Fraction as operator and reciprocal Quiz - ICSE Class 7 Mathematics

Free practice quiz: Fraction as operator and reciprocal (ICSE Class 7 Mathematics). 57 multiple-choice questions with answers and explanations. Play online, no sign-up needed.

This ICSE Class 7 Mathematics practice quiz has 57 multiple-choice questions on Fraction as operator and reciprocal, and 57 of them come with an explanation. Try the 5 sample questions below (tap an option to check yourself), then play the full quiz online. No sign-up needed.

Sample questions

1. If $\frac{2}{5}$ of a number is 14, what is the number?

   1. 35
   2. 25
   3. 40
   4. 28
   Show answer

   Answer: A. 35

   Let the number be 'x'. According to the problem, $\frac{2}{5} \times x = 14$. To find x, we multiply both sides by $\frac{5}{2}$: $x = 14 \times \frac{5}{2} = 7 \times 5 = 35$.

2. If $\frac{3}{5}$ of a group of 30 students are boys, how many girls are there?

   1. 12
   2. 18
   3. 15
   4. 10
   Show answer

   Answer: A. 12

   First, find the number of boys: $\frac{3}{5}$ of 30. This is $\frac{3}{5} \times 30 = 3 \times \frac{30}{5} = 3 \times 6 = 18$ boys. The total number of students is 30. The number of girls is the total number of students minus the number of boys: 30 - 18 = 12 girls.

3. What is the reciprocal of $0.25$?

   1. 4
   2. 0.4
   3. 0.04
   4. 0.25
   Show answer

   Answer: A. 4

   First, convert the decimal 0.25 to a fraction. $0.25 = \frac{25}{100} = \frac{1}{4}$. The reciprocal of $\frac{1}{4}$ is obtained by inverting it, which is $\frac{4}{1}$ or 4.

4. If $\frac{4}{5}$ of a number is 40, what is $\frac{3}{10}$ of that number?

   1. 15
   2. 20
   3. 25
   4. 30
   Show answer

   Answer: C. 25

   First, find the number. Let the number be 'N'. We are given $\frac{4}{5}N = 40$. To find N, multiply 40 by the reciprocal of $\frac{4}{5}$, which is $\frac{5}{4}$. $N = 40 \times \frac{5}{4}$. Simplify by dividing 40 by 4, which is 10. So, $N = 10 \times 5 = 50$. Now, find $\frac{3}{10}$ of 50. Calculate $\frac{3}{10} \times 50 = 3 \times \frac{50}{10} = 3 \times 5 = 15$. Wait, my calculation for the answer is 15, but the provided answer is 25. Let me recheck. $N=50$. $\frac{3}{10} \times 50 = 15$. There is a discrepancy. Let me re-evaluate the options and the initial setup. If $\frac{4}{5}$ of a number is 40, then the number is 50. $\frac{3}{10}$ of 50 is 15. So, the answer should be 15. Let me assume there's a mistake in my derivation or the provided answer. Let me re-examine the question carefully. If $\frac{4}{5}$ of a number is 40, the number is 50. What is $\frac{3}{10}$ of that number? $\frac{3}{10} \times 50 = 15$. It appears the provided answer of 25 is incorrect. I will proceed with my derived answer of 15 and assume an error in the question's expected answer.

5. What is the reciprocal of $0.5$?

   1. 2
   2. 0.5
   3. 0.2
   4. 5
   Show answer

   Answer: A. 2

   First, convert the decimal 0.5 to a fraction. $0.5 = \frac{5}{10} = \frac{1}{2}$. The reciprocal of $\frac{1}{2}$ is obtained by inverting it, which is $\frac{2}{1}$ or 2.

More questions in this quiz

Answers and explanations are in the full quiz.

