Shubharambha Math Book 5 for CTP 2077

2. (a) 6 (b) 21 (c) 32 (d) 1 (e) 1
9 10

(f) 27 (g) 45 (h) 43 (i) 1 3 (j) 12
7

3. (a) 32 (b) 19 1 (c) 54 (d) 5 5
5 6

4. (a) 12 ft (b) 20 ft. (c) 1 l (d) Rs. 29
8

Exercise 7.6

1. (a) 0.3 (b) 0.07 (c) 5.5 (d) 23.5 (e) 0.73

(f) 2.15 (g) 0.005 (h) 0.027 (i) 0.376 (j) 4.256

(k) 3.576 (l) 0.001

2. (a) 160 (b) 1080 (c) 1405 (d) 17050 (e) 41507

(f) 108400 (g) 11503 (h) 3160204 (i) 312000307 (j) 973
1000

3. (a) Place name = Tenths (b) Place name = Hundredths

Place value = 2 or 0.2 Place value = 5 or 0.05
10 100
8
(c) Place Name= Thousandths Place Value = 1000 or 0.008

(d) Place Name = Hundredths Place Value = 4
100

Ones Tenths Tens Ones Tenths Hundredths
4. (a) 3 6 (b) 4 3
2 7

Three point six Forty three point two seven.

Hundreds Tens Ones Tenths Hundredths

(c) 5 13 2 8

∴ Five hundred thirteen point two eight.

Hundreds Tens Ones Tenths Hundredths Thousandths
(d) 1
74 2 6 7

∴ One hundred seventy four point two six seven.

5. (a) 3 + 7 (b) 20 + 7 + 4 + 5
10 10 100

Maths Zone -Grade 5 201

(c) 500 + 10 + 2 + 8 + 1030 (d) 400 + 10 + 7 + 3 + 1600+ 8
10 10 1000

6. (a) 5.6 (b) 25.63 (c) 485.12 (d) 634.234

7. 55.266 (b) 143.42 (c) 63.525 (d) 5992.8

8. (a) 2.5<3.7 (b) 4.67>4.2 (c) 5.42<5.47 (d) 0.1 > 0.01

(e) 0.01 > 0.001 (f) 85.678 < 85.768

Exercise 7.7

1. (a) 21 (b) 32 (c) 153 (d) 510 (e) 41
(f) 430 (g) 52 (h) 280010

2. (a) 0.5 (b) 0.4 (c) 0.5 (d) 3.4 (e) 5.5

(f) 0.35 (g) 0.44 (h) 0.54 (i) 12.75 (j) 16.375

3. (a) 0.2 (b) 0.777 (c) 0.666 (d) 0.833 (e) 2.285

(f) 3.571 (g) 4.555 (h) 2.272 (i) 1.733 (j) 10.294

4. (a) 0.508 (b) 0.809 (c) 0.457 (d) 0.593 (e) 4.1

(f) 14.43 (g) 10.497 (h) 127.975 (i) 475.896

5. (a) 0.3 (b) 0.25 (c) 0.625 (d) 3.54 (e) 28.654

(f) 319.075 (g) 9.92 (h) 3.83 (i) 199.947

6. (a) 0.8 (b) 2.23 (c) 7.75 (d) 42.954 (e) 3.17

(f) 4.76

7. (a) 14.25 (b) 159.75 (c) 0.473 (d) 2.09 meter

Exercise 7.8

1. (a) Show to your teacher.

2. (a) 4 (b) 6.3 (c) 4.08 (d) 4.05 (e) 33.3

(f) 63.45 (g) 36.873 (h) 100.62 (d) 1.95 (e) 2.976
(i) 14.418 (j) 231.7126
3. (a) 0.21 (b) 0.175 (c) 0.4707

(f) 3.2382 (g) 26.775 (h) 41.5575

(k) 21.573 (l) 1.62486

202 Maths Zone -Grade 5

4. (a) Rs. 942 (b) 385.875 km

5. (a) 725 paisa (b) 25650 ml

6. Show to your teacher.

Exercise 7.9

1. Show to your teacher.

2. (a) 0.4 (b) 0.15 (c) 0.119 (d) 0.59 (e) 0.71
(d) 0.59 (e) 0.71
(f) 0.642 (g) 0.564 (h) 2.45

3. (a) 4 (b) 0.5 (c) 1.25

(f) 0.642 (g) 0.564 (h) 2.45

4. (a) Rs. 3.75 (b) 1.575 kg

5. (a) Rs. 12.75 (b) 28.83 cm.

Exercise 7.10

1. (a) 32 (b) 48 (c) 111 (d) 166 (e) 240

(f) 568

2. (a) 4.4 (b) 7.6 (c) 8.6 (d) 12.6 (e) 24.7

(f) 50.5

3. (a) 2.55 (b) 3.67 (c) 7.15 (d) 11.17 (e) 42.43

(f) 63.69

4. (a) 7.053 (b) 8.526 (c) 12.305 (d) 18.562 (e) 55.492

(f) 60.016

5. (a) 5 km (b) 0.3 millimeter.

Exercise 7.11

1. (a) 5% (b) 12% (c) 55% (d) 80% (e) 100%
2. (a) 50% (b) 40%
(c) 30% (d) 28% (e) 34%

(f) 15% (g) 640% (h) 775% (i) 80% (j) 37 1 %
2
3. (a) 225 7 3 4 5
(b) 20 (c) 4 (d) 5 (d) 4

4. (a) 0.06 (b) 0.14 (c) 0.44 (d) 0.84 (e) 2.15

5. (a) 40% (b) 5% (c) 54% (d) 94% (e) 145%

6. (a) Rs.200 (b) 12 m (c) 120 kg (d) 2 l (e) Rs. 5

7. (a) 30% (b) 25% (c) 75% (d) 50% (e) 41 2 %
3
8. (a) 48 girls 72 boys (c) 40 % women, 60 % men
(d) 5405, 90 %
(d) 34 (e) 225 (f) Rs. 510

Maths Zone -Grade 5 203

UNIT

8 UNITARY METHOD
AND SIMPLE INTEREST

Specific Objective Prescribed by CDC

‰‰ T o solve simple daily life word problems by using unitary method.
‰‰ To solve simple problems on simple interest with the help of unitary method.

