Whole Numbers: Overview, Questions, Preparation

• Commutative property

The commutative property of whole numbers states that the result of the addition or multiplication of two whole numbers is the same irrespective of the order in which the operation is performed.

m + n = n + m and m x n = n x m

• Additive identity

When zero is added to a whole number, the result is the number itself.

m + 0 = m

• Multiplicative identity

When 1 is multiplied by a whole number, the result is the number itself.

m x 1 = m

• Associative property

When more than two whole numbers are added or multiplied, they can be grouped in any manner, and the answer will remain unchanged. Irrespective of the grouping, the result remains the same.(m+n) + p = m + (n+p)

(k x l) x m = k x (l x m)

• Distributive property

When an arithmetic operation is performed on a set, it applies the same to all members of the set.

m.(n-p) = m.n - m.p

m.(n+p) = m.n + m.p

The topic of whole numbers is thoroughly explained in Class 9 maths and is a part of the Real Numbers chapter in Class 10. Approximate weightage of this topic in the exams is 2-3 marks.

• Which of these are whole numbers?
  5, ½, 89, 3, -7, 4i

Solution:

All the natural numbers and zero are whole numbers.So, from the given set of numbers

5, 3 and 89 are whole numbers.

• A shopkeeper supplies 16 litres of milk to a society in the morning and 34 litres of milk in the afternoon. If the milk costs Rs 45 per litre, how much money does the shopkeeper make per day

Solution:

According to the question, milk supplied in a day is 16 litres and 34 litres.

The cost of milk per liter is Rs. 45

Amount due= quantity of milk in the morning x rate per liter + quantity of milk in the afternoon x rate per liter

Amount due = 16 x 45 + 34 x 45

= (16 + 34) x 45= 50 x 45 = Rs. 2250

• Find the value of 71265 × 149 – 71265 × 49.

Solution:

Using reverse distributive property,

= 71265 (149 - 49)

= 71265 x 100 = 7126500

Q: What is the relation between a whole number and a natural number?

Q: What kind of number is zero?

Q: Can a negative number be called a whole number?

Q: What is Closure Property?

Q: Is it possible to determine the biggest whole number?