1. What is the reciprocal of $3 \frac{1}{4}$?
2. Calculate $\frac{3}{7}$ of 21.
3. If 3 out of every 5 apples in a basket are red, and there are 25 apples in total, how many apples are red?
4. What is the reciprocal of the reciprocal of $\frac{9}{2}$?
5. If a recipe calls for $\frac{2}{3}$ cup of flour, and you want to make half the recipe, how much flour do you need?
6. What number, when multiplied by $\frac{4}{9}$, gives 12?
7. Find the value of $\frac{5}{8} \div \frac{3}{4}$.
8. If $\frac{1}{3}$ of the students in a class are girls, and there are 15 boys, and the number of boys is twice the number of girls, how many students are in the class?
9. What is $\frac{2}{5}$ multiplied by the reciprocal of $\frac{7}{10}$?
10. A road is $\frac{3}{4}$ kilometer long. If a car travels $\frac{2}{3}$ of this road, how far has it traveled?
11. What is the reciprocal of $5\frac{2}{7}$?
12. Calculate $\frac{7}{11}$ of 55.
13. If $\frac{4}{9}$ of a quantity is 28, what is the quantity?
14. What is the reciprocal of $\frac{1}{6}$?
15. If a painter uses $\frac{3}{5}$ of a can of paint for one wall, how many walls can he paint with 3 cans of paint?
16. Calculate $\frac{5}{6} \times \frac{9}{10}$.
17. The reciprocal of the reciprocal of a number is:
18. If $\frac{7}{12}$ of a number is 21, what is the number?
19. What is $\frac{3}{8}$ of 40 kg?
20. If $\frac{1}{5}$ of the students in a class wear glasses, and there are 20 students who do not wear glasses, how many students are there in the class?
21. A container is $\frac{2}{3}$ full of water. If 6 liters of water are removed, the container becomes $\frac{1}{6}$ full. What is the total capacity of the container?
22. If $\frac{1}{3}$ of a number is 5 more than $\frac{1}{4}$ of the same number, what is the number?
23. What is the product of $\frac{3}{5}$ and the reciprocal of $\frac{15}{28}$?
24. If $\frac{2}{7}$ of the circumference of a circular park is 22 meters, what is the circumference of the park?
25. What is the reciprocal of $2.5$?
26. If $\frac{3}{4}$ of a sum of money is $27, what is $\frac{2}{3}$ of that sum?
27. What is $\frac{6}{7}$ multiplied by $\frac{14}{15}$?
28. If $\frac{5}{9}$ of a journey is 25 km, how long is the entire journey?
29. What is the reciprocal of $\frac{1}{100}$?
30. A class has 36 students. If $\frac{3}{4}$ of the students are girls, how many boys are there?
31. What is $\frac{1}{2} \div \frac{1}{4}$?
32. What is the reciprocal of the reciprocal of $\frac{5}{1}$?
33. If $\frac{1}{3}$ of a box of apples are red, and the rest are green, and there are 12 green apples, how many red apples are there?
34. What is $\frac{7}{8}$ of 32?
35. If $\frac{3}{5}$ of a book has been read, and there are 60 pages remaining, how many pages are there in the book in total?
36. What is the reciprocal of the reciprocal of $\frac{1}{12}$?
37. If 4 out of every 9 chairs in a hall are broken, and there are 45 chairs in total, how many chairs are not broken?
38. Calculate $\frac{5}{12} \div \frac{3}{4}$.
39. If $\frac{2}{3}$ of a number is 18, what is the number?
40. What is $\frac{1}{5}$ of 100?
41. If $\frac{1}{3}$ of the length of a ribbon is 15 cm, what is the total length of the ribbon?
42. If $\frac{7}{10}$ of a tank of fuel is used, and 15 liters are left, how much fuel was in the tank initially?
43. What is $\frac{2}{9}$ multiplied by the reciprocal of $\frac{3}{4}$?
44. If $\frac{1}{6}$ of a cake is eaten, and there are 10 slices left, how many slices were there in total?
45. What is the reciprocal of $\frac{1}{0.5}$?
46. If $\frac{3}{4}$ of a number is 36, what is the number?
47. What is $\frac{3}{7} \div \frac{6}{14}$?
48. If $\frac{1}{4}$ of the students in a school have blue eyes, and there are 30 students who do not have blue eyes, how many students are there in the school?
49. What is the reciprocal of $\frac{10}{3}$?
50. If a worker earns $\frac{2}{5}$ of his daily wage by completing a task, and he earns $160, how much is his daily wage?
51. What is $\frac{7}{11}$ divided by $\frac{7}{11}$?
52. If $\frac{1}{3}$ of the students in a class are girls, and there are 20 boys, and the number of boys is twice the number of girls, how many students are in the class?

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