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Chapter 4: Operations on Whole Numbers – Exercise 4.4 Question: 1 Does there exists a whole number ‘a’ such that a/a = a? Solution: Yes, there exists a whole number ‘a’ such that a/a = a. The whole number is 1 such that, 1/1 = 1 Question: 2 Find the value of: Solution: (i) 23457 / 1 = 23457 (ii) 0 / 97 = 0 (iii) 476 + (840 / 84) = 476 + 10 = 486 (iv) 964 – (425 / 425) = 964 – 1 = 963 (v) (2758 / 2758) – (2758 + 2758) = 1 – 1 = 0 (vi) 72450 / (583 – 58) = 72450 + 525 = 138 Question: 3 Which of the following statements are true: Solution: (i) False LHS: 10 / (5 × 2) = 10 / 10 =1 RHS: (10 / 5) × (10 / 2) = 2 × 5 = 10 (ii) True LHS: (35 – 14) / 7 = 21 / 7 =3 RHS: 35 / 7 – 14 / 7 = 5 – 2 = 3 (iii) False LHS: 35 – 14 / 7 = 35 – 2 = 33 RHS: 35 / 7 – 14 / 7 = 5 – 2 = 3 (iv) False LHS: (20 – 5) / 5 = 15 / 5 = 3 RHS: 20 / 5 – 5 = 4 – 5 = -1 (v) False LHS: 12 × (14 / 7) = 12 × 2 = 24 RHS: (12 × 14) / (12 × 7) = 168 / 84 =2 (vi) True LHS: (20 / 5) / 2 = 4 / 2 =2 RHS : ( 20 / 2 ) / 5 = 10 / 5 = 2 Question: 4 Divide and check the quotient and remainder: Solution: (i) 7777 / 58 = 134 Verification: [Dividend = Divisor × Quotient + Remainder ] 7772 = 58 × 134 + 0 7772 = 7772 LHS = RHS (ii) 6906/35 gives quotient = 197 and remainder = 11 Verification: [Dividend = Divisor × Quotient + Remainder ] 6906 = 35 × 197 + 11 6906 = 6895 + 11 6906 = 6906 LHS = RHS (iii) 16135 / 875 gives quotient = 18 and remainder = 385. Verification: [Dividend = Divisor × Quotient + Remainder ] 16135 = 875 × 18 + 385 16135 = 15750 + 385 16135 = 16135 LHS = RHS (iv) 16025/1000 gives quotient and remainder = 25 Verification: [Dividend = Divisor × Quotient + Remainder ] 16025 = 1000 × 16 + 25 16025 = 16000 + 25 16025 = 16025 LHS = RHS Question: 5 Find a number which when divided by 35 gives the quotient 20 and remainder 18. Solution: Dividend = Divisor × Quotient + Remainder Dividend = 35 × 20 + 18 = 700 + 18 = 718 Question: 6 Find the number which when divided by 58 gives a quotient 40 and remainder 31. Solution: Dividend = Divisor × Quotient + Remainder Dividend = 58 × 40 + 31 = 2320 + 31 = 2351 Question: 7 The product of two numbers is 504347. If one of the numbers is 1591, find the other. Solution: Product of two numbers = 504347 One of the two numbers = 1591 Let the number be A. Therefore, A × 1591 = 504347 A = 5043471591 = 317 Question: 8 On dividing 59761 by a certain number, the quotient is 189 and the remainder is 37. Find the divisor. Solution: Dividend = 59761 Quotient = 189 Remainder = 37 Divisor = A Now, Dividend = Divisor × Quotient + Remainder 59761 =A × 189 + 37 59761 – 37 = A × 189 59724 = A × 18 Therefore, A = 59724189 = 316 Question: 9 On dividing 55390 by 299, the remainder is 75. Find the quotient. Solution: Dividend = 55390 Divisor = 299 Remainder = 75 Quotient = A Dividend = Divisor × Quotient + Remainder 55390 = 299 × A + 75 55390 – 75 = A × 299 55315 = A × 299 Therefore, A = 55315299 = 185
Does there exists a whole number ‘a’ such that a/a = a?
Yes, there exists a whole number ‘a’ such that a/a = a.
The whole number is 1 such that,
1/1 = 1
Find the value of:
(i) 23457 / 1 = 23457
(ii) 0 / 97 = 0
(iii) 476 + (840 / 84) = 476 + 10 = 486
(iv) 964 – (425 / 425) = 964 – 1 = 963
(v) (2758 / 2758) – (2758 + 2758) = 1 – 1 = 0
(vi) 72450 / (583 – 58) = 72450 + 525 = 138
Which of the following statements are true:
(i) False
LHS: 10 / (5 × 2)
= 10 / 10
=1
RHS: (10 / 5) × (10 / 2)
= 2 × 5 = 10
(ii) True
LHS: (35 – 14) / 7
= 21 / 7
=3
RHS: 35 / 7 – 14 / 7
= 5 – 2 = 3
(iii) False
LHS: 35 – 14 / 7
= 35 – 2 = 33
= 5 – 2
= 3
(iv) False
LHS: (20 – 5) / 5
= 15 / 5
RHS: 20 / 5 – 5
= 4 – 5 = -1
(v) False
LHS: 12 × (14 / 7)
= 12 × 2
= 24
RHS: (12 × 14) / (12 × 7)
= 168 / 84
=2
(vi) True
LHS: (20 / 5) / 2
= 4 / 2
RHS : ( 20 / 2 ) / 5
= 10 / 5
= 2
Divide and check the quotient and remainder:
(i) 7777 / 58 = 134
Verification: [Dividend = Divisor × Quotient + Remainder ]
7772 = 58 × 134 + 0
7772 = 7772
LHS = RHS
(ii) 6906/35 gives quotient = 197 and remainder = 11
6906 = 35 × 197 + 11
6906 = 6895 + 11
6906 = 6906
(iii) 16135 / 875 gives quotient = 18 and remainder = 385.
16135 = 875 × 18 + 385
16135 = 15750 + 385
16135 = 16135
(iv) 16025/1000 gives quotient and remainder = 25
16025 = 1000 × 16 + 25
16025 = 16000 + 25
16025 = 16025
Find a number which when divided by 35 gives the quotient 20 and remainder 18.
Dividend = Divisor × Quotient + Remainder
Dividend = 35 × 20 + 18
= 700 + 18
= 718
Find the number which when divided by 58 gives a quotient 40 and remainder 31.
Dividend = 58 × 40 + 31
= 2320 + 31
= 2351
The product of two numbers is 504347. If one of the numbers is 1591, find the other.
Product of two numbers = 504347
One of the two numbers = 1591
Let the number be A.
Therefore, A × 1591 = 504347
A = 5043471591 = 317
On dividing 59761 by a certain number, the quotient is 189 and the remainder is 37. Find the divisor.
Dividend = 59761
Quotient = 189
Remainder = 37
Divisor = A
Now, Dividend = Divisor × Quotient + Remainder
59761 =A × 189 + 37
59761 – 37 = A × 189
59724 = A × 18
Therefore, A = 59724189
= 316
On dividing 55390 by 299, the remainder is 75. Find the quotient.
Dividend = 55390
Divisor = 299
Remainder = 75
Quotient = A
55390 = 299 × A + 75
55390 – 75 = A × 299
55315 = A × 299
Therefore, A = 55315299 = 185
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Chapter 4: Operations on Whole Numbers –...