Prime Mathematics 4

600 620 640 650 660 680 690 700 720 740 760

From the above figure, it is clear that 690 is nearer to 700 than to 600. So,
round off of 690 is 700.
The process of converting the numbers to their nearest ten, hundred,
thousand and so on is called rounding off the numbers.
Rounding off a number to nearest ten is to convert the ones digit to zero for
example 20, 40, 180, 390, 1450 and so on.
Rounding off a number to nearest hundred is to reduce the tens digit and
ones digit to zero. For example, 200 400, 1500, 2700 and so on.
Rounding off a number to nearest thousand is to reduce the hundreds digit,
the tens digit and ones digit to zero. For example, 2,000, 7,000, 15,000,
29,000 and so on.
Example 1: Round off 54 to the nearest ten.

50 51 52 53 54 55 56 57 58 59 60

The number 54 is nearer to 50 than to 60. So, the round off value
of 54 to the nearest ten is 50.

Example 2: Round off 170 to the nearest hundred.

100 110 120 130 140 150 160 170 180 190 200

The number 1 7 0 is nearer to 200 than to 100. So, the round off
value of 1 7 0 to the nearest hundred is 200.

Example 3: Round off 14,570 to the nearest thousand.

14,000 14,100 14,200 14,300 14,400 14,500 14,600 14,700 14,800 14,900 15,000
14,570

The number 14,570 is nearer to 15,000 than to 14,000. So, the
round off value of 14,570 to the nearest thousand is 15,000.

46 Prime Mathematics Book − 4

Exercise 2.8

1. Round off the given numbers to the nearest ten:

37

(i)

30 31 32 33 34 35 36 37 38 39 40

423

(ii)

420 421 422 423 424 425 426 427 428 429 430

1455

(iii)

1450 1451 1452 1453 1454 1455 1456 1457 1458 1459 1460

(iv) 45 (v) 69 (vi) 78 (vii) 437
(viii) 549 (xi) 1025 (x) 3459

2. Round off the given numbers to the nearest hundred:

830

(i)

800 810 820 830 840 850 860 870 880 890 900

650

(ii)

600 610 620 630 640 650 660 670 680 690 700

1465

(iii)

1400 1410 1420 1430 1440 1450 1460 1470 1480 1490 1500

(iv) 95 (v) 950 (vi) 1565 (vii) 2134
(viii) 3295 (ix) 4915 (x) 839

3. Round off the given numbers to the nearest thousand:

4300

(i)

4000 4100 4200 4300 4400 4500 4600 4700 4800 4900 5000

5700

(ii)

5000 5100 5200 5300 5400 5500 5600 5700 5800 5900 6000

6500

(iii)

6000 6100 6200 6300 6400 6500 6600 6700 6800 6900 7000

(iv) 6735 (v) 1495 (vi) 2590 (vii) 7912
(viii) 8145 (xi) 9100 (x) 4235

Prime Mathematics Book − 4 47

Roman Numerals

Let’s recall the Roman numeral system that we have learnt in class III (three).
We know that the Romans used seven symbols to represent the numbers.
They are I, V, X, L, C, D and M. The values of these symbols in Hindu−Arabic
system are as follows:

Roman Numerals I VX LCDM

Hindu−Arabic Numbers 1 5 10 50 100 500 1000

In Roman numeral system, there is no zero and no special symbols for 2, 3,
4, 6, 7, 8 and 9.

Let’s learn the conversion of Roman Numeral system to Hindu Arabic number
system. See some examples:

II = 1 + 1 = 2
XX = 10 + 10 = 20
CCC = 100 + 100 + 100 = 300
MMM = 1000 + 1000 + 1000 = 3000

But, VV, LLL, DD can’t be written.
Rule 1: It means I, X, C, M can be repeated and only upto three times. The
repetition of these symbols means addition. The symbols V, L and D never
repeated.

Let’s see some examples:
IV = 5 – 1 = 4
IX = 10 – 1 = 9
XL = 50 – 10 = 40
XC = 100 – 10 = 90
CD = 500 – 100 = 400
CM = 1000 – 100 = 900

48 Prime Mathematics Book − 4

Rule 2: If the smaller symbol comes before a greater one, then smaller one
is subtracted from the greater one to get the number.
I can be subtracted from V and X only and once only.
X can be subtracted from L and C only and once only.
C can be subtracted from D and M only and once only.
But, we can’t subtracte V, L, D and M.

Let’s observe some examples:
XI = 10 + 1 = 11
XV = 10 + 5 = 15
LX = 50+ 10 = 60
DCL = 500 + 100 + 50 = 650
MDC = 1000 + 500 + 100 = 1600
CLX = 100 + 50 + 10 = 160

Rule 3 : If the smaller symbol comes after a greater one, the smaller one
is added to the greater one to get the number.

Exercise 2.9

1. Write the following Hindu−Arabic numbers to Roman numeral system:

(i) 52 (ii) 65 (iii) 95

(iv) 105 (v) 267 (vi) 389

(vii) 1050 (viii) 431 (ix) 252

(x) 2089 (xi) 3512 (xii) 1537

2. Write the following numbers in Hindu−Arabic system:

(i) LX (ii) DC (iii) MC

(iv) MDC (v) XVI (vi) XLVI

(vii) CXXIV (viii) CLV (ix) CDL

(x) MCV (xi) CXV (xii) XCVI

Prime Mathematics Book − 4 49

Unit Revision Test

1. Write the number in words in Nepali Place Value system by
representing them in a place value table:
(a) 52, 74, 19, 645 (b) 3, 56, 04, 507

2. First represent the given number names in a place value table and
write the numeral in Nepali Place Value system:
(a) Twelve crore fifteen lakh twenty three thousand four hundred
and six.
(b) Forty five crore twenty one lakh ninety eight thousand seven
hundred and ten

3. Represent the given numbers in place value table in International
Place Value system and write in words:
(a) 245, 678, 012. (b) 392, 452, 156

4. Write the number names in numerals representing them in place
value table in International Place Value system:
(a) Four hundred ninety eight million five hundred forty two thousand
six hundred and four.
(b) Six hundred eighty five million eight hundred four thousand six
hundred and twenty five.

5. Write all the possible factors and also mention the prime factors:
(a) 100 (b) 250

6. Write down all the prime numbers:
(a) Less then 50 (b) Between 90 and 100

7. Round off the given numbers to the nearest thousand:
(a) 4444 (b) 7690

8. Round off the given numbers to the nearest hundred:
(a) 712 (b) 5490

9. Write the given Hindu−Arabic numerals in Roman numerals:
(a) 690 (b) 405

10. Write the following Roman numerals in Hindu−Arabic numeral:
(a) CXV (b) MDC

11. Find the HCF of 8,28 and 44

11. Find the LCM of 4,9 and 24

50 Prime Mathematics Book − 4

Answers:

Exercise- 2.1
1. a)

Ten lakhs Lakhs Ten Thousand Thousand Hundred Tens Ones

1 01 4 6 58
b)

Lakhs Ten Thousand Thousand Hundred Tens Ones

2 0 4 0 57

c)

Ten crores crores Ten lakhs Lakhs Ten Thousand Thousand Hundred Tens Ones

57 04 9 0 01

d)

Ten crores crores Ten lakhs Lakhs Ten Thousand Thousand Hundred Tens Ones

2 40 04 7 8 97
e)

Ten crores crores Ten lakhs Lakhs Ten Thousand Thousand Hundred Tens Ones

7 52 30 5 6 04

2 . Show to your teacher.
3. Show to your teacher

4. a) 54, 72, 89, 163 b) 78, 59, 12, 234 c) 89, 76, 54, 321 d) 1, 00, 92, 47, 638 e) 8, 20, 49, 731

5. a) 9,00,00,000 b) 50,00,000 c) 70,00,000 d) 70,00,000 e) 10,00,00,000 f) 7,00,00,000

g) 80,000 h) 70,000 i) 7,00,000

6. a) 31, 45, 789 b) 4, 20, 569 c) 12,45,37, 693 d) 5,27, 48, 961 e) 16, 28, 42, 179

f) 4, 05, 76, 893g) 98, 17, 41, 382 h) 12, 48, 75,396 i) 48, 29, 59, 107.

1. a) !& Exercise: 2.2
b) %* c) #@* d) $%)# e) @%&#% f) *&^%*

2. a) 12 b) 68 c) 353 d)6214 e) 26,453 f) 91,837

3. a) #&% Ö tLg ;o krxQ/ b) @)^@ Ö bO' { xhf/ a};77\ L c) %!,!&) Ö PsfpGg xhf/ Ps ;o ;Q/L

4. a) 756 = Seven hundred fifty six, b) 1,654 = One thousand six hundred fifty four.

c) 40,925 = Forty thousand nine hundred twenty five.

1. a) 2,000,000 b) 30,000,000 c) 1,000,000 Exercise- 2.3
d) 1,000,000 e) 80,000 f) 2,000 g) 2,000 h) 90,000.

2. a) Show to your teacher.

3. a) 3600 b) 40,000 c) 218,000 d) 7,00,000 e) 4,580 f) 17,200

4. a) 238, 342, 605, b) 52, 640, 905, c) 9, 034, 576, d) 345, 298, e) 495, 705

5. a) 241,567,908 = 200,000,000 + 40,000,000 + 1,000,000 + 5,00,000 + 60,000 + 7,000 + 900 + 8

b) Show to your teacher. c) Show to your teacher. d) Show to your teacher. e) Show to your teacher.

6. a) 23,571,987 = .................., b) 354,846,971 =................., c) 45,978,612 = ...................

d) 96, 751,328 = .................. , e) 8,752,196 =...................

7. a) 76,43,273, b) 85, 914,248 c) 9,876 d) 8,562

8. 6532, a) largest = 8720, smallest = 2,078

Prime Mathematics Book − 4 51

Exercise: 2.4
1. a) f(50) = {1,2,5,10,25,50} Prime factors = {2,5}, b) f(150) = {1,2,3,5,10,15,25,30,50,75,150} Prime factors =

{2,3,5}, c) f(200) = {1,2,4,5,8,10,20,25,50,100,200} Prime factors = {2,5}
d) Show to your teacher. e) Show to your teacher. f) Show to your teacher. g) Show to your teacher.
h) Show to your teacher. i) Show to your teacher.

