Selina solutions concise mathematics class 6 icse Solutions for Chapter 5 natural numbers and whole numbers including patterns

Q1) 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 …………….

Q2)Represent the following whole numbers on a number line :

0, 3, 5, 8, 10

Q3)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)

Q4)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

Q5) By rearranging 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

Q6) Is a + b + c = a + (b + c) = (b + a) + c ?

Q7) Which property of addition is satisfied by:

(i) 8 + 7 = 15

(ii) 3+ (5 + 4) = (3 + 5)+ 4

(iii) 8\times\left(8+0\right)=8\times8+8\times0

(iv) \left(7+6\right)\times10=7\times10+6\times10

(v) \left(15-12\right)\times18=15\times18-12\times18

(vi) 16 + 0= 16

(vii) 23 + (-23) = 0

Q8) 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.

Q1) 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?

Q2) 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 ………….

Q3) Write the identify number, if possible for subtraction.

Q6) \left(16-8\right)\times24=…………..=…………

16\times24-8\times24=………….=…………

Is \left(16-8\right)\times24=16\times24-8\times24?\ …………

Is this type of result always true ? ……………

Name the property used here …………..

Q1) Fill in the blanks:

(i) 42\times0=……….

(ii) 592\times1=………

(iii) 328\times572=……….\times328

(iv) 229\times………..=578\times229

(v) 32\times15=32\times6+32\times7+32\times………

(vi) 23\times56=20\times56+…….\times56

(vii) 83\times54+83\times16=83\times\left(……….\right)=83\times…….=………

(viii) 98\times273-75\times273=\left(………\right)\times273=……….\times273

Q2) By rearranging the given numbers, evaluate :

(i) 2 × 487 × 50

(ii) 25 × 444 × 4

(iii) 225 × 20 × 50 × 4

Q3) Use distributive law to evaluate :

(i) 984 × 102

(ii) 385 × 1004

(iii) 446 × 10002

Q4) Evaluate using properties :

(i) 548 × 98

(ii) 924 × 988

(iii) 3023 × 723

Q5)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

Q6) 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.

Q7) Fill in the blanks :

(i) (437 + 3) × (400 – 3) = 397 × ……….

(ii) 66 + 44 + 22 = 11 × (………..) = 11 × ……….

Q8) Evaluate :

(i) 355 × 18

(ii) 6214 × 12

(iii) 15 × 49372

(iv) 9999 × 8

Q1) 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.

Q2) If x is a whole number such that x ÷ x = x, state the value of x.

Q3) Fill in the blanks :

(i) 987 ÷ 1 = …………

(ii) 0 ÷ 987 = ……….

(iii) 336 – (888 ÷ 888) = ……….

(iv) (23 ÷ 23) – (437 ÷ 437) = ………

Q4) Which of the following statements are true ? (i) 12\div\left(6\times2\right)=\left(12\div6\right)\times\left(12\div2\right)

(ii) a\div\left(b-c\right)=\frac{a}{b}-\frac{a}{c\ }

(iii) \left(a-b\right)\div c=\frac{a}{c}-\frac{b}{c}

(iv) \left(15-13\right)\div8=\left(15\div8\right)-\left(13\div8\right)

(v) 8\div\left(15-13\right)=\frac{8}{15}-\frac{8}{13}

Q1) Find the difference between the largest number of four digits and the smallest number of six digits.

Q2) Find the difference between the smallest number of eight digits and the largest number of five digits.

Q3) 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.

Q4) Does there exist a number a such that a ÷ a = a?

Q5) Divide 5936 by 43 to find the quotient and remainder. Also, check your division by using the formula,

dividend = divisor × quotient + remainder.

Q1)

(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

Q2) Complete each of the following magic squares :

Q3) See the following pattern carefully :

(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.

Q5) 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.

(a)

(b)

(c)

(d)

(e)

(f)