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About Fractions and Decimals — Class 7 Olympiad

Multiply and divide fractions and decimals; solve multi-step problems combining fractions with other operations. This topic is part of the Olympiad Class 7 mathematics syllabus (chapter: Module 2). On this page you can practice 56 questions across three difficulty levels — 18 easy, 20 medium, and 18 hard — each with a visual step-by-step solution, plus a timed 33-question mastery test with a live leaderboard. Worked examples and sample questions from the topic are below.

Fractions and Decimals — solved examples for Class 7 Olympiad

Example 1easy

A school has 3/5 of its students enrolled in sports. Of those in sports, 1/4 play football, and 1/2 of the remaining sports students play basketball. The rest of the sports students play athletics. What fraction of the total school students play athletics?
  1. A)3/20
  2. B)1/5
  3. C)9/40
  4. D)1/10

Step-by-step solution

  1. Let the total number of students be 1 (or S).
  2. Students in sports = 3/5 of total students.
  3. Students playing football = (1/4) × (3/5) = 3/20 of total students.
  4. Remaining sports students (after football) = (3/5) - (3/20) = (12/20) - (3/20) = 9/20 of total students.
  5. Students playing basketball = (1/2) × (9/20) = 9/40 of total students.
  6. Students playing athletics (the rest of the sports students) = (Remaining sports students) - (Basketball players) = (9/20) - (9/40) = (18/40) - (9/40) = 9/40 of total students.

Answer: 9/40

Example 2medium

What is the value of the product: (1 - 1/3) × (1 - 1/4) × (1 - 1/5) × ... × (1 - 1/100)?
  1. A)1/100
  2. B)2/100
  3. C)1/50
  4. D)2/50

Step-by-step solution

  1. Simplify each term: (1 - 1/3) = 2/3, (1 - 1/4) = 3/4, (1 - 1/5) = 4/5, ..., (1 - 1/100) = 99/100.
  2. Write out the product: (2/3) × (3/4) × (4/5) × ... × (99/100).
  3. Observe cancellation: The numerator of each fraction cancels the denominator of the previous fraction.
  4. The product simplifies to 2/100, which is 1/50.

Answer: 1/50

Example 3hard

Consider the product P = (1 - 1/2) × (1 - 1/3) × (1 - 1/4) × ... × (1 - 1/100). What is the value of 1/P?
  1. A)1/100
  2. B)100
  3. C)1/99
  4. D)99

Step-by-step solution

  1. Simplify each term: (1 - 1/2) = 1/2, (1 - 1/3) = 2/3, (1 - 1/4) = 3/4, and so on, until (1 - 1/100) = 99/100.
  2. The product P becomes (1/2) × (2/3) × (3/4) × ... × (99/100).
  3. Observe that the numerator of each fraction cancels out the denominator of the previous fraction (a telescoping product).
  4. After cancellation, P = 1/100. Therefore, 1/P = 1/(1/100) = 100.

Answer: 100

Practice questions on Fractions and Decimals

  1. Q1.easy

    Evaluate the product: (1 - 1/2) × (1 - 1/3) × (1 - 1/4) × ... × (1 - 1/10).
    1. A)1/10
    2. B)1/9
    3. C)1/5
    4. D)9/10
    Show answer

    Answer: 1/10

    Hint: Simplify each term inside the parentheses first. You'll notice a pattern that allows for cancellations across the product.

  2. Q2.easy

    A student spends 2/5 of his pocket money on books. From the remaining amount, he spends 1/3 on food. If he is left with ₹360, what was his initial pocket money?
    1. A)₹600
    2. B)₹750
    3. C)₹800
    4. D)₹900
    Show answer

    Answer: ₹900

    Hint: Work backwards from the remaining amount. Determine what fraction of the original money ₹360 represents after all expenditures.

  3. Q3.easy

    What is the 49th digit after the decimal point in the decimal representation of 3/7?
    1. A)1
    2. B)2
    3. C)4
    4. D)8
    Show answer

    Answer: 4

    Hint: Perform long division to find the repeating block of digits in the decimal expansion of 3/7. Then use the length of this block to determine the 49th digit.

  4. Q4.medium

    A number, when multiplied by 0.75 and then divided by 0.2, gives a result of 180. What is 2/3 of the original number?
    1. A)32
    2. B)64
    3. C)80
    4. D)96
    Show answer

    Answer: 32

    Hint: Work backwards from the result to find the original number. Convert decimals to fractions for easier calculation if preferred.

  5. Q5.medium

    The length of a rectangular plot is increased by 1/4 of its original length, and its width is decreased by 1/4 of its original width. What fraction of the original area is the new area?
    1. A)1
    2. B)4/5
    3. C)6/5
    4. D)15/16
    Show answer

    Answer: 15/16

    Hint: Assume original length and width are 'L' and 'W'. Calculate the new length and width in terms of L and W, then find the new area.

  6. Q6.medium

    A car travels 150.5 km using 11.25 litres of petrol. If the petrol tank has a capacity of 45 litres, how many full tanks of petrol are needed to travel a distance of 4816 km?
    1. A)5
    2. B)6
    3. C)8
    4. D)9
    Show answer

    Answer: 8

    Hint: First, find the distance covered per litre of petrol. Then calculate total petrol needed for 4816 km.

  7. Q7.hard

    If 3 / (x + 1 / (2 + 1/3)) = 1, then what is the value of x?
    1. A)18/7
    2. B)15/7
    3. C)21/7
    4. D)17/7
    Show answer

    Answer: 18/7

    Hint: Work from the innermost part of the complex fraction outwards, simplifying step-by-step.

  8. Q8.hard

    What is the value of (0.333...)² + (0.666...)²?
    1. A)1/3
    2. B)4/9
    3. C)5/9
    4. D)2/3
    Show answer

    Answer: 5/9

    Hint: Convert the recurring decimals into their equivalent fractional forms before performing operations.

  9. Q9.hard

    A farmer has a certain number of apples. He sells 1/3 of them to the first customer. Then, he sells 1/4 of the *remaining* apples to the second customer. Finally, he sells 1/5 of the *new remainder* to the third customer. If he is left with 144 apples, how many apples did he have originally?
    1. A)360
    2. B)300
    3. C)288
    4. D)240
    Show answer

    Answer: 360

    Hint: Work backwards from the final number of apples, considering the fractions of remainders sold at each step.

These are 9 of the 56 questions available for Fractions and Decimals. Start practicing above to unlock visual solutions, AI coaching, and the topic leaderboard — completely free.