Maths Zone book 4 2077

Conversion of percentage into fraction

Let's take few examples : c. 15 3 %
a. 11% b. 25% 4

Solution :

a. 11% = 11 Divide the given percentage by
100 100 and remove % symbol.

b. 25% = 25 1 = 1 Same as above process and reduce
100 4 the fraction into lowest term
4
c. 15 34 % = + 3 % Express the mixed number into
15 4 improper fraction and repeat the
above process.
= 15 × 4 + 3 %
4

= 643 %

= 63 × 1 = 63
4 100 400

Conversion of Percentage into decimal

Let's take few examples :

a. 12% b. 50% c. 75 %

Solutions: Divide the given % by 100
and remove % sign to convert
a. 12% = 12 = 0.12 into decimal
100
The decimal point is shifted 2
b. 50% = 50 = 0.50 places to the left.
100

c. 75% = 75 = 0.75
100

Maths Zone – Grade 4 201

Conversion of decimal number into percentage

Let's take few examples : b. 0.07% c. 0.35 %
a. 0.15%
Solutions:

a. 0.15 = (0.15 × 100)% = 15% Multiply the decimal by

b. 0.07 = (0.07 × 100) % = 7% 100% = 100
100

c. 0.35 = (0.35 × 100)% = 35% The decimal point is shifted
2 places to the right.

Percent of Given Number

To find the percent of a given numbers, we have to multiply the given
percent and the number.

Example - 1

Find 15 % of 200
Solution:

15% of 200

= 15% × 200 [ Remove 'of' by '×' sign]

= 15 × 200 [Convert percent into fraction]
100
= 15 × 2

= 30

Example - 2

There are 40 students in a class. If 40% of the students
are girls, find the number of girls and boys of the class.

Solution:
Number of girls in the class

= 40 % of 40

202 Maths Zone – Grade 4

= 40 × 40
100
= 40 × 4

= 16
∴ The number of girls = 16.
And, the number of boys = Total students - Number of girls
= 40 – 16

= 24

Example - 3

Find the percentage of 12 out of 20.

Solution:

12 [First convert into Fraction]
20

= 12 × 5 [Convert into Percentage]
20
100 %

= 12 × 5%

= 60%

Exercise 7.12

1. Express the following fractions as percentage.

a. 7 = b. 15 = c. 45 =
100 100 100

d. 77 = e. 82 = f. 99 =
100 100 100
2. Express the following percentage as fractions and
Decimals.

a. 5% = = b. 18%= =

c. 32% = = d. 55% = =

e. 83% = = f. 97% = =

Maths Zone – Grade 4 203

3. Express the following decimals as percentage.

a. 0.35 = b. 0.06 = c. 0.72 =

d. 0.09 = e. 0.54 = f. 0.87 =

4. Express the following fraction into percentage.

a. 510 b. 3 c. 270 d. 34 e. 1
25 5
7210
f. 190 g. 12 h. 16 i. 37 j.

5. Express the following percentage into fraction.

a. 25% b. 20% c. 50% d. 75% e. 80%
c. 25% of 150
f. 423% g. 581 % h. 16 23%
6. Find the value of the following.

a. 10% of 50 b. 20% of 120

d. 5% of 40 e. 50 % of 100 f. 35% of 200

7. What percent is the following?

a. 10 out of 20 b. 15 out of 50 c. 20 out of 100

d. 40 out of 80 e. 5 out of 10 f. 6 out of 25

8. a. There are 50 students in a class. If there are 20 girls express
girls number in the fraction and find the percentage of girls
in the class.

b. In an examination of 25 full marks Aditi obtained 22 marks.
What percentage of marks did Aditi obtain?

204 Maths Zone – Grade 4

Maths Fun

Instruction to the Teacher
‰‰ A mong the students in a class invite 2 girls and 2 boys in front

and provide dice to each of them.
‰‰ D ivide the remaining students in two groups.
‰‰ P ut the number of the top face of 1st dice as numerator and number

of top face of 2nd dice as denominator.
‰‰ P lay the game under the following conditions and provide 10

points for each condition.
‰‰ Team getting highest points will be the winner.

Conditions

For being first in each condition.
1. Team obtaining proper fraction (If two teams have same fraction,

then replay for the same condition).
2. Team obtaining improper fraction.
3. Team obtaining greater fraction.
4. Team obtaining smaller fraction.
5. Team having the fraction which can be converted into lowest

term.
Maths Zone – Grade 4 205

Practice Zone

Group 'A'

Circle the correct option of the following questions.

1. The fraction of Numerator 4 and denominator 7 is
a. 47 b. 47 c. 77 d. 44

2. What fraction of Jar is empty? 10
6
a. 160 b. 140 c. 1100 d. 110
0

3. Which of the following is not equivalent fraction of 4 ?
6
a. 182 b. 1128 c. 32 d. 1360

4. Which of the following pairs of fractions are not equivalent?

a. 12 and 36 b. 4 and 23 c. 150 and 63 d. 3 and 4
6 8 7

5. The lowest term of 2400 is
3200

a. 3242 b. 32240000 c. 3 d. 8
4 8
2
6. 5 7 is ............ fraction.

a. Proper b. Improper c. Mixed d. Like

7. Which of the following is correct form of Mixed fraction if Divisor

= 5, Remainder = 3 and quotient = 4?

a. 4 5 b. 4 3 c. 5 3 d. 3 4
3 5 4 5
2 1 4
8. What is the sum of the fractions 7 + 7 + 7 in simplest form?

