Extra Curriculum Support

SecA

1. 0.2 × 0.2 = ?

(a) 0.4

(b) 0.04

(c) 0.004

(d) 4.0

2. If 12.543 is distributed into 100 parts, then each part equals

(a) 125.43

(b) 1254.3

(c) 1.2543

(d) 0.12543

3. If the cost of one pencil is Rs. 2.40, then the cost of ten such pencils is:

(a) Rs. 24

(b) Rs. 240

(c) Rs. 10

(d) Rs. 100

4. A ? is a fraction that represents a part of a whole.

(a) Improper Fraction

(b) Proper fraction

(c) Mixed fraction

(d) None of above

5. An ? is a combination of whole and a proper fraction.

(a) Improper Fraction

(b) Proper fraction

(c) Mixed fraction

(d) None of above

Sol

1. Solution : Option (b)

2. Solution : Option (d)

3. Solution : Option (a)

4. Solution : Option (b)

5. Solution : Option (c)

SecB

1. Raju has solved 24 part of an exercise while Sameer solved 12 part of it. Who has solved more?

2. How many 1 14 feet long strips of ribbon can be cut from a ribbon that is 7 12 feet long ?

3. Add the following: 3.25 , 0.075 and 5

Sol

1. Solution : Since 24 = 12

Both Raju and Sameer have solved the same amount of the exercise.

2. Solution :

To determine how many 1 14 feet long strips can be cut from a ribbon that is 7 12 feet long, follow these steps:

Convert the mixed numbers to improper fractions:

7 12 = 152

1 14 = 54 ​ Thus,

Number of strips = TotallengthofribbonLengthofeachstrip = 152 ÷ 54 = 15254

= 152 × 45 = 6

Therefore, you can cut 6 strips of 1 14 feet from a ribbon that is 7 12 feet long.

3. Solution :

3.25 + 0.075 + 5 = 325100 + 751000 + 51 = 3250+75+50001000 = 83251000 = 8.325

SecC

1. If 12 of −34 of a number is 6, what is the number?

2. Solve the following problem involving fractions: A recipe requires 34cup of flour. If you want to make 3 batches of the recipe, how many cups of flour will you need in total?

Sol

1. Solution : Let the number be x.

Write the equation based on the given condition:

12×−34×x = 6

−38×x = 6

x = 6 × 8−3 = -16

Thus, the number is -16.

2. Solution :

Flour needed for one batch = 34cup

Number of batches = 3

Total flour needed = 3 × 34 = 94 = 2.25 cups

You will need a total of 2.25 cups of flour for 3 batches of the recipe.

Problem 1

1. Anita and her friends are working at a community garden. They need to plant 72 flower bulbs in equal rows. They want each row to have the same number of bulbs and ensure that every row has more than 1 but fewer than 10 bulbs. What are the possible numbers of bulbs in each row, and why is it important to organize tasks efficiently in group projects?

Sol

Solution:

To find the possible numbers of bulbs in each row, we need to identify the divisors of 72 that are greater than 1 and less than 10.

First, we find the divisors of 72:

The prime factorization of 72 = 23×32

From this factorization, we can list all the divisors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

Next, we filter out the divisors that are greater than 1 and less than 10: 2, 3, 4, 6, 8, 9

So, the possible numbers of bulbs in each row are:

2 bulbs per row (36 rows)

3 bulbs per row (24 rows)

4 bulbs per row (18 rows)

6 bulbs per row (12 rows)

8 bulbs per row (9 rows)

9 bulbs per row (8 rows)

By organizing tasks efficiently, Anita and her friends can work more effectively in planting the flower bulbs and ensure that their community garden project is a success.

Problem 2

2. Ravi and his three friends want to buy a book that costs ₹185.20. They decide to share the cost equally. How much will each person pay? Also, explain why sharing costs fairly is an important value in friendships and teamwork.

Sol

Solution:

To determine how much each person will pay, we need to divide the total cost of the book by the number of people sharing the cost.

Total cost of the book: ₹185.20

Number of people: 4

To find the amount each person will pay:

Amount per person = ₹ 185.24 = ₹ 46.30

Therefore, each person will pay ₹46.30.

Sharing costs fairly is fundamental to fostering healthy, respectful, and cooperative relationships in both friendships and teamwork. It ensures that everyone feels included and equally responsible, which is essential for the success of any collaborative effort.