2. a) {12, 24, 36, 48, 60} b) {14, 28, 42, 56, 70} c) {21, 42, 63, 84, 105}
d) {25, 50, 75, 100, 125} e) {27, 54, 81, 108, 135} f) {15, 30, 45, 60, 75}
g) {17, 34, 51, 68, 85} h) {32, 64, 96, 128, 160} i) {53, 106, 159, 212, 265}

3. Show to your teacher.

4. Show to your teacher.

5. a) {1, 2, 4, 8} b) {1,7} c) {1, 3, 5, 15} d) {1,2,5, 10, 20} e) {1, 2, 4, 8, 16} f) { 1, 2, 4, 7, 14, 28}
g) {1,2, 4, 8, 16, 32} h) {1, 2, 3, 4, 6, 8, 12, 16, 24, 48} i) {1, 2, 3, 6, 9, 18, 27, 54}
j) {1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72}

6. a) 2×2×5 b) 3×5 c) 2×2×7 d) 3×5×3 e) 2×2×3×5 f) 2×3×2×3 g) 2×5×3×3

h) 2×2×2×2×5 i) 2×2×2×3×5 j) 2×2×2×2×3×3 k) 5×5×7 l) 2×2×5×5 m) 2×2×5×3×3

n) 3×5×5 o) 2×2×2×2×2×2×2 p) 2×5×5×5 q) 5×5×3×5

Exercise: 2.5

1. 50, 82, 56, 786 2. 45, 432, 816 3. 75, 820, 315 4. 812, 56, 343 5. 88, 759, 825

6. a) 2 and 3 b) 2, 3 and 5 c) 2 and 11 d) 2 and 7 e) 2, 5 and 7 f) 2, 3 and 11

1. a) 3 b) 12 c) 4 d) 18 e) 6 Exercise: 2.6 h) 10 i) 8 j) 8
2.a) 3 b) 4 c) 7 d) 9 e) 10 f) 2 g) 14 h) 2 i) 10
f) 25 g) 8

1. a) 10 b) 30 c) 63 Exercise: 2.7 e) 126 f) 100
2. a) 30 b) 60 c) 80 d) 6 k) 60
h) 24 i) 36 d) 60
g) 96 j) 120

1. i) 40 Exercise: 2.8
2. i) 800 ii) 420 iii) 1460 iv) 50 v) 70 vi) 80 vii) 440 viii) 550 ix) 1030 x) 3460
3. i) 4000 ii) 700 iii) 1500 iv) 100 v) 1000 vi) 1600 vii) 2100 viii) 3300 ix) 4900 x) 800
ii) 6000 iii) 7000 iv) 7000 v) 1000 vi) 3000 vii) 8000
viii) 8000 ix) 9000 x) 4000

Exercise: 2.9

1.i) LII ii) LXV iii) XCV iv) CV v) CCLXVII vi) CCCLXXXIX vii) ML viii) CDXXXI
ix) CCLII x) MMLXXXIX
xi) MMMDXII xii) MDXXXVII

2. i) 60 ii) 600 iii) 1100 iv) 1600 v) 16 vi) 46 vii) 124 viii) 155 ix) 450 x) 1105 xi) 115
xii) 96

52 Prime Mathematics Book − 4

U3nit Basic Operation in
Mathematics

Objectives Estimated periods − 26

At the end of this unit, the students will be able to:
• add large whole numbers of 6 digits and more than 6 digits with and without carrying.
• make word problems on addition and solve it.
• subtract large whole numbers of 6 digits and more than 6 digits without borrowing and with

borrowing in any place.
• make word problems on subtraction and solve it.
• multiply a whole number of 3 digits or more than 3 digits by a number of 3 digits.
• write and solve the simple word problems on multiplication.
• divide large whole numbers up to 5 digits by 2 or 3 digit number with or without remainder.
• write and solve the simple word problems on division.
• explain the relation between multiplication and division.
• make and solve the simple simplification problems involving ÷, ×, +, - and ( ) using the order of

operation.

Teaching Materials
Place value chart, abacus, number cards, concrete objects, visible models etc.

Activities
It is better to:
• drill the problems to make and solve by using the place value chart for adding and subtracting
large whole numbers on the basis of the knowledge of previous class.
• ask the students to solve the problems on the board.
• ask the students to make and solve the word problems of addition and subtraction with simple
examples.
• clarify the students about addition and subtraction as inverse relation.
• drill the students to discuss the multiplication by using multiplication table.
• ask the students to make and solve the word problems of multiplication.
• ask the students to drill the problems by using the steps on the basis of discussion about the
division.
• perform the activities about the word problems of division with the help of easier examples.
• clarify the students about multiplication and division as inverse relation.
• clarify the students about multiplication as repeated addition and division as repeated subtraction
process.
• ask the students to simplify the problems of numeral expressions by using the concept of addition
and subtraction.
• ask the students to write and solve the simple word problems related to addition and subtraction
by using brackets from the group discussion.
• involve the students in group activities by making different groups to discuss the problems
involving the basic fundamental operations.
• organize a mathematical race for the students.

Addition
Recall for the students :
7 ones + 9 ones = 16 ones = 10 ones + 6 ones = 1 ten + 6 ones
5 tens + 8 tens = 13 tens = 10 tens + 3 tens = 1 hundred + 3 tens
9 hundreds + 8 hundreds = 17 hundreds = 10 hundreds + 7 hundreds

= 1 thousand + 7 hundreds
6 thousands + 8 thousands = 14 thousands = 10 thousands + 4 thousands

= 1 ten thousands + 4 thousands.

Class Work
Add the following and group them from the above recall :
(1) 9 ones + 6 ones = ....... ones= ........ tens+ ........ones
(2) 12 ones + 9 ones = ....... ones= ........ tens+ ........ones
(3) 25 ones + 13 ones = ....... ones= ........ tens+ ........ones
(4) 6 tens + 9 tens = ....... tens= ........ hundreds+ ........tens
(5) 7 tens + 17 tens = ....... tens= ........ hundreds+ ........tens
(6) 32 tens + 5 tens = ....... tens= ........ hundreds+ ........tens
(7) 40 tens + 7 tens = ....... tens= ........ hundreds+ ........tens
(8) 4 hundreds + 7 hundreds = .......hundreds= ........ thousands+ ........

hundreds
(9) 12 hundreds + 9 hundreds = .......hundreds= ........ thousands+ ........

hundreds
(10) 23 hundreds + 14 hundreds = .......hundreds= ........ thousands+ ........

hundreds

Let’s play ! The fun of addition.
Remember the value of each letter as given in the word below. Write the
numerical value of the following words. Remember, this is your mental
work.

E X A MP L E
2 5 8 10 13 15 2
(a) Apple = 8 + 13 + 13 + 15 + 2 = 51
(b) EXAM = .......................................................
(c) MAP = .......................................................
(d) LAMP = .......................................................

54 Prime Mathematics Book − 4

Addition with and without carrying
While adding two or more numbers, write the numbers in column according
to their place value and add the digits at the same places and re−group into
the higher place taking carry over.

Workedout Examples
Example 1 : Add : 452132 and 325765.
Solution :

452132
+325765

777897

Example 2: Add : 3 2 7 5 6, 4 6 3 7 and 8 6 5.
Solution:

211 6 ones + 7 ones + 5 ones
= 18 ones
32756 = 10 ones + 8 ones
4637 = 1 ten + 8 ones
1 ten is carried over to tens
+ 865 place and so on ……………..
38258

Example 3: Find the total of :
Solution: 576 + 9345 + 81093 + 10587+ 576 + 9345 + 81093 + 10587

= 203202

Example 4: There are 18689 students in Kathmandu district, 15976 students
in Laltipur district and 12787 students in Bhaktapur district studying in
class iv. What is the total numbers of students in three districts?
Solution :
1222
Students in Kathmandu = 1 8 6 8 9
Students in Lalitpur = 15976
Students in Bhaktapur =+1 2 7 8 7
Total students = 47452
∴ The total numbers of students in three districts is 47452.

Prime Mathematics Book − 4 55

Exercise 3.1

1. Perform the following task:

(a) 2 7 5 (b) 5 6 8 (c) 4 3 5 7 (d) 7 5 8 3 5
+312 +276 +2486 +87496

(e) 6 3 8 4 5 6 (f) 3 6 8 5 4 6 7 (g) 4 6 5 3 (h) 5 6 2 5 7
+276597 +9789758 3827 38765
+456
+93876

(i) 4 5 2 5 (j) 3 6 8 3 5 (k) 4 5 8 3 (l) 5 6 8 3
636 97686 645 465
+29 +3798
3873 9397
29 83
+8 +9

(m) 7 8 4 5 6 (n) 3 5 7 6 4 (o) 2 4 8 5 7 6 (p) 3 8 7 6 5 8 3
8769 2859 893495 6938749
687 78476 256867
89 46325 +9567 +48658
+5 468

+2839

2. Perform the following task:
(a) 257 + 8375 + 45
(b) 38756 + 2879 + 89
(c) 8365 + 9347 + 8576 + 8365
(d) 9645 + 97 + 783 + 6945
(e) 743 + 4625 + 19475 + 286589
(f) 88888 + 8888 + 888 + 88 + 8

3. Add the following:
(a) 285, 4676 and 97692
(b) 69821, 3847, 469 and 57
(c) 8769876, 35796528, 49837587 and 78956

56 Prime Mathematics Book − 4

4. Write the missing digits in the following sum:

(a)3 7 (b)4 8 (c) 7 (d) 6 3 2 (e) 4 7 6 8
+2 +3 +6 +8 +49 7 4
63 4 145 16 1 13 5032

5. Solve the following problems:

(a) There are 27856 students in Dhading district, 35247 in Kaski district
and 18758 in Gorkha district. What is the total number of students
in three districts?

