Enhanced Curriculum Support

SecA

1. Pick up the rational numbers from the following given numbers:

67, −12, 0, 10, 1000

2. Write two such rational numbers whose multiplicative inverse is same as they are.

3. The property represented by a + b = b + a is:

(a) closure property

(b) additive identity

(c) associative property

(d) commutative property

4. Which of the following is not true?

(a) Rational numbers are closed under multiplication

(b) Rational numbers are closed under division

(c) Rational numbers are closed under addition

(d) Rational numbers are closed under subtraction

5. What properties, the following expressions show?

(i) 23 + 45 = 45 + 23

(ii) 13 × 23 = 23 × 13

6. The property represented by a × (b + c) = a × b + a × c is:

(a) closure property

(b) distributive property

(c) associative property

(d) commutative property

7. The numerical expression: 38+ −57 = −1956 shows that

(a) Addition of rational numbers is not commutative

(b) Rational numbers are not closed under addition

(c) Rational numbers are closed under multiplication

(d) Rational numbers are closed under addition

8. Which of the following statements is correct:

(i) -5 + 3 ≠ 3 + (-5)

(ii) −812 = 10−15

(iii) 2 is not a natural number

(iv) 17 is not a prime number

(a) Option (iii)

(b) Option (ii)

(c) Option (iv)

(d) Option (i)

SecB

1. Simplify the following expression: 23× 94 + 56.

2. Find the sum and difference of the rational numbers 34 and 56.

3. Represent the rational number 79 on the number line.

4. Check whether the rational number 79 is in its lowest terms. If not, simplify it.

5. Find the product of 25and −34. Also, find the product of the same rational numbers but in reverse order.

SecC

1. If the cost of 4 12 litres of milk is ₹89 12, find the cost of 1 litre of milk.

2. If a car travels 710 kilometers in one minute, how many kilometers will it travel in 15 minutes?

3. If 23of a number is 12, find the number.

4. A box contains 34of a kilogram of chocolates. If each piece weighs 18 kilogram, how many pieces are there in the box?

5. Solve the following: 37 + 514 - 29.

Sec D

1.A group of friends equally shared a cake that weighs 35 kg. If there are 4 friends, how much cake did each person get? Express your answer as a fraction.

2. An elevator descends 35 meters every minute. How many meters will the elevator descend in 12 minutes? Express the answer as a rational number.

3. If the sum of two rational numbers is 712 and one of the numbers is 29, find the other number.

Problem 1

During a study group session, 6 students share 92chocolate bars equally. How much chocolate does each student get? Explain how sharing resources equitably can strengthen bonds among friends and peers.

Problem 2

A community service group collected 73 kilograms of recyclable materials from each member. If there are 9 members, how much material did they collect in total? Discuss the role of civic responsibility in community service and how individual efforts contribute to the greater good.

Problem 3

Rohan and Meera were given an assignment to simplify rational numbers. Rohan finds the solution to be 58 while Meera finds it to be 1016. Meera argues that her answer is correct because she worked hard on it. How should they resolve their difference of opinion while upholding the values of honesty and integrity?

Q1

A group of friends shared a pizza. Two of the friends each ate 38 of the pizza, and the third friend ate 14of the pizza. How much of the pizza was left uneaten? Explain how you calculated your answer.

Q2

In a marathon race, a runner consumes 34 of a energy bar every 10 kilometers. If the race is 42 kilometers long, how many energy bars does the runner need to complete the race? Round your answer to the nearest whole number.

Questions

1. Which of the following is not true?

(a) 23 + 54 = 54 + 23

(b) 23 − 54 = 54 − 23

(c) 23 × 54 = 54 × 23

(d) 23 ÷ 54 = 23 × 45

2. Multiplicative inverse of 01 is:

(a) 1

(b) −1

(c) 0

(d) not defined

3. Three rational numbers lying between −34 and 12 are :

(a) −12, 0 , 34

(b) −14, 14, 34

(c) −14, 0, 14

(d) −54, 0, 14

In examples 4 and 5 , fill in the blanks to make the statements true.

4. The product of a non-zero rational number and its reciprocal is .

5. If x = 13 and y = 67 then xy − yx = ?

6. True/False: Every rational number has a reciprocal.

7. True/False: −45 is larger than −54.

8. Find 47 × 143 ÷ 23

9. Using appropriate properties, find 23 × −57 + 73+ 23 × −27

10. The product of two rational numbers is –7. If one of the number is –10, find the other.

11. Let O, P and Z represent the numbers 0, 3 and -5 respectively on the number line. Points Q, R and S are between O and P such that OQ = QR = RS = SP. What are the rational numbers represented by the points Q, R and S. Next choose a point T between Z and O so that ZT = TO. Which rational number does T represent?

12. A farmer has a field of area of 49 45 ha. He wants to divide it equally among his one son and two daughters. Find the area of each one’s share. (ha means hectare; 1 hectare = 10,000 m2)

13. Why is 45 considered a rational number but 2 is not? Explain in terms of the definitions.

14. Explain why −78 is a rational number. Convert it to its equivalent positive fraction form.

15. Determine which is larger: 57or 68. Show your working.

16. Identify the rational number which is different from the other three : 2/3, −4/5, 1/2, 1/3. Explain your reasoning.

17. Find the rational numbers between −25 and 12.

18. Find multiplicative inverse of: 16+49×43

19. If 23 of the students in a class have brown eyes, and there are 30 students in total, predict how many students you would expect to have brown eyes. Explain whether this fraction would apply to any number of students and why.

