Operation On Whole Numbers ICSE Class-6th RS Aggarwal Goyal Brothers Prakashan Chapter-2. We provide step by step Solutions of Exercise / lesson-2 Operation On Whole Numbers for ICSE Class-6 RS Aggarwal Mathematics .
Our Solutions contain all type Questions with Exe-2 A, Exe-2 B, to develop skill and confidence. Visit official Website CISCE for detail information about ICSE Board Class-6 Mathematics.
| Board | ICSE |
| Publications | Goyal brothers Prakshan |
| Subject | Maths |
| Class | 6th |
| Chapter-2 | Operation On Whole Numbers |
| Writer | RS Aggrawal |
| Book Name | Foundation |
| Topics | Solution of Exe-2 A, Exe-2 B |
| Academic Session | 2021-2022 |
Operation On Whole Numbers ICSE Class-6th RS Aggarwal Goyal Brothers Prakashan Chapter-2
–: Select Topics :–
Properties of Whole Numbers
- Addition and multiplication of any 2 whole number give a whole number.
- Subtraction and division of any 2 whole number may or may not give a whole number.
What is a Number line?
A number line is a picture of a graduated straight and horizontal line in which numbers are written. A number written on the left-hand side of the number line is lesser and number written on the right-hand side of the number line is greater.
Natural numbers
- Numbers that are used for counting and ordering are called natural Numbers.
- 1,2,3,4,5,6… are natural numbers
Whole numbers
- Natural numbers along with zero form the collection of whole numbers.
- 0,1,2,3,4,5… are called whole numbers.
Predecessor and Successor
- A successor of any number is the next number to it, which is obtained by adding 1.
- A predecessor of any number is the previous number to it, which is obtained by subtracting 1.
- For example, predecessor and successor of the number 12 is 12 – 1 and 12 + 1 which is 11 and 13
Properties of Operators: Commutative Associative and Distributive
Division by zero
Division of any whole number by 0 is not defined.
Mathematical operations are simplified due to certain properties that every number follows. They are:
-
Commutative property
Addition and multiplication are commutative for whole numbers. i.e whole numbers can be added or multiplied in any order.
For e.g: 2 + 3 = 5 = 3 + 3 × 4 = 12 = 4 × 3
-
Associative property
Associativity of addition and multiplication
For eg: (5 +6) + 4 = 15 = 5 + (6 + 4)
(2 × 3) × 4 = 24 =2 × (3 × 4)
-
Distributive Property
With distributivity property, 4 × (5 + 3) can be written as (4 × 5) + (4 × 3)
Here, 4 × (5 + 3) = 4 × 13 = 52
Also, (4 × 5) + (4 × 3) = 20 + 32 = 52
There exists certain numbers, when included in mathematical operations like addition and multiplication, the value of the operation remains unchanged. Such numbers are called as identities.
Additive Identity
Additive identity gives the same whole number when added to another whole number.
Zero is the additive identity as a + 0 = a, (a is any whole number).
Multiplicative Identity
Multiplicative identity gives the same whole number when multiplied by another whole number.
1 is the Multiplicative identity as a × 1 = a, (a is any whole number)
Exercise – 2 A, Operation On Whole Numbers ICSE Class-6th RS Aggarwal Goyal Brothers Prakashan
Page 36-37
Question 1
fill in the blanks………
(i) 168 + 259 = …. + 168
(ii) …. + 317 =317
(iii) (37 + 18 ) + …. = 37 + (….. + 56)
(iv) 8 + 3 * 4 = ….
(v)18 * (….. + 23) = (18 * 17) + (18 * ….)
Answer
(i) 168 + 259 = 259 + 168
(ii) 0 + 317 =317
(iii) (37 + 18 ) + 56 = 37 + (68 + 56)
(iv) 8 + 3 * 4 = 20
(v)18 * (17 + 23) = (18 * 17) + (18 * 23)
Question 2
fill in the blanks………
(i) 237 * 1 = ……………………
(ii) 56 * ……….. = 0
(iii) 0/53 = ………………
(iv) 37 * 59 = 59 * ……………..
(v) 0 * 138 = ………………….
(vi)73/73 = …..
Answer
(i) 237 * 1 = 237
(ii) 56 * 0 = 0
(iii) 0/53 = 0
(iv) 37 * 59 = 59 * 37
(v) 0 * 138 = 0
(vi)73/73 = 1
Question 3
Divide 3605 by 29 and verify the division algorithm.
Answer
29 ) 3605 ( 124
Re = 9
Quotient = 124,
Reminder = 9
Dividend = (Divisor * Quotient ) + Reminder
= 29 * 124 + 9
= 3596 + 9 = 3605
Question 4
Find the number which when divided by 45 gives 16 as quotient and 9 as reminder.
Answer
Dividend = (Divisor * Quotient ) + Reminder
Here,
Deviser = 45,
Quotient = 16,
Reminder = 9
= (45 *16 ) + 9
720 + 9
= 729
Question 5
Find the ………………. by 57
Answer
Largest 5 digit number = 99999
on dividing by 57,
57 ) 99999 ( 1754
Reminder = 21
so Required number = 99999-21=99978
Question 6
Find the …………………. by 63
Answer
Smallest six digit number = 100000
On diving by 63,
63 ) 100000 ( 1587
Reminder = 19
Question 7
On dividing …….. find the divisor.