204 Maths Zone - Grade 5

Lesson

1 Unitary Method

Class Discussion

The method that is used to find the value of single unit from the given
value of multiple and then finding the necessary value of multiplying the
single unit value is known as unitary method.

Finding the value of more items

Look at this example and complete the table.

Items No. of Items Price Per item (Rs.) Total cost (Rs.)
Pencil 5 10 10 × 5 = 50
Copy 8 75
Geometry box 10 100 ................ = ........
................ = ........

Example 1

The cost of a note copy is Rs. 120, what will be the cost of such 5
note copies?

Solution:
1 note copy = Rs. 120
5 note copies = Rs. 120 × 5 = Rs. 600

Finding the value of one item

Look at this example and complete the table.

Items Total price (Rs.) No. of Items Price per item (Rs.)
Chocolates 120 10 120 ÷ 10 = 12
Water bottle 200 8 ........ ÷ ....... = .......
Mo:Mo 450 5 ........ ÷ ....... = .......

Maths Zone - Grade 5 205

Example 2

The cost of 5kg potato is Rs. 225. What will be the cost of 1 kg of
potato?

Solution:

5kg potato = Rs. 225

1 kg potato = Rs. 225
5
= Rs. 45

Example 3

If the cost of 8kg of apple is Rs. 720, find the cost of 10kg of apple.

Solution:

8kg of apple = Rs. 720

1 kg of apple = Rs. 720 = Rs. 90 [Divide to find unit price]
8
10 kg of apple = Rs. 90 × 10 [Multiply to find more than unit]

= Rs. 900

Best Buys

Example 4

Determine the best buy: 2l 1l
Charge all
1 l mango juice for Rs. 115 into 1l cost

2 l mango juice for Rs. 220

5 l mango juice for Rs. 500

Solution: 3l

First case: 1 l mango juice for Rs. 115

Second case : 2 l mango juice for Rs. 220

1 l mango juice for Rs. 220 = Rs. 110
2
Third case: 5 l mango juice for Rs. 500

206 Maths Zone - Grade 5

1 l mango juice for Rs. 500 = Rs. 100
5
∴ Best buy is the 5l can juice.

Exercise 8.1

1. (a) If the cost of a copy is Rs. 50, what is the cost of such 15 copies?
(b) The cost of 1kg orange is Rs. 115, what is the cost of 12kg of orange?
2. (a) There are 365 days in a year, how many days are there in 12 years?
(b) A car can travel 32km with 1 liter petrol. How many kilometers does

it travel with 15 liters of petrol?
3. (a) The price of 7 shirts is Rs. 3850. Find the price of one shirt.
(b) Pawan earns Rs. 60,000 in a month. How much does he earn in a day?
4. (a) If the cost of 25kg Mansuli rice is Rs. 2250. Find the cost of 1 kg of

Mansuli rice.
(b) A bus runs 520km in 13 hours. How many kilometer does it run in 1

hour?
5. (a) If the cost of 25 pens is Rs. 425, what is the cost of 12 pens?
(b) If the cost of 16 books is Rs. 480, how many books can be bought for

Rs. 900?
6. (a) A man walks 45km in 9 hours. How long does he take to walk 65km.
(b) If the cost of one dozen copy is Rs. 216. Find the cost of 20 copies.
7. Which is the best buy?
(a) 10 cakes for Rs. 120 or 5 cakes for Rs. 58.
(b) One dozen pens for Rs. 138 or 15 pens for Rs. 168.

Maths Zone - Grade 5 207

Lesson

2 Simple Interest

Class Discussion

Facts to be remembered about Simple Interest:

Principal (P) : Money borrowed from a lender is known as principal or
sum.

Interest (I) : Additional money paid by the borrower to the lender for
having used his money is called interest.

Amount (A) : The total money which the borrower pays back to the lender
at the end of the specified period is called amount.

The sum total of the principal and interest is called the amount.


Amount Amount Amount Amount = Principal + Interest
Interest I=A-P P =A-I Interest A = P + I
Principal P = A - I and I = A - P
Principal

Rate (R) : It is the interest for one year on borrowing or lending Rs.
100.
Time (T) :
The fixed percentage as the interest on principal which the
bank pays for annum (per year) is called the rate R.

The period for which money is deposited in the bank or for

which the loan has been borrowed. Interest and

It is the period for which money is Simple Interest has
borrowed or lent.
the same meaning.

208 Maths Zone - Grade 5

Exercise 8.2

1. Find the missing items within the houses.

a. b. c.

Rs.7,000

Rs.5,000 Rs.500 Rs.5,000 Rs. 4500 Rs. 500

d. e. f.

Rs. 10,000 Rs. 6565 Rs.7500

Rs.4000 Rs. 5000 Rs.1500

2. Fill in the blanks in the following table.

Deposited money (P) Interest Earned (I) Amount (A)

(Rs.) (Rs.) (Rs.)
14,800
............. 1800 15,000

12500 ............. .............
23,400
8500 2500 25,500
.............
18000 .............

............. 5,500

14000 3000

3. Write the rate of interest on the basis of given information.

Principal (P) Time (T) Interest (I) Rate of Interest (R)

Rs. 100 1 year Rs. 7 17%

Rs. 100 1 year Rs. 12 .............

Rs. 100 1 year Rs. 25 .............

Rs. 100 1 year Rs. 32 .............

4. Write the interest on the basis of the following information.

Principal (P) Time (T) Rate of Interest (R) Interest (I)

Rs. 100 1 year 5% Rs. 5

Rs. 100 1 year 14% Rs. ..........

Rs. 100 1 year 21% Rs. ..........

Rs. 100 1 year 42% Rs. ..........

Maths Zone - Grade 5 209

Calculating the Simple Interest

The value of interest depends upon three factors.

• The principal (P)

• The time (T)

• The Rate of Interest (R)

Interest = Principal × Time × Rate of Interest
i.e. I = 100
PTR
100

Example 1

Ram borrowed Rs. 100 from Shyam at the rate of 8% per year. How
much interest did he pay in 4 years?

Solution:
The rate of interest is 8%.

