Exercise 1.5

Exercise 1.5

1. Fill in the blanks.

(i) The difference between the smallest natural number and the smallest whole number is  __________. Answer: one

(ii) 17 × __________ = 34 × 17 Answer: 34

(iii) When __________ is added to a number, it remains the same. Answer: zero

(iv) Division by __________ is not defined. Answer: zero

(v) Multiplication by __________ leaves a number unchanged. Answer: one

2. Say True or False.

(i) 0 is the identity for multiplication of whole numbers. [False]

(ii) Sum of two whole numbers is always less than their product. [False]

(iii) Both addition and multiplication are associative for whole numbers. [True]

(iv) Both addition and multiplication are commutative for whole numbers. [True]

(v) Multiplication is distributive over addition for whole numbers. [True]

3. Name the property being illustrated in each of the cases given below.

(i) 75 + 34 = 34 + 75 → Commutativity for addition

(ii) (12 × 4) × 8 = 12 × (4 × 8) → Associativity for multiplication

(iii) 50 + 0 = 50 → Zero is Additive Identity

(iv) 50 × 1 = 50 → One is Mulitiplicative Identity

(v) 50 × 42 = 50 × 40 + 50 × 2 → Distributivity of multiplication over addition

4. Use the properties of whole numbers and simplify.

(i) 50 × 102

(ii) 500 × 689 − 500 × 89

(iii) 4 × 132 × 25

(iv) 196 + 34 + 104

Solution:

(i) 50 × 102

= (50 × 100) + (50 × 2)

= 5000 + 100 = 5100

(ii) 500 × 689 − 500 × 89

= 500 (689 − 89)

= 500 × 600

= 3,00,000

(iii) 4 × 132 × 25

= 132 × (25 × 4)

= 132 × 100 = 13,200

(iv) 196 + 34 + 104

= (196 + 4) + 100 + 34 ,

= 200 +100 + 34

= 334

Objective Type Questions

5. (53 + 49) × 0 is

(a) 102

(b) 0

(c) 1

(d) 53 + 49 × 0

Answer: (b) 0

6. 59/1 is

(a) 1

(b) 0

(c) 1/59 

(d) 59

Answer: (d) 59

7. The product of a non-zero whole number and its successor is always

(a) an even number

(b) an odd number

(c) zero

(d) none of these

Answer: (a) an even number

8. The whole number that does not have a predecessor is

(a) 10

(b) 0

(c) 1

(d) none of these

Answer: (b) 0

9. Which of the following expressions is not zero?

(a) 0 × 0

(b) 0 + 0

(c) 2 / 0

(d) 0 / 2

Answer: (c) 2/0

10. Which of the following is not true?

(a) (4237 + 5498) + 3439 = 4237 + (5498 + 3439)

(b) (4237 × 5498) × 3439= 4237 × (5498 × 3439)

(c) 4237 + 5498 × 3439 = (4237 + 5498) × 3439

(d) 4237 × (5498 + 3439) = (4237 × 5498) + (4237 × 3439)

Answer: (c) 4237 + 5498 × 3439 = (4237 + 5498) × 3439

Answers:

Exercise 1.5

1) (i) 1 (ii) 34 (iii) 0 (iv) Zero (v) one

2) (i) False (ii) False (iii) True (iv) True (v) True

3) (i) Commutativity for Addition (ii) Associativity for Multiplication (iii) Zero is Additive Identity (iv) One is Multiplicative Identity (v) Distributivity of Multiplication over Addition

4) (i) 5100 (ii) 3,00,000 (iii) 13,200 (iv) 334

5) (b) 0

6) (d) 59

7) (a) an even number

8) (b) 0

9) (c) 2/0

10) (c) 4237+ 5498 × 3439 = (4237 + 5498) × 3439