(b) Mohan Sahu bought a motorcycle for Rs. 75875. He spent Rs. 17680
for its repair. How much money did he spend altogether for the
motorcycle?

(c) The male population of Kavre is 32958, the female population is
28765 and children is 19658. Find the total population of Kavre.

(d) A shopkeeper bought 47875 kg. of potatoes from one whole seller
and 59745 kg from the other. How many kg. of potatoes did he buy
altogether ?

(e) The table given below shows the price of computer, television,
computer table and printer. Answer the following questions.

Items Price

Computer Rs. 25750

Television Rs. 35975

Computer table Rs. 12800

Printer Rs. 14985

(i) Tenjee Sherpa wants to buy a computer with printer and a
computer table. How much money does he pay for them ?

(ii) Bijaya Gupta wants to buy a computer and a television. How
much money does he pay for both ?

(iii) Aaisha wants to buy a computer, a television, a computer table
and a printer. How much money does she pay altogether ?

Prime Mathematics Book − 4 57

6. Solve the following problems:
(a) Mohan had Rs. 475 left after spending Rs. 125 to buy a geometry
box. How much money did he have at the begining ?
(b) Find the sum of the smallest and the greatest number of 6 digits.
(c) Write the greatest numbers of 7 digits and 8 digits. Then, find
their sum.
(d) What is the sum of the smallest and the greatest numbers of 6
digits formed by the digits 2, 4, 6, 0, 8, 5 ?
(e) Write the smallest and greatest numbers of 7 digits formed by the
digits 8, 3, 0, 6, 2, 5, 9. Then, find their sum.

Subtraction
Recall for the students:

4 tens – 2 ones = (4 – 1)tens + 10 ones – 2 ones = 3 tens + 8 ones

3 hundreds – 5 tens = (3 – 1)hundreds + 10 tens – 5 tens
= 2 hundreds + 5 tens

4 thousands – 3 hundreds = (4 – 1)thousands + 10 hundreds – 3 hundreds
= 3 thousands + 7 hundreds

Class Work

Borrow 1 ten or 1 hundred or 1 thousand from tens or hundreds or thousands
place and re−group the numbers from the above recall.
(1) 3 tens – 4 ones = ..........................................
(2) 7 tens – 6 ones = ..........................................
(3) 5 tens – 3 ones = ..........................................
(4) 2 hundreds – 3 tens = ..........................................
(5) 5 hundreds – 7 tens = ..........................................
(6) 4 hundreds – 0 tens = ..........................................
(7) 3 hundreds – 2 tens = ..........................................
(8) 5 thousands – 5 hundreds = ..........................................

58 Prime Mathematics Book − 4

Subtraction without borrowing:
In the case of subtraction without borrowing, we subtract the digits of
individual place value from one number to the another number.

Workedout Examples
Example 1: Subtract 5 6 2 4 7 8 from 7 8 5 9 8 9.
Solution: First we arrange the number according to place value. Then we

subtract the number of second row from the number of first row.
785989

−562478
223511

Exercise: 3.2

1. Perform the following task:

(a) 5 9 8 3 6 (b) 4 1 2 5 6 (c) 5 6 4 8 2 (d) 7 2 5 1 4 6
−26315 −10042 −4250 −412035

2. Subtract :
(a) 3 6 5 2 4 6 from 6 8 9 4 7 9

(b) 2 4 0 3 1 8 2 from 5 9 2 6 5 9 7

(c) 5 4 8 2 5 7 8 3 from 6 7 9 4 8 9 9 5

(d) 2 0 2 3 7 6 2 1 from 7 2 3 4 8 9 7 5

3. Write the missing digits in the following:

(a) 7 5 4 3 6 (b) 8 7 3 5 7 (c) 7 5 2 4
−5 4 1 6 2 −2 3 4 2 4 −2 1 32 54
13214 421 3 2 1 413

Prime Mathematics Book − 4 59

Subtraction with borrowing:
We have already discussed about the subtraction with borrowing in class three.
First we arrange the digits of the given numbers according to place value and
then borrow 1 from higher place digit while subtracting a greater digit from a
smaller digit. We take care to reduce 1 in that digit from where we borrow 1.
Let’s see one example.

Subtract: 2 7 8 5 from 4 2 1 3 • In ones place, 1 ten is borrowed
from tens place.
Th H T O
∴ 1 ten + 3 ones = 13 ones
3 11 10 13 13 ones – 5 ones = 8 ones

4213 • In tens place, 1 is reduced. So in its
−2 7 8 5 place remaining is 0.
1 hundred is borrowed from
1428 hundreds place.

∴ 1 hundred + 0 ten = 10 tens
10 tens – 8 tens = 2 tens

• In hundreds place, 1 is reduced. So,
in its place remaining is 1.
1 thousand is borrowed from
thousands place.

∴ 1 thousand + 1 hundred = 11
hundred
11 hundreds – 7 hundreds = 4
hundreds

• In thousand place, 1 is reduced. So,
in its place remaining is 3.
3 – 2 = 1 thousands.

Workout Examples

Example 1: Subtract: 3 2 5 3 4 from 7 4 2 0 3.
Solution:
11 9
3 1 10 13
74203
−32534
41669

60 Prime Mathematics Book − 4

Example 2: Perform the following sbutraction horizontally: 907235
– 87946
Solution: = 907235 – 87946

= 819289

Example 3: The total population of a town is 2,65,432. If 1,84,756 of
them are male, how many of them are female?
Solution:
13 12 To find the female
1 16 4 3 2 12 population, subtract male
population from the total
265432
−184756 population.

080676

∴ The female population is 80676.

Example 4: What should be added to 28457 to get 43263?
Solution:
What should be
12 added to 4 to get 9,
3 2 12 5 13
Ram ?
43263
−28457 5

14806 Good Ram ! How I subtracted
did you get it? 4 from 9.

∴ 14806 should be added to Can you solve the
28457 to get 43263. above problems?

Yes, Sir!
I can solve

them.

Example 5: Mani had Rs. 25,400. He bought a computer for Rs. 21,750.
How much money is left with him?
Solution:
25400 The price of the computer
−21750 is less than the money which he had.
03650 So, we subtract smaller number from
∴ He has Rs. 3650 left.
the larger number.

Prime Mathematics Book − 4 61

Exercise 3.3

1. Perform the following task:

(a) 5 3 2 5 (b) 6 5 2 4 (c) 3 5 2 1 4 (d) 7 3 2 5 9
−3176 −5876 −17648 −38462

(e) 8 4 2 3 1 (f) 6 2 4 1 7 2 (g) 2 5 0 3 2 0 (h) 7 3 1 0 5 2 4
−56473 −473584 −173435 −5637849

(i) 5 0 0 3 0 0 7 (j) 7 4 5 3 0 8 2 (k) 8 3 4 5 6 2 0 1
−2456989 −4796584 −56749484

2. Find the difference of: (b) 75325 and 63879
(a) 4305 and 3796 (d) 1000000 and 999999
(c) 723483 and 564594 (f) 87865432 and 3956789
(e) 4839051 and 2849373

3. Find the missing numbers in the box:

(a) 2 4 3 4 (b) 8 0 3 (c) 7 8 3 2
16 −3 2 4 7 −3 9 7 6
05 12 9 2 06 7

(d) 7 4 1 2 (e) 2 6 0 2 7 1 4
−5 4 7 5 4 −7 4 7
70 8 328

4. Solve the following word problems:
(a) There are 1342 mangoes in a basket. Out of them 957 mangoes are
rotten. How many mangoes are good?
(b) There are 1605246 apples in a cold store. Out of them 938468
apples are good. How many apples are rotten?
(c) The total population of Nepalganj is 924520. If the male population
is 575875, find the femal population of Nepalganj.

62 Prime Mathematics Book − 4

(d) Rupika earns Rs. 220500 in a year. If she spends Rs. 89580, how
much does she save in a year?

(e) Pramila spent Rs. 89765 to buy a computer and a television set. If
the price of the computer was Rs. 48975, how much was the cost
of the television set?

(f) Salim Ansari bought a watch for Rs. 3750 and a jacket for Rs. 2455.
He had Rs. 7000. How much money is left with him?

5. (a) What is the difference between the largest and the smallest
number of 5 digits?

(b) Find the difference between the least number of 8 digit and the
greatest number of 7 digit?

(c) Write the greatest and the least number of 7 digits formed by the
digits 7, 2, 0, 5, 3, 1, 6. Also find the difference between them.

(d) Find the difference between the greatest number and the least
number of 8 digits formed by the digits 2, 4, 9, 0, 3, 7, 6, 1.

6. (a) What should be added to 5789 to get 7243?
(b) What number should be added to 257835 to get 423052?
(c) By how much is 35673 greater than 28796?
(d) What should be subtracted from 704257 to get 359682?
(e) By how much is 43894 less than 72035?

7. The population of 6 districts of Bagmati zone is given below:
Kathmandu − 60,25,783; Lalitpur − 40, 65, 275

Bhaktapur − 25, 60, 575; Kabhrepalanchok − 15, 30, 978
Rasuwa − 20, 12, 325; Dhading − 23, 15, 287

(a) Which district has the highest population?
(b) Which district has the least population?
(c) Find the difference between the highest and the least population

of two districts.
(d) By how much the population of Lalitpur district is more than

Dhading district?
(e) By how much the population of Rasuwa district is less than Dhading

district?

Prime Mathematics Book − 4 63

Multiplication

Revision

Fill in the boxes as given below:

2+2+2= 3×2 = 6 6+6+6+6= =
3+3+3+3= = 8+8+8+8+8+8 = =
5+5+5+5+5+5 = =

What fact do you get
from the above revision?

From the above revision, I got that
the multiplication is a repeated
addition of the same number.

Look at the following basic multiplication facts:

• The product of any number multiplied by 1 is the number itself.

6 × 1 = 6; 19 × 1 = 19; 237 × 1 = 237

• Although the order of the numbers change, their product remains the
same.
9 × 5 = 45; 5 × 9 = 45

• The product of any number multiplied by 0 (zero) is always 0.

