Extra Curriculum Support

Problem 1

Rahul noticed that he had a balance of −34of his pocket money left after buying a book for a friend. He decided to do some community service and helped his neighbor, who paid him 12of the total amount of his pocket money as a token of appreciation. After the service, he donated the remaining amount to a charity.

1. What value does Rahul demonstrate by helping his neighbor and donating to charity?

2. How much of his pocket money is left after these activities?

Problem 2

During a group project, Aisha and her classmates were dividing the workload equally. Aisha volunteered to do an extra 13of the work to ensure that everything was completed on time. However, one of her friends fell ill and could only contribute −16of the total work. Aisha stepped in to cover for her friend as well.

1. What values do Aisha's actions reflect?

2. Calculate the total fraction of the work that Aisha completed.

Problem 3

During a community clean-up drive, Neha was asked to organize the volunteers. She divided them into two groups: one-third of the volunteers were assigned to clean the park, and the remaining two-thirds were assigned to clean the streets. Neha noticed that the group cleaning the streets needed more help, so she decided to move 13 of the park volunteers to assist with the streets.

1. What value does Neha exhibit by adjusting the volunteers assignments?

2. Calculate the fraction of the total volunteers now assigned to clean the streets.

Q1

Consider the rational numbers 34 and −58.

1. If these numbers are added and then multiplied by their product, what is the resulting value?

2. Explain whether the result is a rational number and justify your reasoning.

Q2

A rational number pq is multiplied by another rational number rs, resulting in 12. If pq is 47, can you determine rs and verify if rs is a positive or negative rational number?

1. Explain the steps involved in your calculation.

Questions

1. The value of −43 - −13 is

(a) – 2 (b) – 3 (c) 2 (d) –1

2. There are ? number of rational numbers between two rational numbers.

3. In any rational number pq, denominator is always a nonzero integer.

4. To reduce the rational number to its standard form, we divide its numerator and denominator by their HCF.

5. A rational number is defined as a number that can be expressed in the form pq, where p and q are integers and

(a) q = 0 (b) q = 1 (c) q ≠ 1 (d) q ≠ 0

6. To reduce a rational number to its standard form, we divide its numerator and denominator by their.

(a) LCM (b) HCF (c) product (d) multiple

7. Additive inverse of 23 is ?.

8. The reciprocal of 1 is ?.

9. Every natural number is a rational number but every rational number need not be a natural number.

10. Sum of two rational numbers is always a rational number.

11. All decimal numbers are also rational numbers.

12. Write the following as rational numbers in their standard forms:

(a) 35% (b) 1.2 (c) -637 (d) 240 ÷ (– 840) (e) 115 ÷ 207

13. If 12 shirts of equal size can be prepared from 27m cloth, what is length of cloth required for each shirt?

14. 150 students are studying English, Maths or both. 62 per cent of the students are studying English and 68 per cent are studying Maths. How many students are studying both?

15. What should be subtracted from −23 to obtain the nearest integer?

16. Write a rational number in which the numerator is less than ‘–7 × 11’ and the denominator is greater than ‘12 + 4’.

Q1

Rohan and his friends are planning a trip to the amusement park. They have to divide the total expenses equally among themselves. The total cost of the trip is represented as −12005 (in rupees), which includes entry tickets, food, and transport. However, one of their friends, Ravi, contributed an additional 2005 to cover extra expenses.

Questions:

1. How much is each friend expected to pay initially?

2. If Ravi’s contribution is taken into account, how does this affect the amount each friend has to pay? Explain the concept of rational numbers in this context.

Sol 1

Solution :

1. Initially, each friend is expected to pay 48 rupees.

2. After accounting for Ravi’s additional contribution of 40 rupees, the 4 friends who did not contribute the extra amount will pay 38 rupees each.

• Ravi will still pay his initial share of 48 rupees (but has already contributed the extra 40 rupees).

Q2

Anita has been given a school project that requires her to divide a large poster into smaller sections. The poster is 58 meters long and needs to be divided into 4 equal parts. However, she realizes that two of the sections need to be slightly smaller and thus reduces each by 116 meters.

Questions:

1. What is the length of each of the four sections before and after the reduction?

2. How does Anita’s adjustment demonstrate an understanding of rational numbers, and why is it important in practical situations like this?

Sol 2

Solution :

1. Before Reduction:

• Total length of the poster = 58 meters.

• Dividing into 4 equal parts:

Length of each part before reduction = 58 ÷ 4 = 58 × 14 = 532 meters.

After Reduction:

• Reduction for two sections = 116 meters each.

• Length of reduced sections = 532 - 116 = 532 - 232 = 332 meters.

• Remaining two sections are unaffected and remain 532 meters each.

2. Understanding Rational Numbers in Practical Use

• Anita’s adjustment involves operations with rational numbers: division and subtraction. This demonstrates:

1. Flexibility in working with fractions to meet specific requirements.

2. Precision in making adjustments to the poster’s sections.

• Importance in practical situations:

• Rational numbers enable accurate measurements and adjustments in real-world projects, like dividing materials evenly or modifying sizes.