206 Maths Zone – Grade 4

a. 77 b. 1 c. 7 d. 1
21 3
9. The improper fraction of the mixed number 374 is
a. 275 12 19 7
b. 7 c. 7 d. 7

10. What is the difference of the fraction 5 - 3 in simplest form?
8 8
a. 28 1 2 8
b. 4 c. 0 d. 16

Group 'B'

1. Find the first five equivalent fractions of the given fractions.

a. 23 b. 83 c. 45

2. Arrange the given fractions into ascending order.

a. 85, 48, 38 b. 141, 161, 2
11

3. Express the following fractions into mixed number.

a. 275 b. 341 c. 460

4. Convert the given mixed number (fraction) into improper

fraction.

a. 3 56 b. 4 71 c. 4 3
5

5. Simplify

a. 87 + -855 46 be.. 447 - 73+ 3 34 fc.. 443 1 - 1 255+ 3 3
d. 7 5 1 5 2 + 12 5
3 2 3
-

6. Solve the following problems.

a. Gokarna's school is 2 1 km from his house. He cycles this distance
2

daily. One day, his cycle tyre got punctured after he had gone

1 1 km. What was the distance he had to walk?
4

Maths Zone – Grade 4 207

b. Rajendra bought 1 1 m cloth from one shop and 2 3 m cloth from
5 5

another. What length of cloth did he buy in all?

Practice Zone

Group 'A'

Circle the correct option of the following questions.

1. Find the possible value of 'A' in decimal form from the given

number line . A

1 2 3

a. 1.22 b. 0.2 c. 2.2 d. 2.02

2. 3.54 is written in decimal system as

a. Three point fifty four b. Three hundred fifty four

c. Point five four d. Three point five four

3. Which of the following number is in Hundredths place in 432.756

a. 4 b. 5 c. 2 d. 6

4. What is the short form of 50 + 7 + 3 ?
100

a. 57.3 b. 57.03 c. 573 d. 5.73

5. The decimal form of the fraction 3 is
4

a. 3.4 b. 4.3 c. 0.75 d. 0.25

6. 525 paisa in rupees and paisa equal to

a. Rs. 5.25 b. Rs. 525 c. Rs. 5 and 25 paisa

d. 525 paisa

208 Maths Zone – Grade 4

7. How many hundredths are there in 1 tenth?

a. 1 b. 10 c. 100 d. 1000

8. Find the greatest decimal number among 0.1, 0.01, 0.001, 0.001.

a. 0.1 b. 0.01 c. 0.001 d. 0.0001

9. What is the sum of 0.35 and 3.5.

a. 35.35 b. 3.355 c. 3.85 d. 0.70

10. 1 ml equal to ................. c. both a and b
a. 10100 l b. 0.001 l

d. None of these

Group 'B'

1. Arrange the given decimal in descending order

a. 0.37 b. 3.7 c. 0.037 d. 37.0

2. Write the decimal in expanded form

134.273

3. Simplify:

a. 6.83 + 5.29 - 8.73 b. 0.75 - 0.05 + 25.7

4. How much is Rs. 827.48 less than Rs. 1000?

5. What should be added to 372.83 to get 585.96?

Maths Zone – Grade 4 209

Practice Zone

Group A

Circle the correct option of the following questions.

1. What is the value of 1 as percentage?
10

a. 1% b. 10% c. 100% d. 1000%

2. 0.37 in percentage is ..........

a. 37% b. 3.7% c. 0.37% d. 37.37%

3. What percentage is 4
100

a. 4% b. 40% c. 0.4% d. 0.04%

4. What percent is 20 out of 50?

a. 20% b. 50% c. 40% d. 100%

Group B

5. There are 100 mangoes in a basket. Out of them, 30 are rotten.
What percentage of mangoes are rotten?

6. What percentage is 50 paisa of a rupee?

7. What percentage is 400 grams of a kilogram?

210 Maths Zone – Grade 4

Answers of Unit 7

Exercise 7.1

1. (a) 2 (b) 4 (c) 9 (d) 4
4 8 18 12

2. (a) 1 : 2, 3, 4 (b) 3 : 6, 9 , 12
3 6 9 12 4 8 12 16

(c) 4 : 8 , 12, 16 (d) 2 : 4 , 6 , 8
5 10 15 20 5 10 15 20

3. Show to your teacher.

4. (a) 4 (b) 3 (c) 3 (d) 5

5. (a) 4 (b) 15 (c) 9 (d) 12 (e) 15 (f) 3

6. (a) 2 , 3, 4, 5 (b) 4 , 6, 8 , 10 (c) 8 , 12, 16, 20
4 6 8 10 6 9 12 15 10 15 20 25

(d) 10, 15, 20, 25 (e) 2 , 3 , 4 , 5
12 18 24 30 14 21 28 35

Exercise 7.2

1. (a) Yes (b) No (c) Yes (d) Yes (e) No (f) Yes

2. (a) 2 (b) 2 (c) 4 (d) 3 (e) 2 (f) 2
335 43 3

3. (a) 3 (b) 2 (c) 3 (d) 5 (e) 3 (f) 1
534 65 4
Exercise 7.3

1 to 3 show to your teacher.

4. A = 1 2 or 6 B = 2 3 or 11
4 4 4 4

5. Show to your teacher.

6. (a) 3 13 (b) 2 12 (c) 2 3 or 2 1 (d) 241 (e) 327 (f) 189
7. (a) 25 6 2

(b) 130 (c) 251 (d) 579 (e) 482 (f) 595

Maths Zone – Grade 4 211

Answer 7.4

1 . Show to your teacher.