Q1

1. A car travels 250.75 kilometers using 15.5 liters of fuel. Calculate the average fuel efficiency in kilometers per liter. How would the efficiency change if the car traveled an additional 50 kilometers using the same amount of fuel?

Sol

Solution: To calculate the average fuel efficiency in kilometers per liter, we will use the formula:

Fuel Efficiency = TotalDistanceTraveledTotalFuelUsed

Calculate the initial fuel efficiency

Total distance traveled: 250.75 kilometers

Total fuel used: 15.5 liters

Initial Fuel Efficiency = 250.75km15.5liters = 16.18 km/l

Calculate the new fuel efficiency if the car travels an additional 50 kilometers using the same amount of fuel

New total distance traveled: 250.75 km + 50 km = 300.75 km

Total fuel used remains the same: 15.5 liters

New Fuel Efficiency = 300.75km15.5liters = 19.39 km/l

The fuel efficiency improves significantly when the car travels an additional 50 kilometers using the same amount of fuel, increasing from 16.18 km/l to 19.39 km/l. This indicates better fuel utilization for the additional distance covered.

Q2

2. A store offers a 15% discount on a product priced at ₹250. If an additional 5% tax is applied after the discount, what is the final price? Explain each step.

Sol

Solution: To find the final price of the product after applying the discount and tax, follow these steps:

Calculate the discount amount:

The original price of the product is ₹250.

The discount is 15%.

Discount amount = 250 × 15100 = 250 × 0.15 = Rs. 37.50

Calculate the price after the discount:

Price after discount = Original price - Discount amount = Rs. 250 - Rs. 37.50 = Rs. 212.50

Calculate the tax amount:

The tax is 5%.

Tax amount = Price after discount × 5100 = Rs. 212.50 × 0.05 = Rs. 10.625

Calculate the final price:

Final price = Price after discount + Tax amount

Final price = Rs. 212.50 + Rs. 10.625 = Rs. 223.125

So, the final price of the product after applying the 15% discount and then adding the 5% tax is Rs. 223.125.

Q3

3. If 23 of a class are boys and the rest are girls, and 12 of the boys and 34 of the girls participate in a sports event, what fraction of the entire class is participating in the event?

Sol

Solution:

To find the fraction of the entire class that is participating in the sports event, we need to calculate the fractions of boys and girls participating and then combine these fractions relative to the whole class.

Determine the fraction of boys and girls in the class:

Let the total number of students in the class be 1 (for simplicity).

Fraction of boys in the class = 23

Fraction of girls in the class = 1 − 23 = 13

Calculate the fraction of boys participating in the event:

Fraction of boys participating = 12 of 23= 12 × 23 = 26= 13

Calculate the fraction of girls participating in the event:

Fraction of girls participating = 34 of 13 = 34 × 13 = 312 = 14

Combine the fractions of boys and girls participating relative to the whole class:

Fraction of the entire class participating = (Fraction of boys participating) + (Fraction of girls participating)

Fraction of the entire class participating = 13 + 14 = 412 + 312 = 712

(Common denominator of 3 and 4 is 12)

So, 712 of the entire class is participating in the sports event.

Questions

1. If 34 of a number is 12, the number is.

(a) 9

(b) 16

(c) 18

(d) 32

2. The next number of the pattern 60, 30, 15 is:

(a) 10

(b) 5

(c) 154

(d)152

3. The decimal expression for 8 rupees 8 paise (in Rupees) is.

(a) 8.8

(b) 8.08

(c) 8.008

(d) 88.0

4. Each side of a regular hexagon is 3.5cm long. The perimeter of the given polygon is.

(a) 17.5 cm

(b) 21 cm

(c) 18.3 cm

(d) 20 cm

Sol

1. Solution: Correct answer is b.

2. Solution: Correct answer is d.

3. Solution: Correct answer is b.

4. Solution: Correct answer is b

Questions

5. Fraction which is the reciprocal of 23 is ?

6. Product of a proper and improper fraction is ? than the improper fraction.

7. The two non-zero fractions whose product is 1, are called the ? of each other.

8. 5 rupees 5 paise = ?

9. 45 mm = ? m.

10. 2.4 × 1000 = ?

