Selina Concise Mathematics Class 6 ICSE Solutions Chapter 5 Natural Numbers and Whole Numbers

Selina Concise Mathematics Class 6 ICSE Solutions Chapter 5 Natural Numbers and Whole Numbers (Including Patterns)

Selina Publishers Concise Mathematics Class 6 ICSE Solutions Chapter 5 Natural Numbers and Whole Numbers (Including Patterns)

Natural Numbers and Whole Numbers Exercise 5A – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Fill in the blanks :
(i) Smallest natural number is …………..
(ii) Smallest whole number is …………
(iii) Largest natural number is …………
(iv) Largest whole number is ………..
(v) All natural numbers are …………
(vi) All whole numbers are not …………
(vii) Successor of 4099 is …………..
(viii) Predecessor of 4330 is …………….
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 5 Natural Numbers and Whole Numbers 1

Question 2.
Represent the following whole numbers on a number line :
0, 3, 5, 8, 10
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 5 Natural Numbers and Whole Numbers 2

Question 3.
State, true or false :
(i) Whole number are closed for addition.
(ii) If a and b are any two whole numbers, then a + b is not a whole number.
(iii) If a and b are any two whole numbers, then a + b = b + a
(iv) 0 + 18= 18 + 0
(v) Addition of whole numbers is associative.
(vi) 10 + 12 + 16 = (10 + 12) + 16 = 10 + (12 + 16)
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 5 Natural Numbers and Whole Numbers 3

Question 4.
Fill in the blanks :
(i) 54 + 234 = 234 + …………
(ii) 332 + 497 = ………… + 332
(iii) 286 + 0 = ………..
(iv) 286 x 1 = ……….
(v) a + (b + c) = (a + ………) + c
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 5 Natural Numbers and Whole Numbers 4

Question 5.
By re-arranging the given numbers, evaluate :
(i) 237 + 308 + 163
(ii) 162 + 253 +338 + 47
(iii) 21 + 22 + 23 + 24 + 25 + 75 + 76 + 77 + 78 + 79
(iv) 1 + 2 + 3 + 4 + 596 + 597 + 598 + 599
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 5 Natural Numbers and Whole Numbers 5

Question 6.
Is a + b + c = a + (b + c) = (b + a) + c ?
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 5 Natural Numbers and Whole Numbers 6

Question 7.
Which property of addition is satisfied by :
(i) 8 + 7 = 15
(ii) 3+ (5 + 4) = (3 + 5)+ 4
(iii) 8 x (8 + 0) = 8 x 8 + 8 x 0
(iv) (7 + 6) x 10 = 7 x 10 + 6 x 10
(v) (15 – 12) x 18 = 15 x 18 – 12 x 18
(vi) 16 + 0= 16
(vii) 23 + (-23) = 0
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 5 Natural Numbers and Whole Numbers 7

Question 8.
State, True or False :
(i) The sum of two odd numbers is an odd number.
(ii) The sum of two odd numbers is an even number.
(iii) The sum of two even numbers is an even number.
(iv) The sum of two even numbers is an odd number.
(v) The sum of an even number and an odd number is odd number.
(vi) Every whole number is a natural number.
(vii) Every natural number is a whole number.
(viii) Every whole number + 0 = The whole number itself.
(ix) Every whole number x 1 = The whole number itself.
(x) Commutativity and associativity are properties of natural numbers and whole numbers both.
(xi) Commutativity and associativity are properties of addition for natural numbers and whole numbers both.
(xii) If x is a whole number then -x is also a whole number.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 5 Natural Numbers and Whole Numbers 8

Natural Numbers and Whole Numbers Exercise 5B – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Consider two whole numbers a and b such that a is greater than b.
(i) Is a – b a whole number? Is this result always true?
(ii) b – a a whole number? Is this result always true?
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 5 Natural Numbers and Whole Numbers 9