2. Show to your teacher.

3. (a) 182 and 132 (b) 165 and 155 (c) 1105 and 195 (d) 192 and 10
12

(e) 24 and 21 (f) 3 and 4 (g) 24 and 25 (h) 9 and 4
42 42 66 30 30 18 18

4. (a) 142 and 192 (b) 1202 and 1200 (c) 182 and 192 (d) 5268 and 40
56
1 43 ∴ 35 42 4 43 4 5
∴ 3 < > ∴ 6 < ∴ 8 < 7

5. (a) 43 (b) 79 (c) 63 (d) 56

6. (a) 1, 2, 3 (b) 3, 6, 8 (c) 1, 3, 4 (d) 2, 4, 5
555 999 777 666

7. (a) 36, 35, 34 (b) 171, 79, 87 (c) 17, 15, 41 (d) 28, 25, 32

Answer 7.5

1. (a) 4 (b) 5 (c) 7 (d) 7
5 7 10 12
2. (a) 1 (b) 3 (c) 4 (d) 2
16 10 15 17
3. (a) 1121 (b) 2201 (c) 3450 7 (d) 3576
3 8
10 (b) 1214 (c) 790 (d) 650 112
4. (a) 260
4 4 5 5
5. (a) 7 5 (b) 6 5 (c) 10 7 (d) 8 9

6. (a) 217 (b) 1 1 (c) 3 2 (d) 4 3
5 9 8
7. (a) 1121 (b) 197 (c) 1179
8. (a) 95 (b) 190 (c) 112 (d) 175 (e) 2 29 (f) 111
9. (a) 57 1
(b) 2 8

212 Maths Zone – Grade 4

Answer 7.6

1. (a) 13 5 (b) 84 (c) 1311 (d) 75
65 18 6
1 1
2. (a) 2 3 (b) 13 (c) 8 6 (d) 5 36
10 4

Answers 7.7

1. (a) 0.2 (b) 0.09 (c) 4.5 (d) 0.63
(e) 23.5 (f) 0.037 (g) 15.9 (h) 17.23
(i) 11.025 (j) 0.347

2. (a) 5 (b) 7 (c) 35 (d) 74
10 100 10 100

(e) 485 (f) 83 (g) 173 or 17 3
10 1000 10 10

(h) 2436 or 24 36 (i) 25032 or 25 32
100 100 1000 1000

3. (a) Tenths, 7 (b) Hundredths, 2
10 100

(c) Thousandths, 8 (d) Hundredths, 3
1000 100

4. (a) Ones Tenths (b) Tens Ones Tenths Hundredths
27 4 23 5

(c) Hundreds Tens Ones Tenths Hundredths
3 7 5 2 1

(d) Hundred Tens Ones Tenths Hundredths Thousands
6
8 17 2 4

5. (a) 4 + 160 (b) 50 + 7 + 4 + 2
10 100

(c) 300 + 10 + 5 + 180+ 1020

(d) 400 + 10 + 7 + 9 + 2 + 10600
10 100

6. (a) 4.7 (b) 25.62 (c) 387.32 (d) 534.167

Maths Zone – Grade 4 213

7. (a) 1.5 < 2.5 (b) 3.6 > 3.4 (c) 5.42 < 5.47

(d) 0.01 < 0.1 (e) 0.45 < 0.54 (f) 78.315> 78.137

Answers 7.8

(a) 1 (b) 1 (c) 3 (d) 11 (e) 7
10 2 5 50 20
52 (h) 141 (i) 443 (j) 1
(f) 41 (g) 6 6 8
2

Answers Exercise 7.9

1. (a) 0.3 (b) 0.6 (c) 0.5 (d) 3.4 (e) 4.5
(f) 0.45 (g) 0.44 (h) 0.46 (i) 2.75 (j) 0.375

Answers 7.10

1. (a) 1.2 (b) 8.5 (c) 1.01 (d) 7.157 (e) 28.67
(f) 0.01 (g) 1.038 (h) 19.727 (i) 38.005 (e) 74.5
2. (a) 1.2 (b) 1.47 (c) 9.598 (d) 25.37
3. (a) 0.3 (b) 0.7 (c) 0.25 (d) 4.28
(f) 10.199
4. (a) 0.6 (b) 0.37 (c) 0.89 (d) 5.191
5. (a) 1.246 (b) 1.242 (c) 4.666 (d) 7.29
6. (a) 10.4cm (b) 19.4cm (c) 19.2cm (d) 28.2cm

Answers 7.11

1. (a) Rs. 0.05 (b) Rs. 0.25 (c) Rs. 0.75 (d) Rs. 2.40

(e) Rs. 7.80 (f) Rs. 20.50

2. (a) 7 paisa (b) 40 paisa (c) 75 paisa (d) Rs. 5 and 25 paisa

(e) Rs. 15 and 75 paisa (f) Rs. 17 and 5 paisa

3. (a) 0.06m (b) 0.15m (c) 0.80m (d) 3.55m

(e) 25.05m (f) 50.20m

4. (a) 5cm (b) 50cm (c) 85cm (d) 7m 35cm

(e) 15m 60cm (f) 18m 7cm

5. (a) 0.008km (b) 0.022km (c) 0.090km (d) 5.065km

(e) 35.009km (f) 65.370km

214 Maths Zone – Grade 4

6. (a) 7m (b) 25m (c) 375m (d) 4km 265m

(e) 27km 37m (f) 44km 8m

7. (a) 0.009kg (b) 0.027kg (c) 0.080kg (d) 3.045kg

(e) 47.008kg (f) 75kg 385g

8. (a) 4g (b) 37g (c) 428g (d) 5 g 437g

(e) 37kg 35g (f) 42kg 7g

9. (a) 0.005l (b) 0.023l (c) 0.060l (d) 4.035l

(e) 32.003l (f) 54.475ml

10. (a) 3ml (b) 54ml (c) 675ml (d) 7l 752ml

(e) 42l 38ml (f) 55l 2ml

Answer 7.12

1 to 3 show to your teacher.

