Class 7 Maths – Chapter 3: Fractions and Decimals Solutions

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Chapter 3 of Class 7 Maths discusses Fractions and Decimals, fundamental mathematical concepts to grasp parts of a whole. Fractions are parts of a number, whereas decimals provide another means of describing these parts in an easier form. This blog entry will give step-by-step solutions to every exercise given in this chapter, with examples, in order to gain a complete grasp of the topic. By the end of this blog, you’ll have a comprehensive understanding of fractions and decimals, and be able to apply this knowledge to solve real-world problems.

Exercise 3.1: Understanding Fractions

  1. Write the following as fractions:
    • a) 0.75
    • b) 1.5
    • c) 2.25
    Solution:
    • a) 0.75 can be written as 75/100, which simplifies to 3/4.
    • b) 1.5 can be written as 3/2.
    • c) 2.25 can be written as 9/4.
  2. Convert the following fractions to decimals:
    • a) 5/8
    • b) 3/4
    • c) 7/10
    Solution:
    • a) 5/8 = 0.625
    • b) 3/4 = 0.75
    • c) 7/10 = 0.7

Exercise 3.2: Addition and Subtraction of Fractions

  1. Add the following fractions:
    • a) 1/4 + 2/4
    • b) 5/8 + 3/8
    • c) 2/5 + 3/5
    Solution:
    • a) 1/4 + 2/4 = 3/4
    • b) 5/8 + 3/8 = 8/8 = 1
    • c) 2/5 + 3/5 = 5/5 = 1
  2. Subtract the following fractions:
    • a) 5/6 – 2/6
    • b) 7/9 – 4/9
    • c) 3/7 – 1/7
    Solution:
    • a) 5/6 – 2/6 = 3/6 = 1/2
    • b) 7/9 – 4/9 = 3/9 = 1/3
    • c) 3/7 – 1/7 = 2/7

Exercise 3.3: Multiplication of Fractions

  1. Multiply the following fractions:
    • a) 2/3 × 3/4
    • b) 5/6 × 2/7
    • c) 1/2 × 4/5
    Solution:
    • a) (2 × 3)/(3 × 4) = 6/12 = 1/2
    • b) (5 × 2)/(6 × 7) = 10/42 = 5/21
    • c) (1 × 4)/(2 × 5) = 4/10 = 2/5
  2. Word Problem:
    A bag of flour weighs 3/5 kg. How much would 4 such bags weigh?
    • Solution: (3/5) × 4 = 12/5 = 2 2/5 kg.

Exercise 3.4: Division of Fractions

  1. Divide the following fractions:
    • a) 3/5 ÷ 2/7
    • b) 5/6 ÷ 2/3
    • c) 7/9 ÷ 3/4
    Solution:
    • a) (3/5) × (7/2) = 21/10
    • b) (5/6) × (3/2) = 15/12 = 5/4
    • c) (7/9) × (4/3) = 28/27
  2. Word Problem:
    If a box weighs 5/8 kg and you divide it into 4 equal parts, what will be the weight of one part?
    • Solution: (5/8) ÷ 4 = 5/32 kg.

Exercise 3.5: Converting Fractions to Decimals and Vice Versa

  1. Convert the following fractions to decimals:
    • a) 4/5
    • b) 7/8
    • c) 11/20
    Solution:
    • a) 4/5 = 0.8
    • b) 7/8 = 0.875
    • c) 11/20 = 0.55
  2. Convert the following decimals to fractions:
    • a) 0.2
    • b) 1.25
    • c) 0.75
    Solution:
    • a) 0.2 = 2/10 = 1/5
    • b) 1.25 = 5/4
    • c) 0.75 = 3/4

Exercise 3.6: Decimal Operations

  1. Add the following decimals:
    • a) 1.2 + 2.4
    • b) 0.75 + 1.5
    • c) 3.6 + 2.8
    Solution:
    • a) 1.2 + 2.4 = 3.6
    • b) 0.75 + 1.5 = 2.25
    • c) 3.6 + 2.8 = 6.4
  2. Subtract the following decimals:
    • a) 5.8 – 2.5
    • b) 4.2 – 1.7
    • c) 6.3 – 3.4
    Solution:
    • a) 5.8 – 2.5 = 3.3
    • b) 4.2 – 1.7 = 2.5
    • c) 6.3 – 3.4 = 2.9

Exercise 3.7: Word Problems Involving Fractions and Decimals

  1. A recipe calls for 2/3 cup of sugar. If you want to make only half the recipe, how much sugar do you need?
    • Solution: (2/3) × (1/2) = 2/6 = 1/3
    • You need 1/3 cup of sugar.
  2. A student scored 8/10 marks in a test. What is the score as a decimal?
    • Solution: 8/10 = 0.8
    • The score as a decimal is 0.8.
  3. A train travels 120 km in 2 hours. What is its speed in km per minute?
    • Solution:
      Speed = Distance / Time
      Speed = 120 km / 120 minutes = 1 km/min.
  4. A student reads 3/5 of a book in one day. How much of the book remains to be read?
    • Solution:
      Remaining = 1 – 3/5 = 5/5 – 3/5 = 2/5
    • 2/5 of the book remains to be read.

Exercise 3.8: Comparing Fractions and Decimals

  1. Which is greater: 3/4 or 0.7?
    • Solution:
      3/4 = 0.75
      Since 0.75 > 0.7, 3/4 is greater.
  2. Which is smaller: 5/8 or 0.625?
    • Solution:
      5/8 = 0.625
      Both are equal.
  3. Compare 4/5 and 0.8. Which is greater?
    • Solution:
      4/5 = 0.8
      Both are equal.
  4. Compare 1/3 and 0.33. Which is greater?
    • Solution:
      1/3 = 0.333…
      0.33 is slightly smaller than 1/3.

Additional Questions for Practice

  1. Simplify the fraction 16/64.
    Solution:
    16/64 simplifies to 1/4.
  2. Convert 0.45 into a fraction.
    Solution:
    0.45 = 45/100 = 9/20.
  3. Find the product of 7/10 and 2/5.
    Solution:
    (7 × 2) / (10 × 5) = 14/50 = 7/25.
  4. Divide 9/8 by 3/4.
    Solution:
    (9/8) ÷ (3/4) = (9/8) × (4/3) = 36/24 = 3/2.
  5. Write 1.2 as a fraction.
    Solution:
    1.2 = 12/10 = 6/5.
  6. Add 3/7 and 2/5.
    Solution:
    (3/7) + (2/5) = (15 + 14) / 35 = 29/35.
  7. Subtract 5/9 from 8/9.
    Solution:
    (8/9) – (5/9) = 3/9 = 1/3.
  8. Multiply 4/11 and 5/7.
    Solution:
    (4 × 5) / (11 × 7) = 20/77.
  9. Divide 3/4 by 1/2.
    Solution:
    (3/4) ÷ (1/2) = (3/4) × (2/1) = 6/4 = 3/2.
  10. What is the reciprocal of 5/6?
    Solution:
    The reciprocal of 5/6 is 6/5.

This blog article has offered a complete guide to Class 7 Maths Chapter 3: Fractions and Decimals, with numerous exercises and solutions to assist you in comprehending how to work with fractions and decimals. Whether it is addition, subtraction, multiplication, division, or converting between decimals and fractions, it is vital to master these skills. By solving these questions and solutions, you will be well-prepared to handle more complex mathematical problems and apply fractions and decimals in real-world scenarios.

Also Read: Class 7 Maths Chapter 2 Worksheet With Solutions

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