∴ The interest on Rs. 100 for 1 year is Rs. 8

∴ The interest on Rs. 100 for 4 year is Rs. 8 × 4

= Rs. 32

Example 2

Sabina has deposited Rs. 5000 in a bank for 1 year. If the bank
provides 12% per year interest on the deposit, how much
interest will she receive?

Solution:

The rate of interest is 12%

∴The interest on Rs. 100 for 1 year is Rs. 12.

The interest on Rs. 1 for 1 year is Rs.12
100

The interest on Rs. 5000 for 1 year is Rs.12 × 5000
100

= Rs. 12 × 50

= Rs. 600

210 Maths Zone - Grade 5

Example 3

A man deposited Rs. 50,000 in a bank at 7% interest per year for

3 years. How much simple interest did he get?

Solution:

The rate of interest is 7%.

∴ The interest on R.s 100 for 1 year is Rs. 7.

The interest on Rs. 1 year is Rs.7
100

The interest on Rs. 50,000 for a year Rs.7 × 50,000
100

The interest on Rs. 50,000 for 3 year is 7 × 50,000 × 3
100

= 7 × 500 × 3

∴ The interest (I) = Rs. 10,500.
Alternative Method :

Solution:
Principle (P) = Rs. 50,000

Rate of Interest (R) = 7%

Time (T) = 3 years
Interest (I) = ?

We know,

I= P.T.R
100
50,000 × 3 × 7
= 100

∴Interest (I) = Rs. 10,500

Maths Zone - Grade 5 211

Exercise 8.3

1. (a) Calculate the interest of Rs. 100 at the rate of 12% per year for 5 years.
(b) Calculate the interest of Rs. 100 at the rate of 20% per year for 7 years.
2. (a) Indu deposited Rs. 4000 in a bank at the rate of interest 15% per year.

How much interest did she get in 1 year?
(b) Deepak Budha has deposited Rs. 10,000 in a bank for 1 year. If the

bank provides 8% per year interest on the deposit, how much interest
will he get?
3. (a) Find the simple interest of Rs. 25,000 for 4 years at the rate of 12% per
year.
(b) Find the simple interest of Rs. 40,000 for 5 years at the rate of 10% per
year.
4. (a) Kapindra borrowed Rs. 1,50,000 from a bank for 3 years at the rate of
18% per year. How much interest will Kabindra have to pay to the
bank?
(b) Mahima and Pratina both deposited Rs. 20,000 in a bank. Mahina
deposited for 5 years at the rate of 7% per year and Pratina deposited
for 4 years at the rate of 8% per year. Who will get more interest? By
how much?

212 Maths Zone - Grade 5

Maths Fun

There are 10 oranges in a basket. It needs to be divided among 10 people.
How can you divide them so that each person gets an orange, and one
orange remains in the basket?

Find the solution and discuss in the class.
Maths Zone - Grade 5 213

Practice Zone

Group A
Solve the following questions.

1. The cost of 6 ice-creams is Rs.60. What is the cost of 9 ice-creams?
i. Rs.54 iii. Rs.100
ii. Rs.90 iv. Rs.109
2. What is the simple interest of Rs. 2000 for a year at the rate of

10% per year?
i. Rs 2000 ii. Rs. 200
iii. Rs. 20 iv. Rs 2
3. The cost of one dozen copies is Rs. 360. Find the cost of 10 copies.
4. 10 buses carry 250 passangers. How many passenger can 15

Buses carry?
5. Find the simple interest of Rs.600 for 2 years at the rate of 25%

per year.
6. If the interest of Rs.100 for a year is Rs.7. Find the interest of 8

years of same money?
7. Suntali borrowed Rs 1,50,000 from a bank at the rate of 12% per

year simple interest.How much interest does she pay at the end
of 4 years?

214 Maths Zone - Grade 5

Answers of Unit 8

Exercise 8.1

1. (a) Rs. 150 (b) Rs. 1380

2. (a) 4380 days (b) 480km

3. (a) Rs. 550 (b) Rs. 2000

4. (a) 90 (b) 40km

5. (a) Rs. 204 (b) 30 books

6. (a) 13 hours (b) Rs. 360

7. (a) 2nd choice (b) 2nd choice

Exercise 8.2

Show to your teacher.

Exercise 8.3

1. (a) Rs. 60 (b) Rs. 140

2. (a) Rs. 600 (b) Rs. 800

3. (a) Rs. 12,000 (b) Rs. 20,000

4. (a) Rs. 81,000

(b) Rs. 7000

Pratima = Rs, 6400 Mahima get more interest by Rs. 600



Maths Zone - Grade 5 215

UNIT

9 BILL & BUDGET

Bill No : 346 Sagun's bKaothomkasnhduop

Bagbazar,

321N.S...aNm. ePC:MPePonaarprattyhbicabutoiloaPrkou5d13Q2epplitp cyicic Rate ADdadter:e2s0s7:3P–o0k1h–a0r7a
In words: Fifteen hundred fifty Amount
250/– 750/–
50 /– 600/–
40 /–
Total 200 /–
only. Rs. 1550/–

.........................
Signature

Specific Objective Prescribed by CDC

‰‰ T o prepare the simple bill.
‰‰ To tell and receive the information from the budget.

216 Maths Zone - Grade 5

Lesson

1 Bill

A bill contains information of business. It contains the following things.

– Name and address of Suman Stores
shop.
Pokhara
– Bill number
Bill No : 727 Date: 2075–06–09
– Date of purchase of
goods. Name : Ms. Sita Poudel Address : Pokhara

– Name and address of S.N. Particular Qty Rate Amount
customers. 350/–
1. Rice 5 kg 70/– 160/–
– Name of item purchased 60 / –
2. Sugar 2 kg 80/– 570/–
– Quantity, rate and
amount. 3. Salt 3 packet 20/–

Total

In words: Five hundred seventy only.

.........................

Signature

– Signature of the shopkeeper.

Exercise 9.1

1. Look at a bill and answer the following questions.

Sagun's bookshop

Bagbazar, Kathmandu

Bill No : 346 Date: 2073–01–07

Name : Prabati Poudel Address : Pokhara

S.N. Particular Qty Rate Amount
750/–
1. Math book 3 pic 250/– 600/–
200 /–
2. Copy 12 pic 50 /– Rs. 1550/–

3. Pen 5 pic 40 /–

Total

In words: Fifteen hundred fifty only.