4. (a) 2% (b) 12% (c) 35% (d) 75% (e) 20%

(f) 90% (g) 50% (h) 50 % or 16 2 % (i) 42 67% or 300 %
(j) 1225 or 62.5 % 3 3 7

5. (a) 14 (b) 51 (c) 12 (d) 43 (e) 45
(f) 1750 (g) 84010 (h) 61
75 12 (d)
6. (a) 20 (b) 24 (c) 2 or 37 2

(e) 50 (f) 70

7. (a) 50% (b) 30% (c) 20 (d) 50% (e) 50% (f) 24%

8. (a) 5200, 40% (b) 88%

Maths Zone – Grade 4 215

8 Unitary Method

Specific Objective Prescribed by CDC

 To solve the dailly life simple problems using unitary method.
216 Maths Zone – Grade 4

Unitary Method

Class Discussion

The unitary method is a technique which is used for solving a problem
by finding the value of a single unit i.e. 1 (by division) and then finding
the necessary value by multiplication the single unit value.

Finding the value of more items.
Look at this example and complete the table.

Items No. of items Price per items (Rs.) Total cost (Rs.)

Note Book 2 25 25 × 2 = 50
Pen 4 15 ..... × ..... =......
Geometry Box 5 75 ..... × ..... =......

Example 1

The cost of a pencil is Rs. 5. What will be the cost of such 10 pencils.

Solution: Multiply the
1 pencil = Rs. 5 number of items
10 pencils = Rs. 5 × 10 = Rs. 50 by its unit cost.
Finding the value of one item

Look at this example and complete the table.

Items Total Price (Rs.) No. of items Price per items (Rs.)

Oranges Rs. 48 6 48 ÷ 6 = 8

Chocolates Rs. 50 5 ..... ÷ ..... =

Ice cream Rs. 80 2 ..... ÷ ..... =

Maths Zone – Grade 4 217

Example 2

The cost of 4 kg potato is Rs. 140. What will be the cost of 1 kg potato?

Solution: Divide the total price
4 kg potato = Rs. 140 by number of items to
find the unit price.
1 kg potato = Rs. 140 ÷ 4 140
4

= Rs. 35

Example 3

If the cost of 10 kg apple is Rs. 800, find the cost of 15 kg of apple.

Solution:

10 kg apple = Rs. 800 Divide to find
unit price.
1 kg apple = Rs. 800 ÷ 10
Multiply to find
= Rs. 80 more that unit.

15 kg apple = 15 × Rs. 80

= Rs. 1200

Exercise 8.1

1. a. Cost of a pen = Rs. 15 Rs. 15
Cost of 5 pens = ...................

= ...................

b. Cost of 1 balloon = Rs. 5

Cost of 10 balloons = ................ Rs. 5
= ................

2. a. Cost of 8 chocolates = Rs. 40 Rs. 40
Cost of 1 chocolates = ................

= ................

218 Maths Zone – Grade 4

b. Cost of 6 erasers = Rs. 35 Rs. 35
Cost of 1 eraser = ...............

= ..............

3. a. If the cost of one Geometry box is Rs. 40, what is the cost of

such 6 Geometry boxes?

b. The price of 1 kg apples is Rs. 85, what is the price of 15 kg

of apples?

4. a. There are 30 days in a months. How many days are there in

17 months?

b. There are 365 days in a year. How many days are there in 9

years?

5. a. The cost of a copy is Rs. 85. Find the cost of one dozen copy.

b. A car can travel 20 km with 1 liter petrol. How many

kilometers does it travel with 15 liters of petrol?

6. a. The cost of 15 kg of sugar is Rs. 375. What is the cost of 1 kg

of Sugar?

b. The price of 5 t-shirts is Rs. 2250. Find the price of 1 t-shirt.

7. a. Sapana bought 15 books for Rs. 1800. What is the cost of 1

book?

b. Kamal earns is 45,000 in a month. How much does he earn

in a day?

8. a. If the total weight of 15 bags is 225 kg. Find the weight of 1

such bag.

b. A bus runs 520 km in 13 hours. How many kilometers does

it run in 1 hour?

9. a. If the cost of 5 pens is Rs. 75, find the cost of such 9 pens.

b. If the length of 12 ropes is 84 m, find the total length of 8

such ropes.

10. a. There are 480 chocolates in 8 packets. How many chocolates

are there in 14 packets?

b. A bus travels 200 km in 5 hours with a uniform speed. How

far does it travel in 4 hours?

Maths Zone – Grade 4 219

Maths Fun

Find out the highest possible number by moving only 2 match sticks
(a)

(b)

220 Maths Zone – Grade 4

Practice Zone

Group A

Circle the correct option of the following questions.