7 × 0 = 0; 27 × 0 = 0; 435 × 0 = 0

• If the grouping of three numbers change, their product remains the
same.

2 × (4 × 6) = 48; (2 × 4) × 6 = 48

• In 14 × 6 = 84, 14 is called the multiplicand, 6 is called the multiplier
and 84 is the product.

• The product divided by the multiplier is equal to the multiplicand and
the product divided by the multiplicand is equal to the multiplier.

In 12 × 6 = 72, 72 ÷ 6 = 12, 72 ÷ 12 = 6

64 Prime Mathematics Book − 4

Class Work

1. Fill in the blanks:

(a) In 13 × 7 = 91, 13 is the ……………………………………, 7 is the
……………………………… and 91 is the ………………………….

(b) In 18 × 6 = 108, the multiplicand is ……………………, the multiplier
is ……………………… and the product is ………………………..

(c) 18 × 1 = ………………………, 54 × 1 = 54, 207 × 1 = ……………….

(d) 374 × ……………… = 374, 8 × 0 = ……………….., 596 × 0 = ……………….

(e) 25 × …………… = 0, …………… × 0 = 0, 96 × ……………… = 0

(f) 5 × 8 = ………. × 5, ……………… × 28 = ………………. × 35

(g) (12 × 7) × 5 = ……… × (7 × 5), 25 × (………. × 12) = (25 × 30) × ………

(h) 8 × 7 = …………….., 56 ÷ 7 = …………………, 56 ÷ 8 = …………………

Multiplication by 10, 20, 30, ……………., 100, 200, …………, 1000, 2000,
……………….

Try to find the idea of
multiplication by the numbers

with zeros at the end.

325 × 10 = 3250 Multiply 325 by 1 and write
one zero at the end of the

product.

124 × 200 = 24800 Multiply 124 by 2 and write
124 × 3000 = 372000 two zeros at the end of the

product.
Multiply 124 by 3 and write
three zeros at the end of

the product.

462 × 20000 = 9240000 Multiply 462 by 2 and write
four zeros at the end of the

product.

Prime Mathematics Book − 4 65

From the above multiplication, it is concluded that when a number is multiplied
by another number with zeros at the end, the product is the multiplication
of multiplicand and non−zero part of multiplier and writing zeros at the end
of the product as the multiplier has.

Class Work

1. Fill in the blanks: (b) 34 × 20 = ……………….
(a) 42 × 10 = ………………. (d) 121 × 3000 = ……………….
(c) 123 × 300 = ………………. (f) 121 × 7000 = ……………….
(e) 212 × 400 = ………………. (h) 423 × 300000 = ……………….
(g) 324 × 20000 = ……………….

2. Fill in the blanks: (b) 70 × …………….. = 21000
(a) 12 × …………….. = 240 (d) ……………. × 4000 = 88000
(c) ……….. × 200 = 8400 (f) …………….. × 60000 = 1320000
(e) 12 × …………….. = 840000 (h) 213 × …………….. = 106500
(g) …………….. × 800 = 32000 (j) …………….. × 3100 = 12400
(i) …………….. × 120 = 360

Multiplication by three digit number

Can you multiply Yes, sir! I can multiply
423 by 265? it.

423 I remember
× 265 265 = 200 + 60 + 5
2115 423 × 5
25380 423 × 60
+ 84600 423 × 200
112095

Example 1: Multiply 543 by 374.
Solution:
543 Multiplier 374 = 300 + 70 + 4
× 374
2172 543 × 4
38010 543 × 70
+ 162900 543 × 300
203082

66 Prime Mathematics Book − 4

Example 2: Multiply 2746 by 462.
Solution:
2746
×462
5492 400 + 60 + 2
2746 × 2
164760 2746 × 60
+1098400
1268652 2746 × 400

Example 3: Multiply three thousands four hundred and thirty five by two
hundred forty two.

Solution: Here,
Multiplicand = Three thousands four hundred and thirty five
= 3435
Multiplier = two hundreds forty two = 242.
Now,

3435 200 + 40 + 2
×242 3435 × 2
6870 3435 × 40
137400 3435 × 200
+687000
831270

Example 4: There are 342 apples in a carton. How many apples are there
in 127 such cartons?

Solution: Here,
Number of apples in a carton = 342
Number of cartons = 127
So, total number of apples = number of apples × number of
cartons = 342 × 127

342 100 + 20 + 7
×127
2394
6840
+34200
43434

∴ There are 43434 apples in 127 cartons.

Prime Mathematics Book − 4 67

Example 5: Find the product of the greatest number of 4 digits and least
number of 3 digits.

Solution: Here,
The greatest number of 4 digits = 9999
The least number of 3 digits = 100
Now, the product of 9999 and 100
= 9999 × 100 = 999900

Exercise: 3.4
1. Find the product of :

(a) 75 × 10 (b) 25 × 70 (c) 125 × 200
(f) 378 × 800
(d) 243 × 600 (e) 3261 × 3000 (i) 2754 × 300

(g) 347 × 6000 (h) 47 × 90000

2. Perform the following multiplications:

(a) 374 × 42 (b) 587 × 54 (d) 3846 × 95
(h) 5259 × 436
(f) 342 × 258 (g) 152 × 204 (k) 2432 × 1521

(i) 5419 × 526 (j) 52135 × 265

3. Perform the following task:

(a) 347 (b) 563 (c) 3479 (d) 2047
×54 ×83
×35 ×79
(g) 4739 (h) 4027
(e) 687 (f) 578 ×427 ×742
×126 ×247

(i) 56896 (j) 68569 (k) 6954 (l) 5964
×234 ×432 ×1243 ×2413

4. Multiply:
(a) Two hundred fifty six by one hundred twenty four.
(b) Six hundred seventy three by two hundred forty.
(c) Eight hundred thirty seven by three hundred forty six.
(d) Two thousand six hundred forty eight by two hundred fifty eight.
(e) Five thousand four hundred six by seven hundred eighty eight.

68 Prime Mathematics Book − 4

5. Solve the following word problems:
(a) The cost of a chair is Rs. 575. What is the cost of such 74 chairs?
(b) The cost of a bicycle is Rs. 3750. What is the cost of such 56
bicycles?
(c) The cost of a pair of shoes is Rs. 1775. What is the cost of such 76
pair of shoes?
(d) There are 144 pens in a box. How many pens are there in 270
boxes?
(e) There are 2514 sweets in a box. If a sweet shop has 175 such
boxes, how many sweets are there in the shop?

6. (a) There are 4525 mangoes in a tree. How many mangoes are there
in 214 such trees?

(b) There are 60 seconds in a minute. How many seconds are there in
3 hours?

(c) An aeroplane can fly 280km in a minute. How many km will it fly
in 4 hours and 30 minutes?

(d) A typist types 65 words per minute. How many words can he type
in 4 hours and 20 minutes?

(e) There are 200 centimetres in 2 metres. How many centimetres are
there in 135 metres?

(f) 1 kilogram is equal to 1000 grams. How many grams are there in 3
kilograms?

6. Solve the following problems:
(a) Find the product of the greatest number of 5 digits and the smallest
number of 4 digits.
(b) Find the product of the greatest number of 6 digits and the least
number of 3 digits.
(c) A box contains 12 packets of pencils. If each packet contains 12
pencils, how many pencils are there in such 20 boxes?
(d) How many hours are there in a year?
(e) The price list of some kitchen items is given below.

Prime Mathematics Book − 4 69

Find the cost of Price list
i) 15 rice cookers. Rice cooker : Rs. 3750
ii) 32 pressure cookers Pressure cooker : Rs. 2650
iii) 10 rice cookers and 3 gas stoves Gas stove : Rs. 5000
Bucket : Rs. 275

iv) 3 pressure cookers and 25 buckets.

Division
Let us subtract 4 from 20 until we get a remainder 0.

20 – 4 = 16, 16 – 4 = 12, 12 – 4 = 8, 8 – 4 = 4, 4 – 4 = 0. 4 is subtracted 5
times from 20 to get remainder 0. So, 20 ÷ 4 = 5

∴ Division is the repeated subtraction of the same number.

Class Work

1. Fill in the blanks as shown in the example:

(a) 6 – 2 = 4 – 2 = 2 – 2 = 0 ∴6÷2=3

(b) 8 – 4 – 4 ∴8÷4=2

12

(c) 12 – 3 = 9 – 3 = 6 – 3 = 3 – 3 = 0 ∴ ………………….. = …………………….
(d) 12 – 2 – 2 – 2 – 2 – 2 – 2 – 2 = 0 ∴ ………………….. = …………………….

1 234567

(e) 15 – 5 = 10 – 5 = 5 – 5 = 0 ∴ ………………….. = …………………….
(f) 16 – 4 – 4 – 4 – 4 = 0 ∴ ………………….. = …………………….

1 234

2. Fill in the blanks as shown in the example:
(a) How many times is 6 to be subtracted from 18 to get 0?
⇒ 18 – 6 = 12 – 6 = 6 – 6 = 0. So, 18 ÷ 6 = 3 times.

(b) How many times is 4 to be subtracted from 12 to get 0?
⇒ ………………………………………………. So, 12 ÷ 4 = ……………..

(c) How many fives are to be subtracted from 25 to get 0?
⇒ ………………………………………………. So, 25 ÷ 5 = ……………..

(d) How many seven are to be subtracted from 42 to get 0?
⇒ ………………………………………………. So, 25 ÷ 5 = ……………..

70 Prime Mathematics Book − 4

Study and learn: ∴ 18 ÷ 6 = 3
6 × 3 = 18 6 equal parts of 18 = 3 ∴ 42 ÷ 7 = 6
7 × 6 = 42 7 equal parts of 42 = 6 ∴ 32 ÷ 8 = 4
8 × 4 = 32 8 equal parts of 32 = 4 ∴ 45 ÷ 9 = 5
9 × 5 = 45 9 equal parts of 45 = 5

From the above observation, it is clear that the division is inverse process of
multiplication.

