6 th 1.5

KALAIMAGAL ACADEMY

6th Standard Samacheer Kalvi Maths

Chapter 1: Numbers — Exercise 1.5 Solutions

EXERCISE 1.5

1. Fill in the blanks.

1. The difference between the smallest natural number and the smallest whole number is 1.
   Explanation: Smallest natural number is 1, smallest whole number is 0. Difference: 1 − 0 = 1.
2. 17 × 34 = 34 × 17
   Explanation: Commutative property of multiplication ($a \times b = b \times a$).
3. When 0 is added to a number, it remains the same.
   Explanation: 0 is the additive identity for whole numbers.
4. Division by 0 is not defined.
   Explanation: Any number divided by zero has an undefined value.
5. Multiplication by 1 leaves a number unchanged.
   Explanation: 1 is the multiplicative identity.

2. Say True or False.

1. 0 is the identity for multiplication of whole numbers.
   Answer: False
   Reason: 1 is the identity for multiplication. 0 is the identity for addition.
2. Sum of two whole numbers is always less than their product.
   Answer: False
   Reason: Counter-example: For 0 and 5, sum is 0 + 5 = 5, product is 0 × 5 = 0. Here, sum is greater than product. Also for 1 and 2, 1 + 2 = 3 > 1 × 2 = 2.
3. Both addition and multiplication are associative for whole numbers.
   Answer: True
   Reason: $a+(b+c) = (a+b)+c$ and $a \times (b \times c) = (a \times b) \times c$ hold true for all whole numbers.
4. Both addition and multiplication are commutative for whole numbers.
   Answer: True
   Reason: $a+b = b+a$ and $a \times b = b \times a$ hold true for all whole numbers.
5. Multiplication is distributive over addition for whole numbers.
   Answer: True
   Reason: $a \times (b + c) = (a \times b) + (a \times c)$ is a fundamental property of whole numbers.

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

1. 75 + 34 = 34 + 75 → Commutative property of addition
2. (12 × 4) × 8 = 12 × (4 × 8) → Associative property of multiplication
3. 50 + 0 = 50 → Additive identity property
4. 50 × 1 = 50 → Multiplicative identity property
5. 50 × 42 = 50 × 40 + 50 × 2 → Distributive property of multiplication over addition

4. Use the properties of whole numbers and simplify.

1. 50 × 102
   = 50 × (100 + 2)
   = (50 × 100) + (50 × 2)    [Distributive Property]
   = 5000 + 100 = 5100
2. 500 × 689 − 500 × 89
   = 500 × (689 − 89)    [Distributive Property]
   = 500 × 600 = 3,00,000
3. 4 × 132 × 25
   = (4 × 25) × 132    [Commutative & Associative Properties]
   = 100 × 132 = 13,200
4. 196 + 34 + 104
   = (196 + 104) + 34    [Commutative & Associative Properties]
   = 300 + 34 = 334