1. The technique which is used to find the value of unit item is
called .....

a. Fraction b. Unitary method

c. Ratio and Proportion

2. How many number of items are there in one dozen?

a. 7 b. 10 c. 12

3. How many ice-cream can be bought for Rs. 120

according to the given figure? Rs. 40/–

a. 3 b. 4 c. 5

4. How many 20 rupees can exchange from Rs.
100?

a. 4 b. 5 c. 6

Group B

8. The cost of 10 marbles is Rs. 80. What is the cost of a marble?
9. The cost of one dozen copy is Rs. 960. Find the cost of a copy.
10. The cost of 8 erasers is Rs. 120. Find the cost of 12 erasers.

Maths Zone – Grade 4 221

Answers of Unit 8

Exercise 8.1

1 & 2 show to your teacher.

3. (a) Rs. 240 (b) Rs. 1275

4. (a) 510 days (b) 3285 days

5. (a) Rs. 1020 (b) 300 km

6. (a) Rs. 25 (b) Rs. 450

7. (a) Rs. 120 (b) Rs. 1500

8. (a) 15 kg (b) 40 km

9. (a) Rs. 135 (b) 56 m

10. (a) 840 chocolates (b) 160 km

222 Maths Zone – Grade 4

9 Bill and Budget

Bill No : Aakriti Pcookheafrfaee shop
Pan No:
CS1o..Nst.umePras'rNticaumlaer:
Qty Date: ..........................
RaAted(dRrse)ss: .A...m....o..u...n..t...(.R...s..).....
In word : Total

Signature

Specific Objective Prescribed by CDC

 To tell, receive and write the information clearly by looking the simple bills (not
including discount, VAT, tax, etc).

Maths Zone – Grade 4 223

Bill and Budget

Reading Bill

Let see the bill. It is a details of goods and services bought and the total money
which is to be paid for it for the customer and trade records for traders.

Sagun Stationary Date : 2074-02-5
Address : Panauti, Kavre
Pokhara, Kaski
Bill No: 30118
Pan No :
Costumers' Name : Paru poudel

S.N. Particular Quantity Rate(Rs) Amounts (Rs)
1 Copies 3 120/-
2 Pen 5 40 100/-
3 Color 2 20 30/-
15 250/-
Total
Signature
In words: Two hundred fifty only.

A bill has the following details. Be careful !!
Read the bill and give the answer.
Amount = Qty × Rate

a. Name and address of shop ...........................................

b. Name and address of customer ......................................

c. Bill Number ............................................

d. Bill Date ...........................................

e. Name of items and quantities ............, ............, ............

f. Total money to be paid Rs ................

224 Maths Zone – Grade 4

Exercise 9.1

Jharana Agro farm Date: 2073-08-25

Pokhara - 27, Kaski

Bill No : 345

Pan No: 2 0 0 1 3 5 2 0 1

Costumers' Name : Sanumaiya Joshi Address: Kathmandu

S.N. Particular Qty Rate (Rs) Amount (Rs)
1. Chicken 3 kg 350 1050
1600
2. Egg 4 sheet 400 200
160
3. Potato 5 kg 40
3010
4. Tomato 2 kg 80

Total

In word : Three thousand and ten only

Signature

Goods once sold will not be taken back.

Read the bill and answer the following questions.
a. What is the cost of 1 sheet egg?
b. What is the total amount of bill?
c. When was the item bought?
d. Write the name and address of shop?
e. If Sanumaiya gives Rs 3500 to the shopkeeper, how
much money does she get return back?
f. What is the total cost of chicken?
g. If shopkeeper gives Rs 10 discount on the total bill.
How much should Sanumaiya pay?

Maths Zone – Grade 4 225

Making the Bill Aakriti coffee shop

Menu of the coffee shop is given below. Pokhara

Prepare bills for following. Hot drinks
1. Milk tea - Rs 20
‰‰ Ram and his family took following: 2. Black tea - Rs 15
milk tea - 3 cup, momo - 2 plates, sauses 3. Coffee (milk) - Rs 50
- 5 stick and finger chip - 1 plate. Prepare 4. Hot lemon - Rs 30
bills for Ram. Cold Drinks
1. Coke/fanta - Rs 40
‰‰ Bishnu and his family took following:
coffee - 2 cup, hot lemon - 1 cup, chowmin Snacks (chicken)
- 3 plates, sauses - 2 zstick, burger - 2
pieces. Prepare bill for Bishnu. 1. momo - Rs 120

2. Chawmin - Rs 100

3. C. momo -Rs 50

4. Sauses - Rs 40/stk

Lunch

1. Rice - Rs 150/plate

2. Sandwitch - Rs 80

3. Burger - Rs 50

Other

1. Finger chip - Rs 30

2. Omlate - Rs 20

3. Butter Toast - Rs 25

‰‰ Sarmila & her family took following: Rice

- 3 plate, Omlate - 3, fingerchip - 4 plate, sandwitch - 2 pices,

coffee - 2 cup. Prepare bill for Sarmila.

Sample Bill

Aakriti coeffee shop

Pokhara
Bill No : Date: ..........................

Pan No:

Costumers' Name : Address: .............................
Qty Rate (Rs) Amount (Rs)
S.N. Particular
1.

Total Signature

In word :

226 Maths Zone – Grade 4

Exercise 9.2

Public Super store's, Bhaktapur display the following
items with price. Prepare the bills for the following
shopping.