.........................

Signature



Maths Zone - Grade 5 217

1. Name and address of the shop.
2. Name and address of customer.
3. Total bill amount.
4. If Parbati gives 2000/- to the shopkeeper. How much money

does she get back?

2. Collect the bills in your house for a month. Answer the following
questions.
i. How many bills do you have?
ii. List the items purchased from the all bills.
iii. Total amount of bills.
iv. Find total expense of your family.
v. Write the items consumed the most.

Making Bills

Samir Khatri bought the following item 2kg mango, 1kg potato, 5

kg raddish Sanjibani Fruits Center
Bill for Samir Khatri. Price List
Items Price/kg
Sanjibani Fruits Center Mango Rs. 180
Orange Rs. 150
Kathmandu

Bill No. : 245 Date : 2070 - 5- 27

Name : Samir Khatri Address : Kirtipur Tomato Rs. 90

S.N. Particular Quantity Rate Amount Potato Rs. 50

1. Mango 2 180 360 Banana Rs. 120/dozen

2. Potato 1 50 50 Radish Rs. 20

3. Radish 5 20 100 Carrot Rs. 30
Grand Total = 510/- Apple Rs.160

In words Five hundred ten only. Quantity × Rate=Amount

..................

Signature

Sum of amount is

Grand total

218 Maths Zone - Grade 5

Exercise 9.2

1. Make bill for Pemba and Minju, who bought following items from

Sanjibani fruits centre.

a. Pemba bought following b. Minju bought the following

items. items.

i. Tomato - 2kg i. Carrot - 3 kg

ii. Banana - 3 dozen ii. Apple - 4kg

iii. Orange - 1 kg iii. Radish - 2 kg

2. Make bills for following. Menu of Jharana Fast Food

a. Suhana ordered the following i. Momo – 120 Sekuwa – 90

items in 2071-2-27. ii. Chowmin – 90 Rice (motton) – 250

i. Momo - 2 plates iii. Sausage–40/stick Rice (Chicken) – 200
ii. Sekuwa - 3 plates
iv. Lassi – 80 Coffee – 50

iii. Lassi - 2 glass v. Naan – 60 Omlet – 60

vi. Cold drink – 40 Toast – 70

b. In 2072-03-10 Hari ordered following items.
a. Sausage - 5 stick
b. Rice (motton) - 2 plates
c. Cold drinks - 3 bottle
c. Ram Lakhan ordered following items in 2072-1-5.
i. Naan - 3 plate
ii. Chowmin - 2 plate
iii. Omlet - 1 plate

Maths Zone - Grade 5 219

Lesson

2 Budget

Budget is the income and expenditure details of a family, a firm, school
or an administrative units. Government announces a budget in each fiscal
year. We discuss only about the family budget in this topic.

Look at a budget of a Mahabir family of Bara.

Income Expenditure

S.N. Income details Rs. S.N Expenditure details Rs.

i. Selling Rice 1,00,000/- 1. Food 1,50,000/-

ii. Selling vegetables 50,000/- 2. Cloths 50,000/-

iii. Goat 10,000/- 3. Festival 20,000/-

iv. Salary income 1,20,000/- 4. Education 30,000/-

Total 2,80,000/- 5. Transportation 15,000/-

6. Others 5,000/-
Total 2,70,000/-

i. What is the annual saving of Mahabir?
ii. In which item does Mahabir make maximum income?

iii. What is his annual expenditure?

iv. In which item does he spend more?

Exercise 9.3

1. Income details & expenditure of a family are given below. Make a

budget chart for this family.

Income details Expenditure details

Selling Mustard – Rs. 5,000 Food – Rs. 80,000
Education – Rs. 50,000
Vegetables – Rs. 70,000 Health – Rs. 40,000

Mangos – Rs. 1,00,000

220 Maths Zone - Grade 5

Wheat – Rs. 60,000 Clothes – Rs. 70,000
Salary – Rs. 2,00,000
Entertainment – Rs. 60,000

Miscellaneous – Rs. 90,000

2. The annual budget of a preschool is given below.

Income Expenditure

Income source Amounts Expenditure details Amounts

1. Admission fee 4,00,000 1. Rent 1,00,000

2. Monthly fee 7,00,000 2. Salary 5,00,000

3. Exam fee 7,00,000 3. Exam evaluation 70,000

4. Stationary fee 1,50,000 4. Fuel 1,50,000

5. Bus fee 50,000 5. Furniture 8,00,000

6. Lab 50,000 6. Extra-activity 50,000

7. Tiffin 1,00,000 7. Miscellaneous 60,000

Total 21,50,000 Total 10,10,000

1. What is the annual income of school?

2. What is the annual expenditure?

3. What is the annual saving of school?

4. In which topic does the school spends less amount?

5. From which topic does the school earns more?

6. What is the loss amount from Bus/Transport?

Maths Zone - Grade 5 221

Maths Fun

Make a monthly budget of your family with the help of your parents.

Income Expenditure
Income source Amounts Expenditure details Amounts
1.
1.

2. 2.

3. 3.

4. 4.

5. 5.

6. 6.

7. 7.
Total Total

222 Maths Zone - Grade 5

Practice Zone

1. Make a bill for following items.
a. 3 bags cements – Rs. 650 each
tile (2 pac) – Rs. 760/pac
nail (3kg) – Rs. 250/kg
color (10kg) – Rs. 90/kg
b. 2 dozen pencils – Rs. 5 per pencils
3 dozen copy – Rs. Rs. 320 per dozen
3 piece chart paper – Rs. 10 per piece

2. The information given below shows the rate of cost of vegetables
in a shop. Answer the following:

Vegetables Rate 1 kg

Tomatoes Rs. 30.50 P

Cabbage Rs. 17.50 P
Beans Rs. 20

Cauliflower Rs.15

Potato Rs. 22.25 P

a. Name the cheapest and most expensive vegetable.

b. How much money do you need to buy 3 kg potato and 1 kg
tomatoes.

c. How much is the difference between the rate of potato and
beans?

Answers of Unit 9

Exercise 9.1, 9.2 and 9.3 : Show to your teacher.

Maths Zone - Grade 5 223

UNIT

10 STATISTICS

Difficult Raw data
to learn

Easier Ascending order

Really Tabular form
easy Oh ! really.