Look at the following basic properties (facts) of division:

• When we divide any number by 1, the quotient will be the number
itself.

e.g. 8 ÷ 1 = 8; 27 ÷ 1 = 27; 237 ÷ 1 = 237

• When we divide any number by itself, the quotient will always be 1.

e.g. 7 ÷ 7 = 1; 12 ÷ 12 = 1; 537 ÷ 537 = 1

• When 0 is divided by any non−zero number, the quotient is always 0.

e.g. 0 ÷ 5 = 0; 0 ÷ 38 = 0; 0 ÷ 212 = 0

• In 15 ÷ 5 = 3, 15 is called dividend, 5 is the divisor and 3 is the
quotient. A number which is left over after finding the quotient is
called the remainder. In case of 15 ÷ 5 = 3, the remainder is 0.

• When dividend is divided by divisor and the remainder is 0, then
the divisor and quotient are called the factors of dividend and the
dividend is the multiple (product) of two factors.

e.g. 10 ÷ 5 = 2 and remainder is 0.

So, 5 and 2 are the factors of 10 and 10 is the product of 5 and 2.

• Let us divide 87 by 4.

4)87(21 Here, divisor × quotient + remainder
−8 = 4 × 21 + 3
×7 = 84 + 3
−4 = 87 which is dividend.

3 ∴ Dividend = divisor × quotient + remainder.

Note for teacher:

Explain by giving different examples that the quotient may be smaller than, equal or greater than the
divisor and the remainder is always less than the divisor.

Prime Mathematics Book − 4 71

Class Work
1. Fill in the blanks:

(a) 7 ÷ 1 = ………………, 27 ÷ ……………. = 27, ……………… ÷ 1 = 127
(b) 8 ÷ ……………… = 8, 26 ÷ 1 = …….………., 217 ÷ 1 = ……………..
(c) 6 ÷ 6 = ………………, 16 ÷ ……………. = 1, …….…… ÷ 25 = 1
(d) 0 ÷ 9 = ……….., 0 ÷ 40 = ………………, …………… ÷ 35 = 0
(e) In 21 ÷ 7 = 3, the dividend is ……………….., the divisor is …………….,

the quotient is ……………. and the remainder is ……………………
(f) In 35 ÷ 5 = 7, 5 is the ……………………, 35 is the ………………….., and 7

is the ………………….
(g) 28 ÷ 4 = 7, the multiple is …………………, the factors are …………….

and …………….
(h) In 19 ÷ 4 = …………… is quotient and ………………… is the remainder.

∴ 19 = ……………….. × ………………. + …………………

Dividing by 10, 100, 200, 3000 etc.

Study and learn

Divide 4237 by 100

100)4237(42 When we divide a number
−400 by 100, we get the quotient by
×237 removing the last two digits of the
−200 dividend. The removed number
×37
will be the remainder.
∴ Quotient = 42
Reminder = 37 which is last two digits of dividend

In 7532 ÷ 100, quotient = 75 and remainder = 32
In 8745 ÷ 1000, quotient = 8 and remainder = 745
In 657 ÷ 10, quotient = 65 and remainder = 7

72 Prime Mathematics Book − 4

Divide 1800 by 30
Solution: 1800 ÷ 30
q1u83o00t0ie=n6t0= Remove the same
= 60 number of zeros from the end
∴ remainder = 0 of the dividend and the divisor.
Then divide the remaining digits
Divide 2400 by 600 of dividend by the remaining
Solution: 2400 ÷ 600
digits of divisor.

= q264u00o00tie=n4t = 4
∴ remainder = 0

Exercise: 3.5

1. Fill in the blanks:

(a) 274 ÷ 10; quotient = ………………., remainder = …………………..

(b) 4392 ÷ 10; quotient = ………………., remainder = …………………..

(c) 2437 ÷ 100; quotient = ………………., remainder = …………………..

(d) 7452 ÷ 100; quotient = ………………., remainder = …………………..

(e) 2789 ÷ 1000; quotient = ………………., remainder = …………………..

(f) 32578 ÷ 1000; quotient = ………………., remainder = …………………..

(g) 52387 ÷ 10000; quotient = ………………., remainder = …………………..

(h) 82357 ÷ 10000; quotient = ………………., remainder = …………………..

2. Find the quotient: (b) 600 ÷ 30 (c) 8000 ÷ 40
(a) 50 ÷ 10 (e) 1200 ÷ 400 (f) 15000 ÷ 500
(d) 2000 ÷ 200 (h) 9000 ÷ 30 (i) 75000 ÷ 500
(g) 24000 ÷ 800 (k) 36000 ÷ 90 (l) 84000 ÷ 1200
(j) 27000 ÷ 900

Prime Mathematics Book − 4 73

Division of a large number by two and three digit numbers:
While dividing a large number by two and three digit number, at first we write
the multiplication table of the given divisor. Then divide as many number of
digits of dividend at the higher places as the divisor has. But, if the divisor is
greater, take one more digit in the dividend then divide by the divisor.

Study and learn:

Example 1: Divide 4938 by 34.
Solution: 34)4938(145 Steps:
−34 i) Divisor 34 has two digits. So, at first we
153
−136 take two digits in the dividend which is
178 49. But 49 > 34.
−170 34 × 1 = 34, 34 × 2 = 68

8 < 34 49 < 68, we cannot divide 49 by 34 for 2
∴ Quotient = 145
times.
Remainder = 8 ii) Bring down 3, so number is 153. 34 × 3 =
102, 34 × 4 = 136, 34 × 5 = 170 153 < 170,
we cannot divide 153 by 34 for 5 times.
Therefore, 34 goes into 153 four times.

iii) Again bring down 8, so number is 178. 34
× 6 = 204. 178 < 204, so 178 is divided by
34 five times.

Example 2: Divide 2456 by 46. Steps:
Solution: 4 6 )2456(53 i) Divisor 46 has two digits. So, at first

−230 we take two digits in the dividend
156 which is 24. But 24<46. So, we take
−138 one more digit in the dividend. Then
18<46 the number is 245.
46 × 1 = 46, 46 × 2 = 92, 46 × 3 = 138
∴ Quotient = 53 46 × 4 = 184, 46 × 5 = 230, 46 × 6 = 276
Remainder = 18 245 < 276 but 245 > 230.
Therefore, 46 divides 245 five times.
74 Prime Mathematics Book − 4 ii) Bring down 6, so the number is 156.
156 < 184. Therefore 46 divides 156
three times.

Example 3: Divide 4938 by 134. Steps:
Solution: 134)4938(36 Divisor 134 has three digits. So,
−402 i) at first we take three digits in the
dividend which is 493. 493 > 134.
918 134 × 1 = 134, 134 × 2 = 268,
−804 134 × 3 = 402, 134 × 4 = 536.
1 1 4 < 134 493 < 536 but 493 > 402.
∴ Quotient = 36
Remainder = 114

Therefore, 134 divides 493, 3 times.

ii) Bring down 8. So, the number is 918.

134 × 6 = 804, 918 > 804 but

134 × 7 = 938, 938 > 918

Therefore, 134 divides 918, 6 times.

Examples 4: If 4060 chairs are arranged equally in 28 rows, how many
chairs are there in each row?
Solution: Here, total chairs = 4060 28)4060(145
No. of rows = 28 −28
Now, no. of chairs in 1 row = 4060 ÷ 28 126
−112
= 145 140
Therefore, 145 chairs in each row. −140

0

Exercise: 3.6 (d) 648 ÷ 36
1. Divide and check your result: (h) 25378 ÷ 56

(a) 418 ÷ 19 (b) 3210 ÷ 15 (c) 238 ÷ 17
(e) 5463 ÷ 24 (f) 8954 ÷ 47 (g) 3957 ÷ 33

2. Divide the following:
(a) 5798 ÷ 243 (b) 7524 ÷ 142 (c) 34572 ÷ 476 (d) 7496 ÷ 312
(e) 57943 ÷ 248 (f) 2940 ÷ 245 (g) 67432 ÷ 624 (h) 31340 ÷ 368

Prime Mathematics Book − 4 75

3. Solve the following word problems:
(a) The cost of 17 watches is Rs. 4131. What is the cost of 1 watch?
(b) 1495 pencils are to be shared equally among 65 students. How
many pencils will each student get?
(c) 1656 plants are planted in 23 columns. How many plants are
planted in each column?
(d) The price of 32 motorcycles is Rs. 3360000. Find the cost of one
motorcycle.
(e) The income of a man for one day is Rs. 432. In how many days does
he earn Rs. 11232?

4. Solve the following problems:
(a) When a number is divided by 42, the quotient and the remainder
are 63 and 24 respectively. Find the number.
(b) When a number is divided by 243, the quotient and the remainder
are 24 and 15 respectively. Find the number.
(c) How many times can 7 be subtracted from 56 to get 0?
(d) How many times can 42 be subtracted from 1470?
(e) The product of two number is 1512. If one the number is 27, find
the other?

Simplification

We are already familiar with the following signs.
'+' is the plus sign which makes the number positive.
' − ' is the minus sign which makes the number negative.
' × ' is the multiplication sign which multiplies the numbers.
' ÷ ' is the division sign which divides the numbers.

For identifying whether a number
is positive or negative, we should see
'+' or '−' with the given number. If there

is no any sign with the number, the
number is always positive.
+ 2 is a positive number.
3 is also positive number.
− 5 is a negative number.

76 Prime Mathematics Book − 4

Let's learn some rules of sign to use plus and minus sign while
doing any mathematical operations.

