 3/12.
Step 3: 4/12 + 3/12 = 7/12.
Answer: 7/12
Example 3: Adding Fractions and Simplifying
Problem: Add 3/8 + 1/8.
Solution:
3/8 + 1/8 = 4/8 = 1/2 (simplify by dividing numerator and denominator by 4).
Answer: 1/2
Example 4: Adding Fractions with Different Denominators
Problem: Add 2/5 + 3/10.
Solution:
Step 1: LCM of 5 and 10 = 10.
Step 2: 2/5 = 4/10.
Step 3: 4/10 + 3/10 = 7/10.
Answer: 7/10
Example 5: Adding a Whole Number and a Fraction
Problem: Add 3 + 2/7.
Solution:
3 = 21/7.
21/7 + 2/7 = 23/7 = 3 2/7.
Answer: 3 2/7
Example 6: Adding Mixed Numbers
Problem: Add 2 1/3 + 1 2/3.
Solution:
Whole parts: 2 + 1 = 3.
Fraction parts: 1/3 + 2/3 = 3/3 = 1.
Total: 3 + 1 = 4.
Answer: 4
Example 7: Adding Mixed Numbers with Unlike Fractions
Problem: Add 1 1/2 + 2 1/3.
Solution:
Whole parts: 1 + 2 = 3.
Fraction parts: 1/2 + 1/3. LCM of 2 and 3 = 6.
1/2 = 3/6, 1/3 = 2/6.
3/6 + 2/6 = 5/6.
Total: 3 + 5/6 = 3 5/6.
Answer: 3 5/6
Example 8: Result Is an Improper Fraction
Problem: Add 3/4 + 5/4.
Solution:
3/4 + 5/4 = 8/4 = 2.
Answer: 2
Example 9: Adding Three Fractions
Problem: Add 1/2 + 1/3 + 1/6.
Solution:
LCM of 2, 3, 6 = 6.
1/2 = 3/6, 1/3 = 2/6, 1/6 = 1/6.
3/6 + 2/6 + 1/6 = 6/6 = 1.
Answer: 1
Example 10: Word Problem on Adding Fractions
Problem: Rina read 1/5 of a book on Monday and 2/5 on Tuesday. What fraction of the book did she read in total?
Solution:
1/5 + 2/5 = 3/5.
Answer: Rina read 3/5 of the book.
Real-World Applications
Where you use addition of fractions:
- Cooking: Adding 1/2 cup of sugar and 1/4 cup of sugar gives 3/4 cup.
- Measurement: Adding lengths measured in fractions (3 1/2 m + 2 1/4 m).
- Time: Adding parts of an hour (1/2 hour + 1/4 hour = 3/4 hour = 45 minutes).
- Money: If you save 1/3 of your pocket money one week and 1/4 the next week, the total saved is 7/12.
Key Points to Remember
- For like fractions: add numerators, keep the denominator.
- For unlike fractions: find the LCM, convert to like fractions, then add.
- Always simplify the answer to its lowest terms.
- If the result is an improper fraction, convert it to a mixed number.
- For mixed numbers: add whole parts and fraction parts separately.
- If the fraction sum is improper, carry 1 to the whole number part.
- The cross-multiplication method (a/b + c/d = (ad + bc)/bd) always works.
Practice Problems
- Add: 3/7 + 2/7.
- Add: 1/4 + 1/6.
- Add: 2/3 + 3/5.
- Add: 5 + 3/8.
- Add: 2 1/4 + 3 1/2.
- Add: 1/2 + 1/4 + 1/8.
Frequently Asked Questions
Q1. How do you add fractions with the same denominator?
Add the numerators and keep the denominator the same. For example, 2/5 + 1/5 = 3/5.
Q2. How do you add fractions with different denominators?
Find the LCM of the denominators. Convert both fractions to equivalent fractions with the LCM as the denominator. Then add the numerators.
Q3. What if the answer is an improper fraction?
Convert it to a mixed number. For example, 7/4 = 1 3/4.
Q4. Do you add the denominators when adding fractions?
No. Never add the denominators. Only add the numerators. The denominator stays the same (for like fractions) or becomes the LCM (for unlike fractions).
Q5. How do you add mixed numbers?
Add the whole number parts together and the fraction parts together. If the fraction sum is improper, convert it and add 1 to the whole number.
Q6. What is the LCM method?
Find the Least Common Multiple of the denominators. Multiply each fraction's numerator and denominator to get the LCM as the common denominator. Then add.
Related Topics
- Subtraction of Fractions
- Like and Unlike Fractions
- Equivalent Fractions
- Multiplication of Fractions
- Introduction to Fractions
- Proper and Improper Fractions
- Mixed Numbers
- Simplest Form of a Fraction
- Comparing Fractions
- Fractions on Number Line
- Unit Fractions
- Word Problems on Fractions
- Types of Fractions
- Addition and Subtraction of Fractions