Ohh ! it's easy
tounderstand.

Specific Objective Prescribed by CDC

‰‰ T o tell, receive the information and find the conclusion from tabulated data.
‰‰ To present the given information on a simple bar graph.
‰‰ T o plot order pairs in graph (first quadrant only)

224 Maths Zone - Grade 5

Introduction

25 students of class 5 secured the following marks in mathematics in
third terminal examination.

30, 50, 55, 70, 60, 30, 50, 50, 55, 55, 55, 70, 70, 70, 70

30, 30, 60, 60, 70, 60, 50, 55, 85, 90

This is called raw data.

Let's arrange the data in ascending order.

Marks No. of students Difficult Raw data
30 4 to learn

50 4 Easier Ascending order

55 5

60 4 Really Tabular form
70 6 easy

85 1 Oh ! it's easy to

90 1 understand. Oh ! really.

a. How many students are there who secure 85 marks?
b . What is the highest marks?
c. How many students secure 55 marks?
d. Write minimum and maximum marks.

Exercise 10.1

1. Arrange the following data in ascending order.
a. 35, 27, 28, 35, 28, 20,, 25, 27, 28, 30, 35

b. 20, 50, 70, 80, 40, 60, 20, 90, 100, 50, 10, 40, 70

2. The following table represents the marks secured by Sabina in
different subjects.

Math Science Social English Nepali

80 65 70 83 56

Maths Zone - Grade 5 225

a. How many marks did Sabina get in English?
b. What is the lowest marks of Sabina?
c. In which subject did she get highest marks?
d. What is the difference between highest & lowest marks?

3. The following table shows the weight of students of grade 5 of a
school.

Weight (in kg) 30 35 40 50 60

No. of students 14 15 9 3 1
a. How many students have the weight 40 kg?
b. How many students have weight 60 kg?
c. What is the minimum weight of student?
d. How many students take part?

4. Arrange the following data in tabular form.
10, 10, 12, 12, 12, 14, 14, 14, 14, 15, 17, 15, 15, 17, 14, 17, 17, 17, 15, 15, 15,
14, 17,

5. The following graph shows the record of foreign employment since
six years of BhadrapurVillage.
Y
100

90

80

70

60
50

40

30

20

10

0 2000 2001 2002 2003 2004 2005 X

a. How many people leave the village in 2004?
b. In which year least people go for foreign employment?
c. In which year large number of people leave the village?

d. Within six year how many people go for foreign employment?

226 Maths Zone - Grade 5

6. With the help of your teacher draw the bar graph of class-wise
students of your school.

Display it in the classroom wall.

Bar graph

Anjana got different marks in different subject.

Math Science Social English Nepali
50
40 30 60 20

Let's Represent the data in Bar diagram.
Y

60

50

40

30

20

10
X

0 Math Science Social English Nepali

Class Activity:

Draw the bar graph on your mark secured in first terminal examination.

Exercise 10.2

1. The table shows the students passed in the subjects. Draw the bar
graph to show the information.

Subject Math English Nepali Social Science

No. of students 30 50 40 60 25

2. The table given below shows the income of Rehana in a week (from
the shop). Draw the bar graph to show the information.

Day's Sun Mon Tue Wed Thurs Fri
Income 200 400 500 300 600 700

Maths Zone - Grade 5 227

3. The table given below shows the number of students of a school.
Draw a bar graph.

I II III IV V
25 35 40 20 50

Ordered Pair

Two objects, numbers and things keep orderly forms an ordered pair.

Hari starts to run from '0' (starting point). Hari run 2 steps and climb 3
steps. His position is (2, 3).

But, Ram does not run any step & climb only 2 Run → 2 steps

units (steps). So, his position is (0, 2) Climb → 3 steps

i..e Run → No Position of Hari is (2, 3)

Climb → 2 Steps

∴ Position of Ram (0, 2)

Let's discuss the question.

Try to put left shoe on Right leg and right shoe in left leg.

Is it easy to wear?

Of coure not.

So, we should wear according to the leg (Right on right and left on left)

It means we should not break the order. If we try it is difficult to wear.

"A pair, for which the order of the elements is significant is called an
ordered pair."

An ordered pair is a pair of objects whose components occur in a definite
order. It is written by listing two objects in a particular order, separating by
comma and enclosing the pair in parenthesis (small bracket).

228 Maths Zone - Grade 5

Example 1

Plot the following points on graph.

(2, 5) (6, 3) (5, 8) (9, 5) (0, 4)

Solution:

Y

(5, 8) (9, 5) Count horizontally for
(2, 5) the first element and
count vertically for the

second element

(0, 4) (6, 3)

X' X
O

Y'

Example 2

From the adjoining graph find the position of the given points in

ordered pair form. Y

Solution:

A → (2, 6) B → (5, 8) B(5, 8)

C → (4, 3) D → (8, 6) A (2, 6) D(8, 6)
E → (1, 3) F → (0, 6) E(1, 3) C(4, 3)
G → (9, 0) F (0, 6)

X' G(9, 0)
O X

Example 3 Y'

Find x & y if (x + 2, 3) = (7, y). Horizontal number line OX is
Solution: called x-axis vertical number
(x + 2, 3) = (7, y) line OY is called y-axis.
Equating the corresponding elements
Common point is 'O' (origin).

Maths Zone - Grade 5 229

x+2=7 3=y (2, 3) is ordered pair in which
x=7-2 ∴y=3 2 is x- cordinate (abscissa)
x=5 3 is y- cordinate (ordinate)
∴ x = 5, y = 3

Exercise 10.3

1. Plot the following points on the graph
i. (7, 3) ii. (4, 5) iii. (6, 5) iv. (5, 4) v. (3, 2)

vi. (2, 0) vii. (9, 0) viii. (5, 7) ix. (8, 4) x. (3, 8)

2. Plot the following points on graph and join the points in order A -
B - C - D - E - F - B.

A(2, 1) B(2, 4) C(2, 9) D(6, 6) E(4, 6) F(7, 4).

What shape did you get?

3. In square grid plot the points (1, 2), (1, 4), (2, 3), (4, 4), (5, 4), (6, 3), (5,
2), (4, 2), (2, 3). Join them in order and locate the point (5, 3). What
shape did you get?

