Fractions Ex 7.6 Class 6 NCERT: Adding and Subtracting Unlike Fractions

Why We Can't Add Unlike Fractions Directly

Unlike fractions are fractions that have different denominators. For example, 1/4 and 2/5 are unlike fractions because their denominators (4 and 5) are different. Think of it like this: you can't add 2 apples and 3 oranges and say you have 5 'apple-oranges'. They are different types of items. Similarly, a 'quarter' (1/4) is a different size slice than a 'fifth' (1/5). To add them, you need to cut them into smaller, equal-sized pieces that are common to both. In maths, this means finding a 'common denominator'. We do this by finding the Least Common Multiple (LCM) of the denominators. This process converts the unlike fractions into equivalent like fractions, which we can then easily add or subtract.

How to Add or Subtract Unlike Fractions: The LCM Method

1. Step 1: Find the LCM of the Denominators — Look at the denominators of the fractions you need to add or subtract. Calculate their Least Common Multiple (LCM). This LCM will be your new common denominator.
2. Step 2: Create Equivalent Fractions — For each fraction, figure out what number you need to multiply its denominator by to get the LCM. Then, multiply the numerator by that same number. This creates an equivalent fraction with the new common denominator.
3. Step 3: Add or Subtract the Numerators — Now that the fractions have the same denominator, simply add or subtract their numerators as the question asks. The denominator stays the same.
4. Step 4: Simplify the Result — If possible, simplify the final fraction to its lowest terms. You can do this by dividing both the numerator and the denominator by their greatest common factor (GCF).

Worked Examples from Fractions Ex 7.6

• Problem 1: Solve 2/3 + 1/7 Step 1: The denominators are 3 and 7. They are unlike. We find the LCM of 3 and 7. Since they are prime numbers, LCM(3, 7) = 3 × 7 = 21. Step 2: Convert the fractions. For 2/3, to make the denominator 21, we multiply by 7. So, (2 × 7) / (3 × 7) = 14/21. For 1/7, to make the denominator 21, we multiply by 3. So, (1 × 3) / (7 × 3) = 3/21. Step 3: Add the new fractions: 14/21 + 3/21 = (14 + 3) / 21 = 17/21. Step 4: 17 and 21 have no common factors other than 1, so the fraction is already in its simplest form. Final Answer: 17/21
• Problem 2: Solve 4/3 - 1/2 Step 1: The denominators are 3 and 2. We find the LCM of 3 and 2. LCM(3, 2) = 6. Step 2: Convert the fractions. For 4/3, to make the denominator 6, we multiply by 2. So, (4 × 2) / (3 × 2) = 8/6. For 1/2, to make the denominator 6, we multiply by 3. So, (1 × 3) / (2 × 3) = 3/6. Step 3: Subtract the new fractions: 8/6 - 3/6 = (8 - 3) / 6 = 5/6. Step 4: 5 and 6 have no common factors, so the fraction is in its simplest form. Final Answer: 5/6

Exam Tip: Don't Forget to Simplify!

A very common mistake is to do all the hard work of finding the LCM and adding correctly, but then forget to simplify the final answer. For example, if your answer is 10/12, you must simplify it to 5/6 by dividing both the top and bottom by 2. Always check if the numerator and denominator share a common factor. Also, if a question involves mixed fractions (like 2 ½), always convert them into improper fractions (5/2) before you start the LCM process. This avoids confusion and makes the calculation straightforward.

Practice Questions with Solutions

• Q: Sarita bought 2/5 metre of ribbon and Lalita 3/4 metre of ribbon. What is the total length of the ribbon they bought? A: Step 1: We need to add the lengths. The problem is 2/5 + 3/4. The denominators are 5 and 4. Step 2: Find the LCM of 5 and 4. LCM(5, 4) = 20. Step 3: Convert to equivalent fractions. 2/5 = (2×4)/(5×4) = 8/20. And 3/4 = (3×5)/(4×5) = 15/20. Step 4: Add the numerators. 8/20 + 15/20 = (8+15)/20 = 23/20 metres. Final answer: They bought 23/20 metres of ribbon. This can also be written as a mixed fraction, 1 3/20 metres.
• Q: Solve: 7/10 - 1/5 A: Step 1: The denominators are 10 and 5. Find the LCM of 10 and 5. The LCM is 10. Step 2: Convert the fractions. 7/10 is already in the correct form. For 1/5, to get a denominator of 10, we multiply by 2. So, 1/5 = (1×2)/(5×2) = 2/10. Step 3: Subtract the numerators. 7/10 - 2/10 = (7-2)/10 = 5/10. Step 4: Simplify the result. Both 5 and 10 are divisible by 5. 5÷5=1 and 10÷5=2. Final answer: 1/2
• Q: A piece of wire 7/8 metre long broke into two pieces. One piece was 1/4 metre long. How long is the other piece? A: Step 1: We need to subtract the length of one piece from the total length. The problem is 7/8 - 1/4. Step 2: The denominators are 8 and 4. The LCM of 8 and 4 is 8. Step 3: Convert the fractions. 7/8 remains the same. 1/4 = (1×2)/(4×2) = 2/8. Step 4: Subtract the numerators. 7/8 - 2/8 = (7-2)/8 = 5/8. Final answer: The other piece is 5/8 metre long.
• Q: Solve: 2 2/3 + 3 1/2 A: Step 1: First, convert the mixed fractions into improper fractions. 2 2/3 = (3×2 + 2)/3 = 8/3. And 3 1/2 = (2×3 + 1)/2 = 7/2. Step 2: The new problem is 8/3 + 7/2. The LCM of the denominators (3 and 2) is 6. Step 3: Convert to equivalent fractions. 8/3 = (8×2)/(3×2) = 16/6. And 7/2 = (7×3)/(2×3) = 21/6. Step 4: Add the numerators. 16/6 + 21/6 = (16+21)/6 = 37/6. Step 5: Convert back to a mixed fraction if needed. 37 ÷ 6 is 6 with a remainder of 1. Final answer: 37/6 or 6 1/6

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