Question 2.
Fill in the blanks :
(i) 8 – 0 = ……….. and 0 – 8 = ……….
8 – 0 ≠ 0 – 8, this shows subtraction of whole numbers is not ………..
(ii) 5 – 10 = ………., which is not a …………
⇒ Subtraction of ……….. is not closed.
(iii) 7 – 18 = ……….. and (7 – 18) – 5 = …………..
18 – 5 = …………. and (7 – 18) – 5 = ………….
Is (7 – 18) – 5 = 7 – (18 – 5) ?
⇒ Subtraction of whose numbers is not ………….
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 5 Natural Numbers and Whole Numbers 10

Question 3.
Write the identify number, if possible for subtraction.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 5 Natural Numbers and Whole Numbers 11

Question 4.
Write the inverse, if possible for subtraction of whole numbers ?
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 5 Natural Numbers and Whole Numbers 12

Question 5.
12 × (9 – 6) = ………….. = ………….
12 × 9 – 12 × 6 = …………. = …………….
Is 12 × (9 – 6) = 12 × 9 – 12 × 6 ? ………….
Is this type of result always true ? ……………
Name the property used here …………..
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 5 Natural Numbers and Whole Numbers 13

Question 6.
(16 – 8) × 24 = ………….. = …………..
16 × 24 – 8 × 24 = …….. – ……….. = ………..
Is (16 – 8) × 24 = 16 × 24 – 8 × 24 ? …………..
Is the type of result always true? ………….
Name the property used here ………………
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 5 Natural Numbers and Whole Numbers 14

Natural Numbers and Whole Numbers Exercise 5C – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Fill in the blanks :
(i) 42 × o = ……….
(ii) 592 × 1 = ………..
(iii) 328 × 573 = ……….. × 328
(iv) 229 × ………… = 578 × 229
(v) 32 × 15 = 32 × 6 + 32 × 7 + 32 × ……….
(vi) 23 × 56 = 20 × 56 + ……… × 56
(vii) 83 × 54 + 83 × 16 = 83 × ( ……….. ) = 83 × ………….. = …………
(viii) 98 × 273 – 75 × 273 = ( …………. ) × 273 = ………… × 273
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 5 Natural Numbers and Whole Numbers 15

Question 2.
By re-arranging the given numbers, evaluate :
(i) 2 × 487 × 50
(ii) 25 × 444 × 4
(iii) 225 × 20 × 50 × 4
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 5 Natural Numbers and Whole Numbers 16

Question 3.
Use distributive law to evaluate :
(i) 984 × 102
(ii) 385 × 1004
(iii) 446 × 10002
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 5 Natural Numbers and Whole Numbers 17

Question 4.
Evaluate using properties :
(i) 548 × 98
(ii) 924 × 988
(iii) 3023 × 723
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 5 Natural Numbers and Whole Numbers 18

Question 5.
Evaluate using properties :
(i) 679 × 8 + 679 × 2
(ii) 284 × 12 – 284 × 2
(iii) 55873 × 94 + 55873 × 6
(iv) 7984 × 15 – 7984 × 5
(v) 8324 × 1945 – 8324 × 945
(vi) 3333 × 987 + 13 × 3333
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 5 Natural Numbers and Whole Numbers 19

Question 6.
Find the product of the :
(i) greatest number of three digits and smallest number of five digits.
(ii) greatest number of four digits and the greatest number of three digits.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 5 Natural Numbers and Whole Numbers 20

Question 7.
Fill in the blanks :
(i) (437 + 3) × (400 – 3) = 397 × ……….
(ii) 66 + 44 + 22 = 11 × (………..) = 11 × ……….
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 5 Natural Numbers and Whole Numbers 21

Question 8.
Evaluate :
(i) 355 × 18
(ii) 6214 × 12
(iii) 15 × 49372
(iv) 9999 × 8
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 5 Natural Numbers and Whole Numbers 22

Natural Numbers and Whole Numbers Exercise 5D – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Show that :
(i) division of whole numbers is not closed
(ii) any whole number divided by 1, always gives the number itself.
(iii) every non-zero whole number divided by itself gives 1 (one).
(iv) zero divided by any non-zero number is zero only.
(v) a whole number divided by 0 is not defined.
For each part, given above, give an example.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 5 Natural Numbers and Whole Numbers 23