Rs. 500 Rs. 450 Rs. 1500 Rs. 900 Rs. 800 Rs. 750 Rs. 320 Rs. 670

Rs. 2000 Rs. 1250 Rs. 1175 Rs. 350 Rs. 870 Rs. 3500 Rs. 770 Rs. 960

a. Aagaman's Shopping b. Hari's Shopping

c. Shanta's Shopping d. Sita's Shopping

Maths Zone – Grade 4 227

10 Statistics

Specific Objective Prescribed by CDC

 To receive and give the information comparatively by counting the units in the given
bar graph.

 To receive and give the information by reading the scale of the data.
 To compare the place or objects given in a map ( far, near, etc).

228 Maths Zone – Grade 4

Temperature

Class Discussion
Temperature is measured using a thermometer. It can be measured in
degree celsius (°C). Normal human body temperature is 37° C.

0° C = Water freezes Boiling point of water

37° C = normal human Normal Human body
body temperature temperature

100° C = Water boils Freezing point of water

Types of thermometer.

Fahrenheit Scale

Temperature can be measured in degree fahrenheit (0° F).
The Fahrenheit scale is marked from 32° F to 212° F. 212° F is
boiling point of water and 32° F is Freezing point of water.
Let's compare °C with °F (degree Celsius with degree Fahrenheit).

0° C Freezing point of 32° f
water

Maths Zone – Grade 4 229

37° C Human Normal 98.6° f
body Temperature

100° C Boiling point of 212° f
water

I am healthy. My
body temperature

is 98.6° F.

If temperature is increased from
98.6°F and decrease from it, human
may become ill.

Exercise 10.1

1. Mark the following point on the following thermometer.

Water boiling point Water freezing Normal body
temperature

230 Maths Zone – Grade 4

2. Find the temperatures shown by following thermometers.

a. –10 0 10 20 30 40 50 60 70 80 90 100 110°C

b. –10 0 10 20 30 40 50 60 70 80 90 100 110°C

c. –10 0 10 20 30 40 50 60 70 80 90 100 110°C

d. –10 0 10 20 30 40 50 60 70 80 90 100 110°C

e. –10 0 10 20 30 40 50 60 70 80 90 100 110°C

3. Weather forecast 6th December 2017.

Maximum Minimum

Dhangadi 22° C 7° C

Nepalgung 23° C 8° C

Dang 20° C 6° C

Bharatpur 19° C 5° C

Pokhara 18° C 6° C

Kathmandu 16° C 3° C

Itahari 21° C 9° C

Dharan 22° C 6° C

a. Which place has the highest maximum temperature?

b. Which place has the highest minimum temperature?

c. Which place has the cowest maximum temperature?

d. Which place has the lowest minimum temperature?

e. Which place is the hotest?

f. Which place is the coldest?

Maths Zone – Grade 4 231

Tabulation of data

Class Discussion

The weight (in kg) of the 20 student of class IV are given below.

33, 28, 28, 28, 34, 33, 26, 26, 30, 28,
32, 33, 33, 28, 30, 34, 33, 27, 27, 27.
Can you give the answer of the following questions quickly?

a. What is the maximum weight of student?
b. How many students are of 28 kg weight?
c. How many students are of 32 kg weight?
We can't give the answer of above questions immediately & easily.

Let's arrange the data in ascending order.
26, 26, 27, 27, 27, 28, 28, 28, 28, 28,
30, 30, 32, 33, 33, 33, 33, 33, 34, 34.

Now, we can answer the questions easily.

Q. What is the maximum and minimum weight?
Again lets plot the data in tabular form.

Weight (kg) No of students
26 2
27 3
28 5
30 2
32 1
33 5
34 2

Now, we can answer the questions easily.

Maximum weight = 34
No. of student 28 kg weight = 5
No of student with 32 kg = 1
Total number of student = 20
Maximum no. of students having same weight = 5 (weight 28 and 33)
It is the tabulation of data which helps to read the data easily.

232 Maths Zone – Grade 4

Example 1

Tabulate the following data. 'x' is used to denote
data and 'f' is used
5,7, 9, 11, 5, 11, 11, 7, 5, 5, 5, 7, 7, 9, 11 to denote no. of
repetition.
Solution: Here,

Data (x) No. of Repetition (f)
5 5
7 4
9 2
11 4

Frequency is number of repetition. It is denoted by f.

Example 2

In sagun's farm house, there are 12 goats ,15 cows, 70 chickens, 9 pigs

and 18 buffaloes. Write this information in table.

Solution:

Animal Number
Goat 12
Cow 15
70
Chicken 9
Pig 18
124
Buffaloes
Total

Exercise 10.2

1. Marks of mathematics of different classes are given below.
Now, tabulate them.
a. Class (iii)  35, 37, 39, 40, 35, 35, 37, 39, 39, 39,
39, 40, 40, 40, 40

Maths Zone – Grade 4 233

b. Class (iv)  42, 43, 46, 47, 49, 42, 42, 43, 43, 43, 43
46, 46, 47, 47, 47, 47, 49, 49, 49

c. Class (v)  41, 42, 43, 44, 45, 42, 43, 43, 43 44, 44,
44, 45, 45, 41, 41, 42

2. In a survey of the students of class 4 in a school, it is
found that 34 students like Maths, 38 like Nepali, 40 like
Science and 10 like English. Tabulate this information in
table.

3. The animal with a farmer is shown in the following table.
Look at the table and answer the following.

SN. Animals Number

1 Goat 20

2. Cow 15

3. Buffaloes 10

4. Hen 75

Total 120

a. How many goats are there?

b. How many cows are there?

c. How may animals does the farmer have?

234 Maths Zone – Grade 4

Bar Graph

The given bar graph represents a school survey of the students about
their interest on the different games.