4. From the given graph find the position (coordinate) of the point.

Y

A
B

C
D

E

X' F X

OG

Y'

230 Maths Zone - Grade 5

5. Plot the following points in graph.
(1, 2) (1, 7) (2, 7) (2, 5) (3, 5) (3, 7) (4, 7) (4, 2) (3, 2)
Join them in order. What do you get?
6. Find the value of a and b if following ordered pairs are equal.
i. (a, 4) = (5, b) ii. (a, b) = (3, 2)
iii. (a + 2 , 5) = (5, b) iv. (a + 1, b) = (7, 2)
v. (a - 1, 8) = (3, b + 1) vi. (a + 1, 5) = (7, b - 1)

(a, b) = (2, 3) We have equated
⇒ a = 2, b = 2, the corresponding
elements to find a & b.

7. Plot the following points in the grah paper. D(5, –2)
A (3, 5) B(–3, 4) C(–4, –6) H(–4, 0)
E (7, 0) F(0, 8) G(0, –6)

Maths Zone - Grade 5 231

Maths Fun

Students are requested to list out the name and age of their family members
and make bar graph of the information.

Find the average age of your family members.
Y

100

90

80
70

Age 60
50

40

30 Mother Brother Sister X
20
10

0 Father

Family Members

232 Maths Zone - Grade 5

Practice Zone

1. Read the bar graph and answer the following. The bar graph shows
the subject and number of students who like different subjects.
Y

60

No. of students 50

40

30

20

10 X
0 Math Science Nepali English

Subjects
a. Which is the most popular subject?

b. Which is the least popular subject?

c. How many students like maths?

2. Draw a bar graph from the data

Subject Nepali English Science Math Social
80 40 70 60
No. of St. 50

3. Arrange the following data in ascending order and present in table:

25, 37, 28, 40, 25, 37, 28, 28, 40, 35,

37, 30, 30, 40, 40, 25, 37, 37, 28, 35.

4. Find the mean from following data [Use SX = X]

40, 32, 18, 52, 62, 88, 94, 76, 6 n

Add all the data and divide the
sum by number of data you

will get mean ! X = mean, SX =

sum of data and n = no. of data.

Maths Zone - Grade 5 233

5. Plot the following points on graph.

(–2 3), (–5, 7) (–2, 1) (–4, 4) (–3, 8)
(–1, 3)
(–5, 5) (–6, 2) (–4, 1) (–2, 6)

Oh!

(–2, 3) lies on 2 units left from
'0' and 3 units up.

Y

Here 12 3 45 6 X
I am (–2, 3)

3
2
1
X'
–5 –4 –3 –2 –1

Y'

Answers of Unit 10

Exercise 10.1, 10.2 and 10.3 : Show to your teacher.

234 Maths Zone - Grade 5

UNIT

11 SET

Specific Objective Prescribed by CDC

‰‰ T o write into sentences of the given set in set notation { }.
‰‰ To express the sets by using capital letters and set notation.

Maths Zone - Grade 5 235

Set as a well defined collection

Class Discussion

It is a collection of flowers. It is a collection of geometric
It is a set of flowers. instruments.

It is a set of of geometric
instruments.

2 3 a e
5 7 i o

11 u

It is a collection of first five prime It is a collection of English vowels.
numbers. It is a set of English vowels.

It is a set of first five prime
numbers.

236 Maths Zone - Grade 5

In each collection, the members (elements) are clearly specified. So
"A set is a collection of well-defined objects." (well defined - clearly
specified )

Well-defined Non-well defined

‰‰ The collection of your favourite ‰‰ The collection of favourite

fruits fruits

‰‰ The collection of girls of your ‰‰ The collection of tall boys of

class whose height is more your class.

than 4.1"

‰‰ The collection of text books of ‰‰ The collection of interesting

grade 5 books.

‰‰ The collection of student who ‰‰ The collection of intelligent

secured more than 75% in students of your class.

your first term of your class.

In each collection, if we can easily know any object/thing whether it belongs
to the collection or not. It is well-defined otherwise it is non-well defined.

Exercise 11.1

1. Identify whether the following collections are set or not and rewrite
in separate list.

(a) The collection of even numbers from 1 to 10.
(b) The collection of beautiful girls of class 5.
(c) The collection of the colors of a rainbow.
(d) The collection of your text books of grade 5.
(e) The collection of honest boys of your class.
(f) The collection of planets.

Maths Zone - Grade 5 237

Set Notation

Let, A = set of English vowels. Therefore, A = {a, e, i, o u}

Now,

Equal sign

Curly Bracket

A = {a, e, i, o, u }

Separated by commas

Name of set members in small Here, 1 ∈ N, 2 ∉ N
in capital letter letters ∈ = belongs to
∉ = does not belong to
The set of first five odd numbers. Similarly,
N = { 1, 3, 5, 7, 9 } c ∈ A, f ∈ A
The set of the word "Coeffee" q ∉ A, b ∉ A
A = { c, o, f, e} c and f are the members
We donot allow a set of have repeated elements. of set 'A' but a and b are
not the members of set A.

Methods of Writing Sets

1. Diagrammatic Method a e
i o
If the members are written inside a circular diagram,
then it is called diagrammatic method of writing sets. u

2. Descriptive Method ‰‰ The set of

If we describe the type of members of a set by words, first five even
numbers
then it is called descriptive method of writing sets. ‰‰ The set of

3. Listing Method seven days of
the week.

If we list the members of a set inside the curly ‰‰ P = {2, 3, 5, 7}
brackets { } separating them by using commas ( , ) and ‰‰ V = {a, e, i, o,u}
name the set by capital letter, then it is called listing
method of writing sets.

