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
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Verification: [Dividend = Divisor × Quotient + Remainder ]
7772 = 58 × 134 + 0
7772 = 7772
LHS = RHS
(ii) 6906/35 gives quotient = 197 and remainder = 11
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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.
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Verification: [Dividend = Divisor × Quotient + Remainder ]
16135 = 875 × 18 + 385
16135 = 15750 + 385
16135 = 16135
LHS = RHS
(iv) 16025/1000 gives quotient and remainder = 25
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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