The name of games are written on y
the Horizontal line (X-axis).
50
Number of students who like the
games are written on the vertical No. of Students 40
line (Y-axis).
30
Find the height of each bar.
20
The bar which represents
volleyball reaches upto 30. 10

This shows 30 students like 0 Volleyball Cricket Kabadi Football x
volleyball.
Games

Similarly, 40 students like cricket.

a. How may students like football?

b. How many students like Kabadi?

Exercise 10.3 Y

1. The graph shows the survey No. of Students 60
50
of students who prefer 40 X
30
different cold drinks. Use 20
10
graph and answer the
0 Coca Fanta Sprite Dew
following.
a. How many students said Cold Drinks

that fanta is their favorite
drinks?

b. Which cold drinks is choosen the most?

c. Which drinks was chosen by 10 students?

Maths Zone – Grade 4 235

2. The graph shows Diyanka's score in mathematics test.
Use graph and answer the following.

a. In which test did No. of Students Y
Diyanka score least 70
mark?

b. What is Diyanka's score 60
in test 1? 50
40

c. Which is the best test 30
for Diyanka? 20

d. What is the score 10 1 23 4X
difference between 4th 0
Test
test and 2nd test?

3. In the survey of the school, it is found that 10 students
use car, 30 students use school bus, 40 students use cycle
to come to school and 70 students come on foot. Draw a
bar graph to represent this information. (Complete the
following graph)

Y

40

No. of Students 30

20

10

0 School Cycle X
Car bus
Foot

Means of Transportation

236 Maths Zone – Grade 4

Coordinate

Class Discussion 6
Let's observe the figure along side. 5

Numbers are written on vertical and 4

horizontal lines. 3

We walk first on horizontal line and

we climb on vertical line to get the 2

fruits. 1

You want apple. How can you get it?

Start to walk from zero, reach upto 0123456

'2', then climb 2 you get it.

ie. 2 unit walk and 2 unit climb.
We write (2, 2) for the location of apple.

How can we find orange?

Walk 4 units and climb 2, units ie. (4, 2) for orange.

These (2, 2), (4, 2) are called ordered pair or co-ordinates.

Example

Find the position of fruits using ordered pair as above.

a. Orange ( , ) b. Apple ( , ) c. Banana ( , )

c. Litchi ( , ) d. Mango ( , )

Rectangular axis y

‰‰ The horizontal line is called x-axis. x' x
‰‰ The red line xox' is x-axis. O

‰‰ The vertical line is called y-axis yoy' is y'
y-axis.

‰‰ Meeting point of these two lines is called origin which is also
called starting point.

Maths Zone – Grade 4 237

A, B, C, D, E, F, G, H, I, J, K, L are the 14
different points on the graph. 13
12
What is the co-ordinate of A? 11
10
It's easy to find. First start from '0' walk 2
on horizontal line (on x-axis) and climb '3' 9
on vertical line (y-axis) i.e. (2, 3) 8
7
2  x-coordinate

3  y-coordinate

Similarly the location of points B is (3, 2). 6

5

Exercise 10.4 4
3

1. Find the coordinates of the other 2

points. 1

a. C b. D c. E 0123456

d. F e. G f. H

g. I h. J i. K j. L

2. Plot the following points on the graph.
a. (1, 3) b. (2, 2) c. (3, 0) d. (3, 5) e. (6, 3)

f. (2, 3) g. (4, 5) h. (2, 6) i. (7, 3) j. (3, 3)

k. (2, 9) l. (3, 3) m. (3, 7) n. (5, 1) o. (3, 7)

3. Plot the following points on graph & join them.
a. A(1, 3), B(7, 3), C(7,6) and D(1, 6)

b. P(1, 1), Q(7, 1), R(7, 7) and S(1, 7)

238 Maths Zone – Grade 4

4. Use the graph given below and write the coordinates at
them. A, B, C, D, E, F, G, H.
Y

I H
B G

A F
E
D
C

X

Maths Zone – Grade 4 239

Maths Fun

‰‰ How to find squares of numbers below 100.
‰‰ You have to memorize squares from 1 to 30.
Trick - 1

For 31 to 50

‰‰ Lets say 412
‰‰ (50 – 9)
‰‰ (–9)2 = 81, will be the last 2 digits
‰‰ First 2 digits will be 25-9 = 16, 25 is a standard number which can

be used for all calculations.
‰‰ Hence 1681.

Concept of Carry over

‰‰ Lets say 36

‰‰ (50 – 14)

‰‰ What will be the first two digits?

‰‰ (–14)2 = 96,

‰‰ Note : 1 will be taken as carry over for first 2 digits.

‰‰ What will be the first 2 digits. For more than
50, find the trick
‰‰ 25 – 14 + 1 = 12,

‰‰ Hence 1296 yourself.