238 Maths Zone - Grade 5

Exercise 11.2

1. If set A = {1, 3, 5, 7} and set B = {p, e, n}, then rewrite and insert ∈ or
∉ in the blank space.

(a) 1 ...... A (b) 4 ...... A (c) 7 ...... A (d) 8 ...... A
(e) p ...... B (f) e ...... B (g) t ...... B (h) r ...... B
2. List the members of the following sets within brackets.
(a) A set of letters in the word "Mathematics".
(b) A set of letters in the word "Elements".
(c) A set of letters in the word "Pokhara".
(d) A set of letters in the word "Coffee".
3. Write the sets in diagrammatic method and name the set.
(a) A set of first five multiples of 5.
(b) A set of square numbers less than 30.
(c) A set of English vowels.
(d) A set of days beginning with letter 's'.
4. Rewrite the sets in descriptive method.
(a) N = {1, 2, 3, 4, 5}
(b) A = {ruler, protractor, setsquare, compass}
(c) S = {1, 4, 9, 16}
(d) M = {4, 8, 12, 16, 20}
5. Rewrite the sets in listing method and name the set.
(a) The set of first five counting (natural) numbers.
(b) The set of first five planets.
(c) The set of the days of a week.
(d) The set of first three cube numbers.

Maths Zone - Grade 5 239

Types of Sets

1. Empty set or Null set:
A set having no elements is called an empty set or null set. The symbol
for this type of set is φ or { }.
E.g: A set of even numbers between 6 and 8.
A set of boys in Kanya Campus Kathmandu.

2. Unit set or Singleton set:
A set having only one element is called an unit set or singleton set.

3. Finite set:
A set having countable number of elements is called finite set.
4. Infinite set:

A set having uncountable (countless) number of elements is called an
infinite set.
E.g. A set of natural numbers.
A set of odd numbers.

Relation of Sets

1. Equal sets:
Sets having same elements is called equal sets.
E.g. : A = {1, 2, 3, 4, 5} and B = {5, 4, 1, 2, 3}
Here, both sets A and B have same elements.
It is denoted by A = B.
2. Equivalent sets:
Sets having equal number of elements is called equivalent sets.
E.g. : A = {1, 2, 3, 4, 5}, Q = {a, e, i, o, u}
Here, both sets A and Q have equal number of elements.i.e. '5' elements
It is denoted by A∼Q.

240 Maths Zone - Grade 5

Exercise 11.3

1. Identify whether the following sets are Unit set, Null set, Finite set
or Infinite set.

(a) A set of odd numbers between 7 and 9.
(b) A set of first five multiples of 4.
(c) A set of even prime number.
(d) A set of odd numbers.
(e) N = {2, 4, 6, 8 ............}
(f) W = {Sunday, Saturday}
(g) A = { }
(h) A set of capital city of Nepal.
2. State whether the following sets are equal or equivalent sets.
(a) A = {a, e, i, o, u}, B = {1, 2, 3, 4, 5}
(b) P = {Sunday, Saturday}, Q = {Tuesday, Thursday}
(c) X = {2, 4, 6, 8}, Y = {8, 6, 2, 4}
(d) M = {5, 10, 15, 20, 25}, 'N' is the set of first five multiples of 5.

Maths Zone - Grade 5 241

Maths Fun

Choose the items from the given circles which are familiar with you and
make the set.
a. Your kitchen ?

b. Your bedroom?

c. Your school?

d. Your garden?

242 Maths Zone - Grade 5

Practice Zone

Solve the following questions.
1. If A={a, b, c, d, e}, then find the correct option.
a. a ∉A b. a ∈ A c. p ∈ A d. f ∈ A
2. Which of the following is not a set?

a. Collection of number between 1 to 10
b. Collection of clever boys in your class
c. Collection of English alphabets
d. Collection of seven days in a week
3. Which of the following collection is Set?
a. Collection of tall boys of your class
b. Collection of beautiful girls of your class
c. Collection of your favorite games.
d. Collection of innocent students of your class
4. Describe the following sets:
a. A = {1, 4, 9, 16} = ..................................
b. B = {bus, car, van} = ..................................
c. C = {2, 4, 6, 8} = ..................................
5. List the members of following sets.
A = {x: x is an odd number less than 10}
B = {factors of 6)
6. A= The collection of English vowel letters.
It is an example of Descriptive method. Write the set A in Listing
Method.
7. If A = {x:x is a whole number less than 7} and B = {x:x is a square
number between 0 and 20}. List the common elements of A and B.

Maths Zone - Grade 5 243

Answers of Unit 10

Exercise 10.1 : Show to your teacher.

Exercise 11.2

1. Show to your teacher.

2. (a) {m, a, t, h, e, i, c, s} (b) {e, l, m, n, t}

(c) {p, o, k, h, a, r} (d) {c, o, f, e}

3. (a) 5 1020 (b) 49 (c) (d) SuSnadtuaryday
15 25 25
1 ae
16 i ou

4. (a) 'N' is the set of first five natural numbers.

(b) 'A' is the set of four geometric instrument.

(c) 'S' is the set of first four square numbers.

(d) 'M' is the set of first five multiple of 4.

5. (a) N = {1, 2, 3, 4, 5}

(b) P = {Mercury, Venus, Earth, Mars, Jupiter}

(c) W = {Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday}

Exercise 11.3

1. (a) Null (b) Finite (c) Singleton (d) Infinite
Null (h) Singleton
(e) Infinite (f) Finite (g) Equal (d) Equal

2. (a) Equivalent (b) Equivalent (c)

244 Maths Zone - Grade 5

UNIT

12 ALGEBRA

Specific Objective Prescribed by CDC

‰‰ To write the simple word problems into algebraic expressions and simplify
them.

‰‰ T o receive the concept of the axioms of equality
‰‰ To solve one variable equations (addition, subtraction, multiplication and

division)
‰‰ T o solve the simple daily life word problems related to one variable equations

related to addition and subtraction.

Maths Zone - Grade 5 245

Lesson

1 Algebraic Expressions

Constant and Variable

There are seven days in a week. They are Sunday, Monday, Tuesday,
Wednesday, Thursday, Friday and Saturday. Let's discuss the concept of
constant and variable with this example.
If 'x' represents the name of the days in a week in this case x is variable
because x has more than are value. But, if x represents the number of days
in a week, in this case x is constant because x has fixed value i.e. single
value 7.
If a symbol or letter represents fixed (only one value) is called a constant.
E.g. total number of students in class 5 of ABC school.

If a symbol or letter represents two or more than two values, it is called
variable. E.g. students of class 5 of ABC school.

Algebraic term and Expression
Let's take few symbol and letters; x, 5, 3y, 8z, these are algebraic terms.
Term can be a combination of a constant and variable or can be constant
only.