Q1

Sanmesh who is working in a multinational company earns Rs. 150000 per month. Out of his earnings he spend 110 th on food items, 14th on shopping with family, 15th of remaining on education of his two kids and rest of money he puts on his savings.

Based on the above information, answer the following questions:

(i) How much money did he spend on the food items?

(ii) How much money did he spend on the shopping?

(iii) Calculate the amount spend by Sanmesh on education of children.

Sol 1

Solution:

Sanmesh's monthly earnings: Rs. 150,000

(i) Expenditure on Food Items:

Amount spent on food items = 110 × 150,000 = 15,000

(ii) Expenditure on Shopping:

Amount spent on shopping = 14 × 150,000 = 37,500

(iii) Expenditure on Education of Children:

Remaining amount = Total earnings - (Amount spent on food items + Amount spent on shopping) = 150,000 − (15,000 + 37,500) = 150,000 − 52,500 = 97,500

Now, calculate how much Sanmesh spent on education of his children, which is 15th of the remaining amount:

Amount spent on education = 15 × 97,500 = 19,500

So,

(i) Sanmesh spent Rs. 15,000 on food items.

(ii) Sanmesh spent Rs. 37,500 on shopping.

(iii) Sanmesh spent Rs. 19,500 on the education of his children.

Q2

A school receives a donation of Rs. 15,000 to purchase classroom supplies. The funds are allocated as follows: 13 on stationery items, 15 on educational games, 14 of the remaining on art supplies. The remainder is used for purchasing books.

(a) How much money is spent on stationery items ?

(b) What is the amount allocated for educational games ?

(c) Calculate the expenditure on art supplies.

(d) How much money is spent on purchasing books ?

Sol 2

Solution: Given:

Total donation received = Rs. 15,000

(a)

Allocation for stationery items = 13 of Rs. 15,000 Amount spent on stationery items = 13 × 15000 = Rs. 5,000

So, Rs. 5,000 is spent on stationery items.

(b)

Remaining after stationery items = Rs. 15,000 - Rs. 5,000 = Rs. 10,000

Allocation for educational games = 15 of Rs. 10,000 = 15 × 10000 = Rs. 2,000

So, Rs. 2,000 is allocated for educational games.

(c)

Remaining after educational games = Rs. 10,000 - Rs. 2,000 = Rs. 8,000

Allocation for art supplies = 14 of Rs. 8,000 = 14 × 8000 = Rs. 2,000

So, Rs. 2,000 is spent on art supplies.

(d)

Remaining after art supplies = Rs. 8,000 - Rs. 2,000 = Rs. 6,000

Therefore, Rs. 6,000 is spent on purchasing books.

Q3

Three friends Rajeev, Sarita and Rahul go to purchase some sweets, namkin and cold drinks for a party. The following chart shows the price and available stock of sweets and namkin in the shop.

(a) After purchasing 500gm of sweet laddu, jalebi and barfi each, Rajeev had Rs. 150 left with him. How much money does Rajeev had before the purchase?

(b) Rajeev wants to purchase one packet of Mixture and two packets of potato chips with the remaining Rs. 150. Explain whether he can purchase it or not.

(c) Rahul had Rs. 200 and wants to purchase one packet of Mixture, one packet of potato chips, 250gm Sweet laddu and one bottle of cold drink. But due to insufficient money he had to reduce the quantity of one of the item. Find out the name of that item along with reason.

(d) Sarita had Rs. 250 and wants to purchase those items which were not purchased by her friends. Choose the correct list of items she will purchase.

(i) Jalebi

(ii) (Roasted) Dry fruits

(iii) Barfi

(iv) Potato chips

Sol 3

Solution:

(a) Rajeev spent on sweets as follows:

Laddu: 500g at Rs. 350 per kg

Jalebi: 500g at Rs. 400 per kg

Barfi: 500g at Rs. 400 per kg

Total cost = (500g × 3501000) + (500g × 4001000) + (500g × 4001000) = Rs. (175 + 200 + 200) = Rs. 575

Given that Rajeev had Rs. 150 left after these purchases, his initial amount of money was:

Initial amount = Total cost + Remaining money = Rs. 575 + Rs. 150 = Rs. 725

So, Rajeev initially had Rs. 725.

(b) The cost for one packet of mixture and two packets of potato chips:

Mixture: Rs. 40 per packet

Potato chips: Rs. 60 per packet

Total cost = Rs. 40 + 2 × Rs. 60 = 40 + 120 = Rs. 160

Since Rajeev only has Rs. 150 left, he cannot afford these items.

(c) Rahul wants to buy:

Mixture: 1 packet (Rs. 40)

Potato chips: 1 packet Rs. 60

Laddu: 250g at Rs. 350 per kg = Rs 3502 = Rs. 175

Cold drink: 1 bottle (Rs. 35)

Total cost = 40 + 60 + 175 + 35 = Rs. 310

Since Rahul has only Rs. 200, he needs to reduce the quantity of one item. The item he would reduce is the Sweet Laddu because it costs Rs. 175, which is higher than the cost of other items.

(d) Sarita has Rs. 250 and wants to buy items not purchased by her friends:

Items not purchased: Jalebi, Roasted Dry Fruits, Barfi

Comparing the prices:

Jalebi: Rs. 400 per kg

Roasted Dry Fruits: Rs. 980 per kg

Barfi: Rs. 400 per kg

Considering affordability with Rs. 250:

Jalebi (250g): 250g at Rs. 400 per kg = Rs. 4002 = Rs. 200

So, the correct list of items Sarita will purchase is: (i) Jalebi

Thus, Sarita will purchase Jalebi.