Rule 1: Addition of '+' (plus) sign numbers.
When we add the numbers with '+' (plus) sign only, the sum is also
of '+' sign.
(+ number) + (+number) = + number
For example: (+7) + (+2) = +9; (5) + (12) = 17

Rule 2: Addition of '−' (minus) sign numbers.
When we add the numbers with '−' (minus) sign only, the sum is
also of '−' sign.
(− number) + (− number) = − number
For example: (−8) + (−5) = −13; (−10) + (−12) = −22

Rule 3: Addition of '+' and '−' sign numbers:

When we add the numbers with '+' (plus) and '−' (minus) signs,

always subtract the smaller number from the greater one. The

result is '+' sign number if the greater number is '+' (plus).
Or, the result is '−' sign number if the greater number is '−'
(minus)
(+ number) + (− number) = (+ number) or (− number)
For example : (+8) + (−3) = +5, because (+8) > (−3)

(+7) + (−12) = −5, because (−12) < (+7)
(−15) + (11) = −4, because (−15) < (11)

Rule 4: Multiplication of '+' (plus) signed numbers:
When we multiply the numbers with '+' (plus) sing only, the product
is also of '+' (plus) sign.
(+ number) × (+ number) = (+ number)
For example: (+7) × (+3) = (+21); (9) × (7) = 63

(+5) × (+8) × (+12) = + 480

Rule 5: Multiplication of '−' (minus) singed numbers:
When we multiply the numbers with '−' sign only, the product is
also of '+' (plus) sign.
(− number) × (− number) = (+ number)
For example: (−9) × (−5) = +45; (−12) × (−7) = +84

Prime Mathematics Book − 4 77

Rule 6: Multiplication of '+' (plus) sing number and '−' (minus) sign
number:
When we multiply the numbers with '+' (plus) sign and '−' (minus)
sign, the product is of '−' (minus) sign.
(+ number) × (− number) = (− number)
(− number) × (+ number) = (− number)

For example: (+7) × (−6) = −42
(−8) × (+7) = − 56

Rule 7: The rule of sign of division are exactly same as the sign rules of
multiplication:
(a) (+ number) ÷ (+ number) = (+ number)

(+15) ÷ (+3) = +5

(b) (+ number) ÷ (− number) = (− number)
(+15) ÷ (−3) = −5

(c) (− number) ÷ (+ number) = (− number)
(−18) ÷ (+6) = −3

(d) (− number) ÷ (− number) = (+ number)
(−20) ÷ (−4) = +5

Exercise: 3.7

1. Add the following: (b) (+12) + (+27)
(a) (+8) + (+6) (d) (+4) + (+7)
(c) (+10) + (+19) (f) (+13) + (+25)
(e) (+19) + (+32) (h) (+12) + (+19) + (+21)
(g) (+5) + (+7) + (+9)

(i) (+6) + (+3) + (+7) + (+8) (j) (+31) + (+42) + (+21) + (+37)

2. Add the following: (b) (−2) + (−7)
(a) (+3) + (−8) (d) (−12) + (−17)
(c) (−6) + (−9)

78 Prime Mathematics Book − 4

(e) (−25) + (−32) (f) (−34) + (−21)
(−2) + (−5) + (−9)
(g) (−3) + (−5) + (−8) (h) (−12) + (−17) + (−21) + (−32)

(i) (−10) + (−17) + (−19) (j)

(k) (−32) + (−45) + (−27) + (−42)

3. Add the following: (b) (+12) + (−5)
(a) (+8) + (−3) (d) (+12) + (−21)
(c) (+4) + (−9) (f) (−8) + (+17)
(e) (−10) + (+17) (h) (−7) + (−6) + (+3)
(g) (−34) + (+21) (j) (−3) + (+4) + (+7) + (−6)
(i) (−4) + (−8) + (+5)
(k) (+6) + (+9) + (+5) + (−25)

4. Multiply the following: (b) (+6) × (+5)
(a) (+4) × (+7) (d) (+5) × (+8) × (+7)
(c) (+9) × (+6) (f) (−5) × (−9)
(e) (+7) × (+9) × (+12) (h) (−16) × (−14)
(g) (−12) × (−13) (j) (+8) × (−9)
(i) (+3) × (−8) (l) (−7) × (+4)
(k) (+5) × (−16) (n) (−23) × (+12)
(m) (−12) × (+6)

5. Divide the following: (b) (+14) ÷ (+7)
(a) (+9) ÷ (+3) (d) (+21) ÷ (−3)
(c) (+36) ÷ (+9) (f) (+56) ÷ (−8)
(e) (+42) ÷ (−6) (h) (−33) ÷ (+11)
(g) (−28) ÷ (+7) (j) (−8) ÷ (−2)
(i) (−96) ÷ (+12) (l) (−24) ÷ (−6)
(k) (−72) ÷ (−9)

Prime Mathematics Book − 4 79

Order of operation
We know that there are four fundamental operations in mathematics which
are addition, subtraction, multiplication and division.
A mathematical problem may contain two or more than two operations. Such
problem is solved by performing these operations in a proper order to get a
result.
The order of operation while simplifying the mathematical problem are :
(i) Division (ii) Multiplication (iii) Addition (iv) Subtraction

First ÷ (Division)

Multiplication after division × (Multiply)

Addition after multiplication + (Addition)

Subtraction at last − (Subtraction)

If we do not follow the order of operations, we will get the different answer
of the same problem. Look at the following example:

Operation in order Operation with out order
9+2×3 9+2×3

=9+6 = 11 × 3
= 15 (correct answer) = 33 (incorrect answer)

In the above example, when we performed the multiplication at first, we
got one answer and when we performed the addition at first, we got another
answer. But the correct answer of the above example is 15. So, to follow the
order of operation is important to solve such type of problems.

Study and learn the following examples:

Example 1: Simplify: 6 + 3 × 7

Solution: Here,

6+3×7

= 6 + 21 First multiply 3 × 7

= 27 Addition of 6 and 21

Example 2: Simplify: 5 + 6 × 4 − 13

Solution: Here,

5 + 6 × 4 − 13

= 5 + 24 − 13 First multiply 6 × 4

= 29 − 13 Addition of 5 and 24

= 16 Subtraction 13 from 29

80 Prime Mathematics Book − 4

Example 3: Simplify: 12 + 8 ÷ 4 − 4 × 5

Solution: Here,

12 + 8 ÷ 4 − 4 × 5

= 12 + 2 − 4 × 5 First divide 8 by 4

= 12 + 2 − 20 Multiply 4 × 5

= 14 − 20 Add 12 from 2

= −6 Subtract 14 from 20

Example 4: Simplify: 36 − 24 × 84 ÷ 21 + 15

Solution: Here,

36 − 24 × 84 ÷ 21 + 15

= 36 − 24 × 4 + 15 First divide 84 by 21

= 36 − 96 + 15 Multiply 24 × 4

= 36 + 15 - 96 Taking together +ve signed number

= 51 − 96 Add 36 and 15

= −45 Subtract 51 from 96

Example 5: 7 is subtracted from the product of 5 and 8. Express it in
mathematical form and then simplify.

Solution: The mathematical expression of the given statement is 5 × 8 − 7
= 40 − 7
= 33

Simplify the following: Class Work
9−3+4
(1) 5 + 8 −4 (2) (3) 4 + 3 × 5
=
== =

== (6) 12 × 3 − 15
=
(4) 12 − 2 × 4 (5) 6 × 3 + 7 =
= =
= =

(7) 20 ÷ 4 + 3 (8) 36 ÷ 9 − 2 (9) 21 + 3 × 4 − 8
= = =
= = =

Prime Mathematics Book − 4 81

(10) 9 + 16 ÷ 4 − 7 (11) 8 × 18 ÷ 6 − 19 (12) 45 ÷ 9 − 6 × 2
= = =
= = =

Exercise: 3.8

1. Simplify: (b) 6 − 9 + 8
(a) 12 + 7 − 9 (d) 8 − 3 + 6 − 5
(c) 49 + 35 − 52 (f) 32 − 19 + 45 − 12
(e) 12 + 32 − 15 − 17

2. Simplify: (b) 12 × 8 + 25
(a) 6 × 4 + 7 (d) 9 × 5 − 14
(c) 32 + 7 × 9 (f) 52 − 4 × 9
(e) 19 − 6 × 4

3. Simplify: (b) 4 × 8 − 26 + 17
(a) 18 + 4 × 7 − 27 (d) 36 ÷ 9 × 3 + 18
(c) 5 + 7 × 4 − 13 (f) 96 ÷ 12 + 7 × 5
(e) 14 − 45 ÷ 9 × 2 (h) 65 ÷ 13 × 4 − 17
(g) 48 ÷ 8 − 3 × 4
(i) 9 × 7 + 65 ÷ 5

4. Simplify:

(a) 45 − 5 × 7 + 24 − 17 (b) 13 × 4 + 32 − 4 × 5
12 × 6 + 35 − 72 ÷ 8
(c) 49 ÷ 7 × 5 + 19 − 31 (d) 42 + 90 ÷ 15 − 13 × 4
68 ÷ 17 × 9 + 18 − 29
(e) 17 + 27 ÷ 9 × 4 − 24 (f)

(g) 52 + 121 ÷ 11 − 14 × 3 + 16 (h)

5. Solve the following word problems:
(a) 9 is subtracted from the sum of 6 and 7.
(b) 13 is added to the product of 12 and 4.
(c) The product of 5 and 8 is added to 29.
(d) The product of 7 and 5 is subtracted from 39.
(e) The quotient of 45 divided by 9 is subtracted from 12.
(f) The quotient of 96 divided by 8 is added to the product of 7 and 4.

82 Prime Mathematics Book − 4

Simplification Involving Brackets
There are three types of brackets that we may use in simplification problems.
These three brackets are :

( ) Small or round bracket
{ } Middle or curly bracket
[ ] Large or square bracket
When we simplify the problems involving these brackets, we perform the
operation within bracket at first in the order of operations. The order of
operations of brackets are as follows:
At first, do the operations in order inside ( ) brackets
Then, do the operations in order inside { } brackets
Then, do the operations in order inside [ ] brackets
Thus, the order of operations in simplification can be concluded as BODMAS
where B stands for brackets, O stands for ‘of’ (multiply), D stands for division,
M stands for multiplication, A stands for addition and S for subtraction.
So, at first we perform the operation within brackets, then division, then
multiplication, then addition and at last subtraction.

