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2. Find the product of the following. The numbers 1, 2, 3, 4, 5 ... are called natural numbers.
a. 2 × 127 × 50 b. 1,234 × 4 X 25 c. 40 × 625 × 25
d. 125 × 426 × 8 e. 5 × 650 × 10 All natural numbers together with Oare called whole numbers.

3. Solve the following using the distributive property of multiplication over addition. Every natural number is a whole number whereas O is a whole number that is not a natural number.
a. 20 × 7 + 12 × 7 b. 16 × 12 + 16 × 8 c. 25 × 7 + 8 × 25
d. 6,725 × 99 + 6,725 e.42 × 860 + 860 × 58 The smallest natural number is 1. The smallest whole number is 0.

4. Solve the following using the distributive property of multiplication over addition. Addition and multiplication of whole numbers always gives a whole number. The closure property holds true
a. 642 × 110 b. 857 × 102 C. 46× 506 for the addition and multiplication of whole numbers.
d. 112 × 1,004 e. 678 ×10,001
Subtraction and division do not satisfy the closure property of whole numbers.

5. Radha secured 96 marks in mathematics and 69 marks in social studies in the final examination,
whereas Sudha secured 69 marks in social studies and 96 marks in mathematics. Who secured better marks in Addition and multiplication satisfy the commutative property of whole numbers.
the combined subjects? Which property is applicable to find the sum? Thus, a + b = b + a and a × b = b × a
6. There are two bookshops in a shopping arcade. Shop A sold 245 copies of the latest Harry Potter book per
day and Shop B sold 305 copies of the same per day. Find the total number of books sold by Shop A and Shop where a and b are any two whole numbers.
B in 10 days. Name the property of whole numbers used for finding the answer. Subtraction and division do not satisfy the commutative property of whole numbers.
7. The population of a village is 84,975. One out of every 11 persons is educated in the village. Find the Addition and multiplication satisfy the associative property of whole numbers. Thus, (a + b) + c = a + (b + c)
number of educated and uneducated people in the village. and (a × b) × c = a × (b × c)
8. Determine the product of the greatest number of four digits and the smallest number of three digits.
Also find the product of the smallest number of four digits and the greatest number of three digits. where a, b and c are any three whole numbers.
Find the difference between the twoproducts.
9. New tables and chairs are required for a class of 50 students. A table costs ₹180 and a chair U20. Use Subtraction and division do not satisfy the associative property of whole numbers.
the distributive property of multiplication over addition to find the total cost of the tables and chairs.

For whole numbers, the additive identity is 0 and the multiplicative identity is 1 .
10. Study the following patterns and write the next two steps for each pattern.
a. 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 55 If we multiply 0 with any whole number, the answer is always 0.
11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 + 19 + 20 = 155
21 + 22 + 23 + 24 + 25 + 26 + 27 + 28 + 29 + 30 = 255 If we divide 0 by any whole number, the answer is always 0.
31 + 32 + 33 + 34 + 35 + 36 + 37 + 38 + 39 + 40 = 355
- - - - - - - - - - - Division by 0 is not defined.
- - - - - - - - - - -
b. (1 × 2) + (2 × 3) = 2 × 3 × 4 When any whole number (other than 0) is divided by itself, the quotient is always 1.
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(1 × 2) + (2 × 3) + (3 × 4) = 3 × 4 × 5 Multiplication is distributive over addition for whole numbers.
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(1 × 2) + (2 × 3) + (3 × 4) + (4 × 5) = 4 × 5 × 6 For division of whole numbers, the relationship-
3 dividend = ( divisor × quotient) + remainder - holds true.

Numbers can be arranged in simple elementary shapes, which makes it easy to understand their properties.
Being aware of patterns in numbers helps to make mental calculations.
d. 1
1 + 1 1.Find the smallest whole number that can be added to 750 so that the resulting number is divisible by 13.
1 + 2 + 1 2.Find the smallest whole number that must be subtracted from 13,666 to get a number exactly divisible by 78.
1 + 3 + 3 + 1 3.Using the distributive property of whole numbers, find the product of 12,345 × 6,789 - 12,345 × 5,789.
1 + 4 + 6 + 4 + 1