240 Maths Zone – Grade 4

Practice Zone

Group 'A'

1. Water freezes at ................. degree Celsius.

2. Normal body temperature is ............. degree Fahrenheit.

3. Water boils at

a. 100° C b. 0° C c. 32° F

4. Human body temperature 98.6° F is equal to

a. 45° C b. 37° C c. 39° C

5. Starting from origin 3 unit running & 2 unit climbing gives the
coordinate

a. (3, 2) b. (2, 3) c. (5, 0)

6. Sum of the term 4x, 3x, 2y is

a. x + 2y b. 9xy c. 7x + 2y

7. Which are the next 2 term of pattern 5, 10, 15, 20 .......?

a. 21, 22 b. 30, 40 c. 25, 30

Group 'B'

1. Plot the following points on graph.

a. (2, 5) b. (7, 3) c. (8, 1)

d. (3, 0)

2. Arrange the following data in tabular form.

2, 3 , 2, 5, 7, 7, 5, 7, 7, 7, 5, 5, 5, 5, 2, 3, 2, 3, 9, 8, 9

Maths Zone – Grade 4 241

3. Look at the bar graph, which No. of Students Y
shows the students' likes subjects.
35
i. Which subject is more popular? 30
25
ii. Which subject is liked by less 20
people?

iii. Find the number of people who 15 X
like maths & science. 10 X
5
4. From the given bar graph answer
the following questions. Math Eng. Sci. Nep.

i. Total no. of students on class 6 Subjects
are .............
No. of Students Y
ii. In a survey of the students of 60
class 4 in a school, in which
class there are maximum no. of 50
students? 40

iii. Total no. of students from class 30
6 to 9 are........ 20
10
iv. By how many number of
students of class 8 are m o r e 6 78 9
than number of students of
class 7............................ Classes

5. Daily wages of the people are given below.

Wages 200 400 700 500 1000
Name Saugat Samrat Tina Bina Sagun

Prepare a bar graph using the information.

242 Maths Zone – Grade 4

6. Find the coordinate of P, Q, R, S from the following graph


YY Y
P

Q P Q R
P S R
S
O R XO R S X

XO

7. Ananda Super store's, Syangja display the following items
with price. Prepare the bills for the following shopping.

Rs. 600 Rs. 550 Rs. 1400 Rs. 800 Rs. 900 Rs. 950 Rs. 420 Rs. 570

Rs. 3000 Rs. 1850 Rs. 2575 Rs. 150 Rs. 570 Rs. 3800 Rs. 370 Rs. 860

a. Sharmila's Shopping b. Sabina's Shopping

Maths Zone – Grade 4 243

Answers of Unit 10

Exercise 10.2

1. a. Marks Students b. Marks Students c. Marks Students

35 3 42 3 41 3
5 42 3
37 2 43 3 43 4
5 44 4
39 5 46 20 Total 17

40 5 47

Total 15 Total

2. Subject Students

Math 34

Nepali 38

Science 40

English 10

Total 122

3. a. 20 b. 15 c. 120

244 Maths Zone – Grade 4

11 Set

Specific Objective Prescribed by CDC

 To list the elements of a named set.
 To write the elements of a set in notation from { }.
 To list the name of the days, months, alphabets, etc and write it in set

notation { }.
Maths Zone - Grade 4 245

Making the Set

Class Discussion

It is a collection of birds It is a collection of animals
It is a set of birds It is a set of animals.

It is a collection of fruits, It is a collection of modern
It is a set of fruits communication devices.
It is a set of modern
It is a collection of geometrical communication devices
instruments.
1 2 3
It is a set of geometrical 4 5
Instruments
It is a collection of first five
246 Maths Zone - Grade 4 natural numbers.

It is a set of first five natural
numbers

In each collection, the members (elements) are clearly specified.
So, A set is a collection of well defined objects.
Well defined: Clearly specified/State clearly.

Let's see few examples of well-defined and not well defined collections.

Well-defined Non-well defined

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

favourite fruits fruits

‰‰ The collection of boys of ‰‰ The collection of tall boys of

your class whose height is your class.

more than 4.2"
‰‰ The collection of text book of ‰‰ The collection of interesting

grade 4 books.

‰‰ The collection of the student ‰‰ The collection of intelligent

who secured more than 80% students of your class.

in your first term of your

class.

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

Exercise 11.1

1. Cross out the odd one and write the name of set of
remaining objectives.

a. b.

c. d.

2 4 6
8 5

2. Rewrite well-defined and non-welldefined collection in
separate list.
a. The collection of numbers from 1 to 5.
b. The collection of the girls having long hair.
c. The collection of the beautiful girls of your class.
d. The collection of first five prime numbers.
e. The collection of the boys who run faster.
f. The collection of the tall students of your class.
g. The collection of the colors of a rainbow.
h. The collection of your favourite vegetables.

Set Notation

Class Discussion
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
∉ = doesnot belongs 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 do not allow a set to have repeated of set 'A' but a and b are
elements. 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
first five even

If we describe the type of members of a set by ‰‰ numbers of
The set
words, then it is called descriptive method of writing seven days of

sets. the week.

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

Exercise 11.2

1. Insert ∈ or ∉ appropriately in the blank space.

a. a ......... {a, e, i, o, u} b. b ............... {p, i, r, o, t}

c. m ....... {m, a, t, h} d. p .......... {p, e, n, c, i, l}

2. If set A = {2, 4, 6, 8, 10} and set B = {m, u, n, a}, then

insert ∈ or ∉ in the blank space.

a. 2 ......... A b. 8 ......... A

c. 9 ......... A d. u ......... B

e. a ........ B f. a .......... B

g. p ........ B h. t .......... B

3. Identify each of the following as true or false.

a. A belongs to the set of vowels of English Alphabet

b. A square belongs to the set of plane figure.

c. Lion does not blong to the set of plane figure.

d. July does not belongs to the set of animals.

e. 'Math' '2' does not belongs to prime numbers.
4. List the members of each of the following sets within { }.

a. Sunday b. c. a e

Monday, 1 2

Tuesday 3 4 5 i o u

d. A set of first five English Months.

e. A set of even numbers less than 10.
f. A set of prime numbers between 10 to 20.