Sol

5. Solution: 32

6. Solution: less than

7. Solution: Reciprocal

8. Solution: 5.05

9. Solution: 0.045

10. Solution: 2400

Questions

11. Ramu finishes 13part of a work in 1 hour. How much part of the work will be finished in 215hours?

12. Kavita had a piece of rope of length 9.5 m. She needed some small pieces of rope of length 1.9 m each. How many pieces of the required length will she get out of this rope?

13. Three boys earned a total of 235.50. What was the average amount earned per boy?

14. Observe the 3 products given in Example 32 and now give the answers of the following questions.

(i) Does interchanging the fractions in the example,12×58, affect the answer?

(ii) Is the value of the fraction in the product greater or less than the value of either fraction?

15. A rule for finding the approximate length of diagonal of a square is to multiply the length of a side of the square by 1.414.Find the length of the diagonal when :

(a) The length of a side of the square is 8.3 cm. (b) The length of a side of the square is exactly 7.875 cm

Sol

11. Solution:

The part of the work finished by Ramu in 1 hour = 13.

So, the part of the work finished by Ramu in 215hours = 1115.

Ramu will finish 1115 part of the work in 215 hours.

12. Solution:

The length of the rope = 9.5 m

The length of a small piece of rope = 1.9 m

Number of small pieces = 9.5 m ÷ 1.9 m = 9.5×101.9×10 = 5

So, she will get 5 small pieces of rope.

13. Solution:

Three boys earned = 235.50

The average amount earned per boy = 235.53

14. Solution:

(i) By interchanging 12×58 we get 58 × 12 = 516 which is same as the product we get in Example 32 by multiplying 12 and 58.

This means that interchanging the fractions does not affect the answer.

(ii) By observing the 3 products given in the solution of Example 32, we come to know that the value of the fractions in the products are as follows.

(a) The product of two fractions whose value is less than 1 i.e. the proper fractions is less than each of the fractions that are multiplied.

(b) The product of a proper and an improper fraction is less than the improper fractions and greater than the proper fraction.

(c) The product of two improper fractions is greater than each of the two fractions.

15. Solution:

(a) The length of a side of the square is 8.3 cm Multiply the side length by 1.414:

d = 8.3 × 1.414

Calculate the result: d ≈ 8.3 × 1.414 = 11.7462

So, the length of the diagonal is approximately 11.7462 cm.

(b) The length of a side of the square is exactly 7.875 cm Multiply the side length by 1.414:

d = 7.875 × 1.414

Calculate the result:

d ≈ 7.875 × 1.414 = 11.13375

So, the length of the diagonal is approximately 11.13375 cm

Q1

1.Sana's class is organizing a bake sale to raise money for a school trip. They decided to bake cookies and cakes to sell. They recorded their sales and costs for each type of baked good.

Sales Record

Cookies

Price per cookie: ₹ 15.75

Number of cookies sold: 40

Cakes

Price per cake: ₹ 120.50

Number of cakes sold: 15

Ingredients Cost

Cookies

Flour: 2.5 kg at ₹20 per kg

Sugar: 1.5 kg at ₹30 per kg

Chocolate: 0.75 kg at ₹50 per kg

Cakes

Flour: 5 kg at ₹20 per kg

Sugar: 3 kg at ₹30 per kg

__{.m-red}Eggs: 2 dozen at ₹60 per dozen

1.What is the total revenue earned from selling cookies and cakes?

2.What is the total cost of ingredients for cookies and cakes?

3.How much profit did Sana's class make from the bake sale?

4.If the class decides to reduce the price of each cake by 10%, how much would each cake cost?

5.If they sell 20 more cookies at the original price, how much additional revenue will they generate?

Q2

2. Case Study: Sharing the Cake Ravi and his friends decided to bake a cake and share it equally. The cake was divided into 8 equal slices. After everyone had taken a share, 3 slices were left. Ravi wanted to know how much of the cake each person received.

Questions:

1.If 5 people shared the cake equally, what fraction of the cake did each person get?

2.How much of the cake is left, and express it as a fraction.

3.Ravi's friend Aisha took two slices of the cake. What fraction of the cake did Aisha eat?

4.If they wanted to divide the remaining 3 slices equally among the 5 people, what fraction of a slice would each person get?