NCERT Solutions for Fractions and Decimals Ex 2.1 Class 7

Welcome to YoLearn.ai! In CBSE Class 7 Maths Chapter 2, Exercise 2.1 focuses on operations with fractions. This exercise is the core foundation where you learn to add, subtract, compare, and order fractions. Whether you are dealing with like fractions, unlike fractions, or mixed fractions, mastering this exercise will make the rest of the chapter incredibly easy. In this guide, we will break down the entire exercise with step-by-step visual logic, clear worked examples, and practical tips so you can solve every problem with confidence. Grab your notebook, open up your YoLearn digital sketchpad, and let's master fractions together!

Understanding Fraction Operations

A fraction represents a part of a whole. To perform addition or subtraction, fractions must speak the same 'language'. This means their denominators (the bottom numbers) must be identical. If you have 1/2 of a chocolate bar and 1/3 of a chocolate bar, you cannot simply add the numerators because the pieces are of different sizes. By finding the Least Common Multiple (LCM) of 2 and 3, which is 6, we convert them into equivalent fractions: 3/6 and 2/6. Now, the slices are equal in size, and we can easily add them to get 5/6. This simple visual logic of converting unlike fractions to like fractions using LCM is the entire secret to solving Exercise 2.1.

Steps to Add or Subtract Unlike Fractions

  1. Identify the Denominators — Look at the denominators of the given fractions. If they are already identical (like fractions), simply add or subtract the numerators. If they are different (unlike fractions), proceed to find the LCM.
  2. Find the LCM — Find the Least Common Multiple (LCM) of all the unlike denominators. This LCM will be the new common denominator for all your terms.
  3. Convert to Equivalent Fractions — Multiply both the numerator and denominator of each fraction by the appropriate number so that each denominator becomes equal to the LCM.
  4. Perform the Operation and Simplify — Add or subtract the new numerators while keeping the common denominator same. Finally, reduce the fraction to its simplest form, or convert it to a mixed fraction if it is improper.

Worked Examples from Exercise 2.1

  • Example 1: Solve 2 - 3/5. Step 1: Write the whole number 2 as a fraction: 2/1. Step 2: The denominators are 1 and 5. Their LCM is 5. Step 3: Convert 2/1 to an equivalent fraction with denominator 5: (2 5) / (1 5) = 10/5. Step 4: Subtract: 10/5 - 3/5 = (10 - 3) / 5 = 7/5. Step 5: Convert 7/5 into a mixed fraction: 1 2/5.
  • Example 2: Arrange in descending order: 2/9, 2/3, 8/21. Step 1: Find the LCM of the denominators 9, 3, and 21. Prime factorization gives: 9 = 3 3, 3 = 3, 21 = 3 7. LCM = 3 3 7 = 63. Step 2: Convert each to equivalent fractions with denominator 63: 2/9 = (2 7) / (9 7) = 14/63 2/3 = (2 21) / (3 21) = 42/63 8/21 = (8 3) / (21 * 3) = 24/63 Step 3: Compare the numerators: 42 > 24 > 14. Step 4: Write down in descending order: 2/3 > 8/21 > 2/9.

Common Pitfalls & Exam Tips

The Direct Addition Trap: A common mistake is directly adding numerators and denominators. Writing 2/3 + 1/5 = 3/8 is completely wrong! Always find the LCM first.

Simplifying the Final Answer: CBSE evaluators look for answers in their simplest terms or mixed fraction form. If your answer is 12/8, reduce it to 3/2 and write it as 1 1/2 to secure full marks.

Practice Questions with Solutions

  • Q: Solve: 3/5 + 2/7 A: Step 1: Find the LCM of denominators 5 and 7. Since both are prime numbers, LCM = 5 7 = 35. Step 2: Convert both fractions to equivalent fractions with denominator 35: 3/5 = (3 7) / (5 7) = 21/35 2/7 = (2 5) / (7 * 5) = 10/35 Step 3: Add the numerators together: (21 + 10) / 35 = 31/35. Final answer: 31/35
  • Q: Subtract: 8 1/2 - 3 5/8 A: Step 1: Convert the mixed fractions to improper fractions: 8 1/2 = (8 2 + 1) / 2 = 17/2 3 5/8 = (3 8 + 5) / 8 = 29/8 Step 2: Find the LCM of denominators 2 and 8, which is 8. Step 3: Convert 17/2 to have a denominator of 8: (17 4) / (2 4) = 68/8. Step 4: Subtract: 68/8 - 29/8 = (68 - 29) / 8 = 39/8. Step 5: Convert 39/8 to a mixed fraction: 4 7/8. Final answer: 4 7/8
  • Q: A rectangular sheet of paper is 12 1/2 cm long and 10 2/3 cm wide. Find its perimeter. A: Step 1: Write down the perimeter formula: Perimeter = 2 (Length + Width). Step 2: Convert mixed fractions to improper fractions: Length = 12 1/2 = 25/2 cm Width = 10 2/3 = 32/3 cm Step 3: Add Length and Width: 25/2 + 32/3. LCM of 2 and 3 is 6. (25 3)/6 + (32 2)/6 = 75/6 + 64/6 = 139/6 cm. Step 4: Calculate the total perimeter: 2 (139/6) = 278/6 = 139/3 cm. Step 5: Convert to a mixed fraction: 46 1/3 cm. Final answer: 46 1/3 cm
  • Q: Salil wants to put a picture in a frame. The picture is 7 3/5 cm wide. To fit in the frame, the picture cannot be more than 7 3/10 cm wide. How much should the picture be trimmed? A: Step 1: Find the difference between the actual width and the required width: Difference = 7 3/5 - 7 3/10 Step 2: Convert the mixed fractions to improper fractions: 7 3/5 = 38/5 7 3/10 = 73/10 Step 3: Find the LCM of 5 and 10, which is 10. Step 4: Convert 38/5 to an equivalent fraction: (38 2) / (5 2) = 76/10. Step 5: Subtract the values: 76/10 - 73/10 = 3/10 cm. Final answer: The picture should be trimmed by 3/10 cm.

Frequently Asked Questions

What is the difference between like and unlike fractions?

Like fractions have the exact same denominators (e.g., 2/7 and 5/7), making them easy to add or subtract directly. Unlike fractions have different denominators (e.g., 2/3 and 1/4) and require you to find the LCM before performing operations.

How do you convert a mixed fraction into an improper fraction?

Multiply the whole number part by the denominator of the fraction, add the numerator to this product, and write the final sum over the original denominator. For example, 3 2/5 becomes (3 * 5 + 2)/5 = 17/5.

Do we need to find the LCM when multiplying fractions too?

No, LCM is only required for adding, subtracting, or comparing fractions. For multiplication, you directly multiply the numerators together and the denominators together without changing them.