Let's study and learn the following examples:

Example 1: Simplify: 10 + 25 − (12 − 8)

Solution: Here,

10 + 25 − (12 − 8)

= 10 + 25 − 4 Subtract 8 from 12 inside ( ).

= 35 − 4

= 31

Example 2: Simplify: 7 × 8 + (35 − 14) − 49

Solution Here,

7 × 8 + (35 − 14) − 49

= 7 × 8 + 21 − 49 Subtract 14 from 35 inside ( ).

= 56 + 21 − 49

= 77 − 49

= 28

Prime Mathematics Book − 4 83

Example 3: Simplify: 4 × 7 − (4 × 6) ÷ 3

Solution: Here,

4 × 7 − (4 × 6) ÷ 3

= 4 × 7 − 24 ÷ 3 Multiply 4 and 6 inside ( ).

=4×7−8

= 28 − 8

= 20

Example 4: Simplify: 24 + {50 ÷ (14 − 4) − 3} − 17

Solution: Here,

24 + {50 ÷ (14 − 4) − 3} − 17

= 24 + {50 ÷ 10 − 3} − 17 Subtract 4 from 14 inside ( ).

= 24 + {5 − 3} − 17 Divide 50 by 10 inside { }.

= 24 + 2 − 17 Subtract 3 from 5 inside [ ].

= 26 − 17

=9

Example 5: Simplify: 25 − [20 − {3 × 6 − (5 × 3) + 6} + 9] + 4
Solution: Here,

25 − [20 − {3 × 6 − (5 × 3) + 6} + 9] + 4
= 25 − [20 − {3 × 6 − 15 + 6} + 9] + 4
= 25 − [20 − {18 − 15 + 6} + 9] + 4
= 25 − [20 − {24 − 15} + 9] + 4
= 25 − [20 − 9 + 9] + 4
= 25 − [29 − 9] + 4
= 25 − 20 + 4
= 29 − 20
=9

84 Prime Mathematics Book − 4

Exercise: 3.9

1. Simplify:

(a) 8 + (9 + 7) (b) 6 + (8 − 5)

(c) 21 − (12 + 5) (d) 18 − (17 − 9)

(e) 7 × (5 − 3) (f) 8 × (6 + 5)

(g) 27 ÷ (6 + 3) (h) (37 + 18) ÷ 11

(i) 40 ÷ (4 − 3) (j) (7 + 3) × (9 − 5)

(k) (12 + 13) ÷ (9 − 4) (l) 8 + (12 − 18 ÷ 6)

(m) (15 + 12 ÷ 4) + (6 ÷ 3)

2. Simplify: (b) 5 × 3 + (18 − 13) − 27
(a) 8 + (12 − 3) ÷ 3 (d) 25 − {17 + (15 − 11)}
(c) 3 × 6 − (8 × 4) ÷ 16 (f) 16 ÷ {6 + (2 × 1)}
(e) 5 × {6 + (9 − 4)} (h) (9 × 6) − (45 ÷ 9) + 18
(g) {48 − (5 × 12 ÷ 4)} + 27
(i) {17 - (2 × 10 ÷ 5)} - 5

3. Simplify:
(a) 24 + {48 ÷ (13 − 5) − 2} − 19
(b) 4 × 3 + {29 − (28 − 7 × 2) ÷ 7}
(c) 17 + [6 + {8 − 5 + (5 × 26 ÷ 13)}]
(d) 3 × [20 − {5 + (9 − 3)}]
(e) 21 + {60 ÷ (9 − 4) − 6} + 8
(f) 28 − [12 + {16 − (36 ÷ 9 × 3)}]
(g) 27 + [54 − {72 ÷ (7 + 5 × 2 − 11) + 3} + 23]

Prime Mathematics Book − 4 85

Unit Revision Test

1. Complete the following additions:

(a) 3 4 7 8 9 2 (b) 8 4 2 4 7 (c) 9 9 9 9 9
76546 3683 9098
+4823 325
+47 73958
+7247

2. What is sum of the smallest and the greatest number of 4 digits
formed by the digits 7, 2, 0, 4, ?

3. Jamir spent Rs. 728 to buy a shirt, Rs. 563 to buy books and Rs.
986 to buy a calculator. How much money did he spend altogether?

4. Complete the following subtraction:

(a) 9 5 7 3 1 (b)9 2 1 0 5 2 (c) 4 7 3 2 3 7 5
−54265 −562573 −2473176

5. Ganesh Rai earns Rs. 9670 from service and Rs. 7563 from his business
every month. If he spends Rs. 12745 every month, how much does
he save in a month?

6. Perform the following multiplications:

(a) 2 7 5 3 (b) 3 5 6 4 (c) 8 3 2 0 6
×46 ×247 ×7000

7. A train travels 4732 Km in a day. How many Km does it travel in 130
days?

8. Perform the following divisions:

( a) 648 ÷ 36 ( b) 5626 ÷ 24 ( c) 8792 ÷ 314

9. The product of two numbers is 3645. If one of the numbers is 15,
find the other.

10. The cost of a calculator is Rs. 225. How many calculators can be
bought for Rs. 2700?

11. Simplify:

( a) 9 × 6 + 17 − 35 ( b) 8 + (9 − 3) − 4

( c) (15 − 6) − (5 × 7) ( d) {(7 − 3) × 6} ÷ (8 − 2)

86 Prime Mathematics Book − 4

Answers:

Exercise: 3.1

1. a) 587 b) 844 c) 6843 d) 163331 e) 915053 f) 13475225
k) 9138 l)15637
g) 8936 h) 188898 i) 5290 j) 138329 e) 311432
f) 98760
m) 88006 n) 88255 o) 1230114 p) 11120857 e) 11901009

2. a) 8677 b) 41724 c) 34653 d) 17470

3. a) 102653 b) 74194 c)94482947

4. Show to your teacher.

5. a) 81861 b) 93555 c) 81381 d) 107620
iii) 89510 d) 1069988
e) i) 53535 ii) 61725 c)1099999988

6. a) Rs.600 b) 1099999

Exercise:3.2

1. a) 33521 b) 31214c) 52232d) 313111

2. a) 324233 b) 3523415 c) 13123212 d) 52111354

3. Show to your teacher.

Exercise:3.3

1. a) 2149 b) 648 c) 17566 d) 34797 e) 27758 f) 150588

g) 76885 h) 1672675 i) 2546018 j) 2656498 k) 26706717

2. a) 509 b) 11446 c) 158889 d) 1 e) 1989678 f) 83908643

3. Show to your teacher.

4. a) 385 b) 666778 c) 348645 d) 130920 e) 40790 f) 795

5. a) 89999 b) 1 c) 7653210, 1023567 difference 6629643 d) 87408531

6. a) 454 b) 165217 c) 6877 d) 344575 e) 28141

7. a) Kathmandu b) Kabhrepalanchok c) 4494805 d) 1749988 e) 302962

Exercise: 3.4

1. a) 750 b) 1750 c) 25000 d) 145800 e) 9783000 f) 302400
f) 2292924
g) 2082000 h) 4230000 i) 826200 e) 31008 f) 142766
l) 14391132
2. a) 15708 b) 31698 c) 365370 d) 88236 e) 86562
k) 8643822 f) 3000 gms
g) 2850394 h) 13815775 i) 3699072 e) 4259928
e) 439950
3. a) 12145 b) 44477 c) 187866 d) 169901 e) 13500 cm

g) 2023553 h) 2988034 i) 13313664 j) 29621808 iv) Rs. 14825

4. a) 31744 b) 161520 c) 289602 d) 682668

5. a) 42550 b) 210000 c) 134900 d) 38880

6. a) 968350 b) 10800 sec c) 75600 km d) 16900 words

7. a) 99999000 b) 99999900 c) 2880 d) 8760 hours

e) i) Rs. 56250 ii) Rs. 84800 iii) Rs. 52500

Exercise-3.5

1. Quotient Remainder
a) 27 4
b) 439 2
c) 24 37

Prime Mathematics Book − 4 87

d) 74 52 d) 10 e) 3 f) 30 g) 30 h) 300 i) 150 j) 30
e) 2 789
f) 32 578
g) 5 2387
h) 8 2357
2. a) 5 b) 20 c) 200
l) 70
k) 400

Exercise: 3.6

1. a) 22 b) 214 c) 14 d) 18

e) Quotient = 227 Remainder = 15

f) Quotient = 190 Remainder = 24

g) Quotient = 119 Remainder = 30

h) Quotient = 453 Remainder = 10

2. a) Quotient = 23 Remainder = 209 b) Quotient = 52 Remainder = 140
c) Quotient = 72 Remainder = 300 d) Quotient = 24 Remainder = 8
e) Quotient = 233 Remainder = 159 f) Quotient = 12 Remainder = 0
g) Quotient = 108 Remainder = 40 h) Quotient = 85 Remainder = 60

3. a) 243 b) 23 c) 72 d) 1,05,000 e) 26
4. a) 2670
b) 5847 c) 8 d) 35 e) 56

1. a) 14 b) 39 c) 29 d) 11 e) 51 Exercise 3.7 h) 52 i) 24 j) 131 k) -146
2. a) -5 b) -9 c) -15 d) -29 e) -57 f) 38 g) 21 h) -16 i) -46 j) -82 k) -5
3. a) 5 b) 7 c) -5 d) -9 e) 7 f) -55 g)-16 h) -10 i) -7 j) 2 k) -80
4. a) 28 b) 30 c) 54 d) 280 e) 756 g) 9 g) -13 h) 224 i) -24 j) -72
f) 45 g) 156 k) 8 l) 4
l) -28 m) -72 n) -276 e) -7 h) -3 i) -8 j) 4
5. a) 3 b) 2 c) 4 d) -9 f) -7 g) -4

1. a) 10 b) 5 c) 32 d) 6 Exercise: 3.8 g) -6 h) 3 i) 76
2. a) 31 b) 121 c) 95 d) 31 e) 12 f) 46 g) 37 h) 25
3. a) 19 b) 23 c) 20 d) 30 e) -5 f) 16
4. a) 17 b) 64 c) 23 d) 98 e) 4 f) 43
5. a) 4 b) 61 c) 69 d) 4 e) 5 f) -4
e) 7 f) 40

1. a) 24 b) 9 c) 4 d) 10 Exercise: 3.9 g) 3 h) 5 i) 40 j) 40
k) 5 l) 17 m) 20 e) 14 f) 88
b) -7 c) 16 d) 4 g) 60 h) 67 i) 8
2. a) 11 b) 39 c) 36 d) 27 e) 55 f) 2 g) 89
3. a) 9 e) 35 f) 12

88 Prime Mathematics Book − 4

U4nit Measurements

(Time, Money, Length, Weight, Capacity)

Estimated periods − 29

Objectives

At the end of this unit, the students will be able to:
• tell time
• convert the units of time
• perform addition, subtraction, multiplication and division of money
• convert units of distances
• convert units of mass (gram and kilogram)
• perform addition and subtraction involved with cm, m and km, mg, g, and kg

Teaching Materials
• Watch/clock, calender, coins and notes of different denomination,
• balance and weights, scales, tapes, measuring vessels.