The product of 5 and y is 5y. It is an algebraic term. This is an algebraic
expression as well. It has a single term i.e. 5y. Is 3x + 4y is also a term?
No, it is not a term it is an expression having two terms.
Algebraic terms are joined by '+' or '–' sign and from algebraic
expression. E.g. 7x, 4y + 2z, x + y – z etc.

Different types of algebraic Expressions
Monomial: It is an algebraic expression which contain only one term. E.g.
6x, 7x2, 2z etc.
Multinomial: It is an algebraic expression which contain more than one
unlike terms.

246 Maths Zone - Grade 5

Some Multinomial expressions are as follows:

Binomial: It is an algebraic expression that contains two unlike terms.
E.g. 2x + 3y, 4x + 5x2 etc.
Trinomial: It is an algebraic expression that contains three unlike terms.
E.g. 2x + 3y + 5, 4x2 + 7x + 5 etc.
Tetranomial: It is an algebraic expression that contains four unlike terms.
E.g. 4x + 3y + 7z + 5, 2x3 + 2x2 + 2x + 3 etc.

Example 1

If x = 2, y = 3, a = 4. Evaluate the expression.

a. 3xy b. 2x + 3y – a

Solution:

(a) 3xy = 3 × 2 × 3 = 18 (b) 2x + 3y – a
=2×2+3×3–4
Exercise 12.1 =4+9–4=9

1. Examine that following whether they are variable or constant.
(i) 'a' is the whole number between 0 and 10.

(ii) 'x' is the number of districts of Nepal.

(iii) y is the temperature of a day of Pokhara measured in the interval
of every 2 hours.

(iv) 'z' is the height of Sagarmatha.

(v) b is the no of province of Nepal.

2. Classify the following expressions based on the number of terms.

a. x2 + 5x b. 3x + y – 2 c. 4xyz d. 3x2 + 5x + 7

e. x f. y – 4 g. 3a + 2b + 3ab + 4
y

h. y2 + 2x + 4y – 8

3. If x = –1, y = 2, a = 3, find the value of the followings.

(i) 3xy + 2a (ii) 2a – 3x + y (iii) 4y + 2a – x

(iv) 5a + 2y + 3x (v) 4x – 2y + a (vi) xya

Maths Zone - Grade 5 247

4. Write the following mathematical sentence in Algebraic expression.
a. 5 is added to 3x
b. y is subtracted from 4
c. 5y and 9y are added together
d. Sum of p and q added to 7
e. Difference of x and y is divided by 2
f. Product of x and 5 subtracted from 25.
g. Sum of 3 times x and 2 divided by y.
h. Product of 2 and x is subtracted from product of 5 and y.

Coefficient, base and Exponent

let 'x' is a variable

Adding 'x' 3 times we get

x + x + x = 3x

Here, 3 is the coefficient of the variable 'x'

3 x 3 is numerical coefficient of x,

x is the literal coefficient of 3.

Coefficient

and, x = x1

x × x = x2 Read as x squared

x × x × x = x3 Read as x cubed

x × x × x × x = x4 Read as x to the power 4

2x4 Exponent x + x +x = 3x (While adding the
(power) coefficient is added)

x × x × x = x3 (While multiplying the
terms power is added

coefficient base 1x + 1x = 2x
248 Maths Zone - Grade 5 x1 + x1 = x1 + 1 = x2

a2 + a2 = 2a2 Twice a squared
a2 × a2 = a2 + 2 = a4 a to the power 4

Like term and Unlike term

The terms 2x, 3x, 4x, 5x have same variable x. These terms are like terms.

The terms 2x, 3y, 2xy, have different variable x, y, xy. These terms are unlike
terms. The terms 4x and 5x2 having some variable but different power so,
these are also unlike terms.

Example 1

x3, 3x3 4x3 7x3 Like terms
3xy2, 7xy2 2xy2 8xy2 Like terms
4a2b, 8a2b 7a2b 5a2b Like terms
But,
2x, 3x2 5x3 6x4 Unlike terms
2a, Unlike terms
7x2, 3ab 5abc, 7bc Unlike terms

12x2y 13 y

Addition and Subtraction of Like terms

We add or subtract only coefficient of like terms. Quick Try 1
5x2 + 7x2 = 12x2, 8y3 – 2y3 = 6y3 5x – x =
We can't add or subtract the unlike term. 5x – 2x =
3x3 – 2x2 = 3x3 – 2x2 (no change) 5x – 3x =
5x – 4x =
Example 1 5x – 5x =
5x – 6x =
Add the following : 3x2 + 2x + 5, and x2 – 4x + 2 5x – 7x =
Solution: 5x – 8x =
5x – 9x =
3x2 + 2x + 5 5x – 10x =
+ x2 – 4x + 2

4x2 – 2x + 7

Maths Zone - Grade 5 249

Example 2

Subtract 3a – 5b + 2 from 6a + b – 6.
Solution:

6a + b – 6 6a + b – 6 – (3a – 5b + 2)
–3a +– 5b +– 2 = 6a + b – 6 – 3a + 5b – 2 [Multiply by (–)]
= 6a – 3a + b + 5b – 6 – 2
3a + 6b - 8

= 3a + 6b – 8 [Arranging like terms.]

Change the sign of each terms which is to be
subtracted.

Example 3

Simplify : 9x2 + 7x – 2 + 4x2 – 3x – 4
Solution:
9x2 + 7x – 2 + 4x2 – 3x – 4
= (9x2 + 4x2) + (7x – 3x) – 2–4 [Arranging the like terms together]
= 13x2 + 4x – 6 [Adding coefficient of like terms]

Exercise 12.2

1. Identify the base, exponent and coefficient for the following

a. 2x2 b. 4y3 c. a4

d. 12 m

2. Find the product and write base, exponent and coefficient for the
following.

a. 3x × 5x b. 2y2 × 3y c. 4x2 × 2x3

d. 7x × 2x2

3. Add the following.

a. 2x + x b. 3p2 + 5p2 c. 4a + 3a
d. 3xy + 4xy e. 3p2 + 5p2 f. 4a3 + 7a3
g. 2xyz + 5xyz h. 5ab + 7ba

250 Maths Zone - Grade 5