Question 2.
If x is a whole number such that x ÷ x = x, state the value of x.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 5 Natural Numbers and Whole Numbers 24

Question 3.
Fill in the blanks :
(i) 987 + 1 = …………
(ii) 0 + 987 = ……….
(iii) 336 – (888 + 888) = ……….
(iv) (23 + 23) – (437 + 437) = ………
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 5 Natural Numbers and Whole Numbers 25

Question 4.
Which of the following statements are true ?
(i) 12 ÷ (6 × 2) = (12 ÷ 6) × (12 ÷ 2)
(ii) a ÷ (b – c) = \(\frac { a }{ b } -\frac { a }{ c }\)
(iii) (a – b) ÷ c = \(\frac { a }{ c } -\frac { b }{ c }\)
(vi) (15 – 13) ÷ 8 = (15 ÷ 8) – (13 ÷ 8)
(v) 8 ÷ (15 – 13) = \(\frac { 8 }{ 15 } -\frac { 8 }{ 13 }\)
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 5 Natural Numbers and Whole Numbers 26

Natural Numbers and Whole Numbers Exercise 5E – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Find the difference between the largest number of four digits and the smallest number of six digits.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 5 Natural Numbers and Whole Numbers 27

Question 2.
Find the difference between the smallest number of eight digits and the largest number of five digits.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 5 Natural Numbers and Whole Numbers 28

Question 3.
The product of two numbers is 528. If the product of their unit’s digits is 8 and the product of their ten’s digits is 4 ; find the numbers.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 5 Natural Numbers and Whole Numbers 29
Question 4.
Does there exist a number a such that a ÷ a = a?
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 5 Natural Numbers and Whole Numbers 30

Question 5.
Divide 5936 by 43 to find the quotient and remainder. Also, check your division by using the formula,
dividend = divisor × quotient + remainder.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 5 Natural Numbers and Whole Numbers 31

Natural Numbers and Whole Numbers Exercise 5F – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
(i) 1 × 9 + 1 = 10
12 × 9 + 2 = 110
123 × 9 + 3 = 1110
(ii) 9 × 9 + 7 = 88
98 × 9 + 6 = 888
987 × 9 + 5 = 8888
(iii) 1 × 8 + 1 = 9
12 × 8 + 2 = 98
123 × 8 + 3 = 987
(iv) 111 ÷ 3 = 37
222 ÷ 6 = 37
333 ÷ 9 = 37
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 5 Natural Numbers and Whole Numbers 32

Question 2.
Complete each of the following magic squares :
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 5 Natural Numbers and Whole Numbers f 2
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 5 Natural Numbers and Whole Numbers 33
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 5 Natural Numbers and Whole Numbers 34

Question 3.
See the following pattern carefully :
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 5 Natural Numbers and Whole Numbers f 3
(i) If n denotes the number of figure and S denotes the number of matches ; find S in terms of n.
(ii) Find how many matches are required to make the :
(1) 15th figure
(2) 40th figure
(iii) Write a discretion of the pattern in words.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 5 Natural Numbers and Whole Numbers 35

Question 4.
(i) In the following pattern, draw the next two figures.
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 5 Natural Numbers and Whole Numbers f 4
(ii) Construct a table to describe the figures in the above pattern.
(iii) If n denotes the number of figure and L denotes the number of matches, find L in terms of n.
(iv) Find how may matches are required to make the :
(1) 12th figure
(2) 20th figure
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 5 Natural Numbers and Whole Numbers 36

Question 5.
In each of the following patterns, construct next figure.
(i) In each case, if n denotes the number of figure and F denotes the number of matchsticks used, find F in terms of n.
(ii) Also find, in each case, how many matches are required to make the : 16th figure and 30th figure.
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 5 Natural Numbers and Whole Numbers f 5
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 5 Natural Numbers and Whole Numbers f 5.1
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 5 Natural Numbers and Whole Numbers 37
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 5 Natural Numbers and Whole Numbers 38

Selina Concise Mathematics Class 6 ICSE Solutions