Activities

It is better to:
• discuss about the conversion of units of time
• discuss about the conversion from rupees to paisa and paisa to rupees
• discuss about the conversion of units of mass (gram and kilogram) and units of length

(cm, m, km)
• organize a game to find out the instruments of measurments
• organize a mathematical race using problem based on measurments.

Time

Bouddha, Mahankal -6, Ktm.
Cell: 9841427157, 9851187157

az} fv @)&$ Aprial/May 2017

Sun dial Hour glass Wrist watch Calendar

Read the following:

• Sun dial and hour glass were used to measure time in olden times.

• Wrist watch, wall / table clock , digital clock are modern means of
measuring time.

• A calendar is also used for time purposes.

• Face of a clock or watch is called dial .Dial of a clock or watch is divided
into 12 equal parts, 1 to 12. It consists three hands .The shortest and
thick hand is called hour hand which shows hours .The longest and thick
hand is called minute hand which shows minutes .The long and thin
hand is called second hand which shows seconds.

• 1 complete rotation by second hand
is 60 seconds. 1 complete rotation
by minute hand is 60 minutes and 1
complete rotation by hour hand is a
12 hours.

When the second hand makes 1
complete rotation, the minute hand Winding screw
1 Second hand
makes 60 th of complete rotation.

60 second = 1 minute and thus Hour hand

∴ 1 Minute hand
60
1 second = minutes

When the minute hand makes 1 complete rotation, the hour hand
1 th
makes 12 of its complete rotation.

∴ 60 minutes = 1 hour and thus 1 minute = 1 hours
60

90 Prime Mathematics Book − 4

Telling time

11 12 1 11 12 1 11 12 1Time to 11 12 1 11 12 1
10 2 10 2 10 2 Time past 10 2 10 2
93 93 93
84 84 84 9 39 3

765 765 765 84 84
20 minutes to 5 45 minutes past 4 765 765
Quarter to 5 (4:45) Half past
(4:40) 15 minutes past 7 10 minutes past 8
or quarter past 7 (7:15) (8:10)

• Time between midnight and mid day is a.m.
a.m. = ante meridiem (Latin) = before noon.
Time between mid day and mid night is p.m.
p.m = post meridiem (Latin) = after noon .

Exercise: 4.1

1. Write down the time shown by the following clocks in words and in
digits:

(a) 11 12 1 (b) 11 12 1 (c) 11 12 1

10 2 10 2 10 2

93 93 93

84 84 84
765 765 765

(d) 11 12 1 (e) 11 12 1 (f) 11 12 1

10 2 10 2 10 2
93 93 93

84 84 84
765 765 765

2. Draw the minute hand and hour hand in their correct position to
show the following times:

(a) 11 12 1 (b) 11 12 1 (c) 11 12 1

10 2 10 2 10 2

93 93 93
84 84 84
765 765 765

10 past 6 Quarter past 2 Half past 9

Prime Mathematics Book − 4 91

(d) 11 12 1 (e) 11 12 1 (f) 11 12 1

10 2 10 2 10 2

93 93 93
84
765 84 84
765 765
20 mins to 3
Quarter to 1 5 mins to 12

3. Write the time in a.m. or p.m.: (b) 7:00 in the evening
(a) 6:15 in the morning (d) 2:40 in the afternoon.
(c) 1:25 at night (f) 11:12 at night
(e) 10:10 in the morning

4. Fill in the blanks:
(a) It is 11:00 a.m. It will be …………… after 2 hours.
(b) It is 1:30 a.m. It will be …………….. after 5 hours.
(c) It is 1:00 p.m. It was ……………… before 3 hours.
(d) It is exact noon. It was ………….. before 4 hours.
(e) It is exact midnight. It was ………… before 7 hours.
(f) It is exact noon. It will be …………….. after 3 hours.

5. Convert the following :
(a) 30 minutes into seconds.
(b) 130 seconds into minutes and seconds.
(c) 2 hours into seconds.
(d) 6 minutes 20 seconds into seconds.
(e) 3 minutes and 40 seconds into seconds.

6. Change the following:
(a) 7 hours into minutes.
(b) 2 hours 15 minutes into minutes.
(c) 90 minutes into hours and minutes .
(d) 95 seconds into minutes and seconds.
(e) 2 hours, 30 minutes and 15 seconds into seconds.

7. Add:
(a) 3 hours 35 minutes and 6 hours 20 minutes.
(b) 8 hours 40 minutes and 6 hour 05 minutes.
(c) 10 hours 20 minutes 10 seconds and 3 hour 21 minutes 36 seconds.
(d) 8 hours 45 minutes 35 seconds and 7 hours 30 minutes 45 seconds.

92 Prime Mathematics Book − 4

8. Subtract :
(a) 2 hours 25 minutes from 6 hour 45 minutes.
(b) 5 hours 10 minutes from 9 hours 30 minutes.
(c) 10 hour 20 minutes 20 seconds from 20 hours 40 minutes 30
seconds.
(d) 14 hours 20 minutes 40 seconds from 21 hours 15 minutes 20
seconds.

9. Solve the following word problems :
(a) It is 1:45 p.m. What will be the time after 3 hour 45 minutes?
(b) In an examination, Sunita took 2 hours 30 minutes for written and
45 minutes for practical . For how long was she in the exam hall?
(c) The departure time of an aeroplane was at 3:45 p.m. Due to bad
weather it departed at 5:30 p.m. How long was the flight delayed ?
(d) Out of 24 hours in a day, a labour works for 14 hour 45 minutes.
How much time does he get to rest?

Days,Weeks, Months and Years

Read the following:

The duration from sunrise to next
sunrise is taken as a day. During this
time, the hour hand of the clock
makes. two complete rotations.
∴ 1 day = 24 hours.

On Saturday the school Day I Ii Iii Iv V Vi Vii
remains closed. It comes
after seven days again. The Sun Eng. C. Math Nep. Sci. Soci. Comp. Opt. Math
duration of 7 days is called
a week. Mon '' '' '' '' '' Health ''
∴ 1 week =7 days.
Tue '' '' '' '' '' Comp ''

Wed '' '' '' '' '' '' ''

Thu '' '' '' '' '' '' ''

Fri Game '' '' '' '' Health Game

Sat L E AVE − −

Prime Mathematics Book − 4 93

Teachers and school staffs Chaitra 2074 Mar/Apr 2017
get their salary on the first
of each month, after 30 Sun Mon Tue Wed Thu Fri Sat
days.
4 18 5 19 6 20 7 21 1 15 2 16 3 17
8 22 9 23 10 24

∴ 30 days = 1 month. Some 11 25 12 26 13 27 14 28 15 29 16 30 17 31
months have 28 or 29 or 31 18 1 19 2 20 3 21 4 22 5 23 6 24 7
or 32 days. 25 8 26 9 27 10 28 11 29 12 30 13

This year Kusum’s birth day is on 20th March . It will come again after a year
or after 365 days.

∴ 365 days = 1 year. Note: In leap year ∴ 366 days = 1 year
or 12 months = 1 year.

Workout Examples

Example 1: Convert 3 weeks and 5 days into days:
Solution: 3 weeks 5 days.
= 3×7 days + 5 days [ 1 week = 7 days ]
= 21 days + 5 days
= 26 days
∴ 3 week and 5 days =26 days

Example 2: Convert 42 days in to weeks:
Solution : 42 days
= (42 ÷ 7) weeks [ 7 days =1 week ]
= 6 weeks
∴ 42 days = 6 weeks

Example 3: Convert 2 years 3 months into days:
Solution: 2 years 3 months
= 2×365 days + 3×30 days [ 365 days =1 year]
= 730 days + 90 days [30 days = 1 month ]
= 820 days
∴ 2 years 3 months = 820 days

Example 4: Convert 125 days into months and days:
Solution: 125 days
= (125 ÷ 30) months 30)125(4
= 4 months 5 days −120
5

94 Prime Mathematics Book − 4

Example 5: Convert 52 months into year and months: 12)52(4 years
Solution: 52 months −48
4 months
= ( 52 ÷ 12) years [ 12 months = 1 year ]
= 4 years 4 months

Example 6: Add 2 years 9 months 24 days and 8 years 4 months 10 days:

Solution : year month day

2 9 24

+8 4 10

11 (10+1) 14 (12+2) 34 (30+4)

= 11 years 2 months 4 days

Example 7: Subtract : 4 weeks 5 days from 8 weeks 3 days:
Solution : weeks days
78 1 310
=7days 7 7 + 3 = 10

-4 5

35

= 3 weeks 5 days.

Exercise: 4.2

1. Convert the following into days:

(a) 5 weeks (b) 7 months

(c) 3 years (d) 4 weeks 2 days

(e) 8 months 15 days (f) 6 years 6 months 10 days

2. Convert the following into months:

(a) 5 years (b) 2 years 5 months

(c) 12 years (d) 90 days

3. Convert the following into years and months:

(a) 18 months (b) 130 months

(c) 1175 days (d) 850 days

Prime Mathematics Book − 4 95