Answer
Dividend = (Divisor * Quotient ) + Reminder
Here,
Dividend – 1653,
Quotient = 45,
Reminder = 33
then divisor = 1653 = (divisor * 45) + 33
45 * divisor = 1653-33 = 1620
divisor = 1620/45
= 36
Question 8
Use distributive ……
(i) 576 ….
(ii) 385 …..
(iii) 365 …..
(iv) 407 …….
Answer
(i) Using distributive law [a(b+c)]
= 576 (285 + 115)
= 576 (400)
230400
(ii) 385 * 178 – 385 * 78
Using distributive law [a(b+c)]
= 85 (178 – 78)
= 385 (100)
= 38500
(iii) 365 * 645 + 135 * 645
Using distributive law [a(b+c)]
= 645 (36 + 135)
= 645 (500)
= 322500
(iv) 407 * 168 – 307 * 168
Using distributive law [a(b+c)]
= 168 (407 – 307)
168 (100)
16800
Question 9
Using the most ……… product :
(i) ……..
(ii) ………..
(iii) ……….
(iv) …………
Answer
(i) 5 * 648 * 20
= 5 * 20 * 648
=64800
(ii) 8 * 329 * 25
= 8 * 25 * 329
= 65800
(iii) 8 * 12 * 25 * 7
= 56 * 300
= 16800
(iv) 125 * 40 * 8 * 25
= 1000 * 1000
= 1000000
Question 10
Divide and ……. algorithm :
(i) ….
(ii) …..
(iii) ….
Answer
(i) 87 ) 3680 (42
Reminder = 26
Dividend = (Divisor * Quotient ) + Reminder
(87 * 42)+ 26
=3654 + 26
=3680
(ii) 327 ) 17368 (53
Reminder 37
Dividend = (Divisor * Quotient ) + Reminder
(327 * 53)+ 37
17331 + 37
= 17368
(iii) 265 ) 32679 (123
Reminder 84
Dividend = (Divisor * Quotient ) + Reminder
(265 * 123)+ 84
= 32595 + 84
= 32679
Question 11
Verify each of the following :
(i) ………..
(ii)………….
(ii)…………
(iv)……….
Answer
(i) 2867 + 986
= 986 – 2867
[so (a+b) = (b+a)]
2867 – 2867 = 986 – 986
0=0
(ii)
368 * 215
= 215 * 368
[so (a+b) = (b+a)]
Commutative law of multiplication
(iii) (156 + 273 ) + 74= 156 + (273 + 74)
[so (a+b) = (b+a)]
Associative law of multiplication
(iv) (85 * 55) * 110 = 86 * (55 * 1110)
[so (a+b) = (b+a)]
Associative law of multiplication
Question 12
Simplify :
(i) ………..
(ii)………..
(ii)………..
(iv)………….
(v)…………..
Answer
(i)
39 – 18 / 3+ 2 * 3
= 39 – 6 + 2 * 3
= 39 – 6 + 6 = 39
(ii)
8 + 2 * 5
= 8 + 10 = 18
(iii)
5 + 8 – 6 / 2
= 5 * 8 – 3
(iv)
=19 – 9 * 2
= 19 – 18 = 1
(v)
15 / 5 * 4 / 2
= 3 * 2 = 6
RS Aggarwal Solutions Operation On Whole Numbers ICSE Class-6th Goyal Brothers Prakashan Exercise – 2 B
Page 38-39
Question 1
Study following pattern, in each case write the next three step…………
(i)
111 / 3 = 37
222 / 6 = 37
333 / 9 = 37
444 / 12 = 37
(ii)
999999 * 1 = 0999999
999999 * 2 = 1999998
999999 * 3 = 2999998
999999 * 4 = 3999996
(iii) ……………..
Answer
(i)
111 / 3 = 37
222 / 6 = 37
333 / 9 = 37
444 / 12 = 37
555 / 15 = 37
666 / 18 = 37
777 / 21 = 37
(ii)
999999 * 5 = 4999995
999999 * 6 = 5999994
999999 * 7 = 6999993
(iii)
123456789 * 45 = 555555555
123456789 * 54 = 666666666
123456789 * 63 = 7777777777
123456789 * 36 = 444444444
Question 2
Observe ……………… that follow :…………..
(i) ……….
(ii)…………
(iii)………..
Answer
(i) 5
(ii) 13 + 14 + 15 + 16 + 17 = 75
(iii) No, since the sum is a multiple of 5, and 92 is not a multiple of 5.
Question 3
Complete each one of the ……………. missing number :
(i) …….
(ii)……….
(iii)…………..
(iv)………..
Answer
(i)
| 4 | 9 | 2 |
| 3 | 5 | 7 |
| 8 | 1 | 6 |
In each row/colum, the sum = 15
(ii)
| 16 | 2 | 12 |
| 6 | 10 | 14 |
| 8 | 18 | 4 |
In each row/colum, the sum = 30
(iii)
| 2 | 15 | 16 | 5 |
| 9 | 12 | 11 | 6 |
| 13 | 8 | 7 | 10 |
| 14 | 3 | 4 | 17 |
In each row/colum, the sum = 38
(iv)
| 7 | 18 | 17 | 4 |
| 8 | 13 | 14 | 11 |
| 12 | 9 | 10 | 15 |
| 19 | 6 | 5 | 16 |
In each row/colum, the sum = 46
–: End of Operation On Whole Numbers ICSE Class-6th RS Aggrawal Solutions :–
Return to- RS Aggarwal Solutions for ICSE Class-6 Goyal Brothers Prakashan
Thanks
