Ch. 02. Whole Numbers
लेखक
ॐ जितेन्द्र सिंह तोमर
M.A., B.Ed., DNYS, MASSCOM.
10/4/10/2/2022
2.1 Natural Numbers
The collection of the counting numbers form Natural Numbers.
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 ....... ∞
2.2 Whole Numbers
The collection of the natural numbers along with zero form whole numbers.
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 ....... ∞
2.3 Predecessor and successor
Successor –> More than one of actual Number.
Add 1 to get Successor
Predecessor –> Less than one of actual Number.
Subtract 1 to get Predecessor
2.4 Properties Of Whole Numbers
a) Closure property : Whole numbers are closed under addition and also under multiplication.
a + b = c
a × b = c
(Not for Subtraction and Division)
Mind it that
i) Division to Zero by any Number is always Zero.
0/(Whole Number) = 0
ii) Division by zero is always not defined.
(Whole Number)/0 = ∞
b) Commutative Property : Whole numbers are commutative for Addition and multiplication.
a + b = b + a
a × b = b × a
(Not for Subtraction and Division)
c) Distributive Property
Whole numbers shows Distributive Property of multiplication over addition or subtraction
a × (b + c) = ab + ac
a × (b – c) = ab – ac
d) Inverse Property of Distributivity
Whole numbers shows Distributive Property of multiplication over addition or subtraction
ab + ac = a (b + c)
ab – ac = a (b – c)
* Zero is the identity for addition of whole numbers.
a + 0 = a
m + 0 = m
x + 0 = x
* The whole number 1 is the identity for multiplication of whole numbers.
a × 1 = a
m × 1 = m
x × 1= x
Chapter 2
Whole Numbers
Points to Remember:
• Whale Number: The natural number along with zers 0, form the collection of whole numbers. 0 is the smallest whole number.
Predecessor of Number
predecessor is that number which comes Immediately before the given natural number. It's obtained by subtracting 1 from the given number.
for e.g. Predecer of 45 in 45–1=44
Succesur of a Number:
The succesur of a whole number is the number
For e.g. succesur 45 x 45+1= 46
Every whole number has it's succesur
are present of whole number on the number line
Division of a whole numbers by pers is not defined.
0 is called the ADDITIVE IDENTITY (because adding 0 to any number, does not change the wunder),
1 is called the MULTIPLICATIVE IDENTITY becasse mutiplying any Number with 1, does not change the number
Dot patterns: We shall review some types of dot patterns of numbers: (1) LINE: Every number can be arranged as a line.
••••••
E.g. The number 5 is shown as
(2) SQUARE:
• •
• •
E.g. The number 4 is shown as
(3) RECTANGLE:
E.g. The number 8 is shown as
• • • •
• • • •
(4) TRIANGLE:
Eg. The number 6 can be shown as
•
• •
• • •
Questions:
1. Determine the three consecutive whole numbers which come immediately before 17999.
2. How many whole numbers are there between 25 and 657
3. Find the predecessor of the smallest 3-digit number.
4. Find the sum of predecessor of smallest 3-digit number and successor of greatest 3-digit number.
5. Find the product of successor and predecessor of 99.
6. Find the value of: 65×95+65x5.
7. Simplify: 169×20+169x40+169×30.
8. Find the product of: 824×4×25.
9. What is the sum of the original number and the new number if the digits 2 and 7 are interchanged in the number 2997?
10. Find the value of 1+2–3–4+5–6+7+8–9.
11. What should be added to (7020) so that the sum is (14750-10)7
12. Find the successor of the largest number formed by using the digit 7.3.54,1 only once.
13. Ravi spends ₹450 on lunch and dinner. How much money he has to spend on lunch and dinner for a week?
14. Find the value of: 735+ (150 ÷10).
15. Find the product of largest 4-digit number and smallest whole number.
16. A milkman supply 50 liters of milk on Monday. The next day, he supply 40 liters of milk. If the cost of milk be ₹75/ liter. How much did the milkman earned?
17. Find the value of: 22765 × 145–22765 × 45.
18. If the cost of one bat is ₹500 and one ball is ₹50. Then find the cost of 40 bats and 40 balls.
19. The digit 2 and 3 of a number 73024 are interchanged. Find the difference between the two numbers.
20. There are 70 boxes containing 25 bottles cach. If 5 more bottles were added in each box. Find the total number of bottles.
20.
21. 1f66-12-792, then find the value of 660 x 120.
22. Which least number should be added to 356, to make it exactly divisible by 5.
23. Which least number should be subtracted from 999 so that 33 divided the new number exactly?
24. Find the product of smallest 3-digit number and its successor.
25. Find the value of
437×149+437×21–437×70.
26. Find the product of largest one digit number and smallest 3-digit number.
27. How many times the digit 2 occurs in tens place in the whole numbers from 100 to 300?
28. Find the value of 2x 3567x 50.
29. The school canteen charges 20 for lunch and 5 for milk each day. How much money will be charged In 8 days on these things?
30. Find the value of 1507–(625/25)
31. What is the difference between the predecessor and successor of the greatest 5-digit number?
32. What is the sum of the predecessor of 701 and successor of 299?
33. Find the value of: 3+7(5+1)÷3–2.
34. Find the value of:
8937 x 648+8937 x 122+8937 × 230.
35. What is the difference between the successor of the least 5-digit number and the predecessor of the greatest 3-digit numbers?
36. The difference between 85 and the number obtained by reversing the digit is?
37. By using dot (.) patterns, which smaller 2-digit number can be arranged in all the three ways namely a line, a triangle and a rectangle? 330
38.Find the value of: 24÷ (9÷ 3).
39. A car driver filled his car petrol tank with 65 liters of petrol on Monday. On Tuesday, he fills the tank 35 liters of petrol. If the cost of petrol be 89/liter. How much did the driver spend?
40. Find the value of: 10+40÷8 x 2-9.
Answers:
Answers:
1) 17996, 17997, 17998
2) 39
3) 99
4)
5.
1099
9800
6.
6500
7.
8.
15210
82400
9.
10989
10.
11.
1
75
12.
75432
13.
14.
3150
750
15.
0
16.
17.
6750
2276500
18.
22000
19.
990
20.
2100
21.
79200
22.
4
23.
9
24.
10100
25.
43700
26.
900
20
27.
28.
356700
29.
200
30.
1482
31.
2
32.
1000
33.
15
34.
35.
8937000
9003
36.
27
37.
10
38.
8
39.
8900
40.
11
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