Page 17 - Maths Skills - 7

Integers 15

5. Find the products.
(i) (– 11) × 2 × (– 3) (ii) 0 × (– 3) × (– 271)

(iii) (– 5) × (– 10) × 6 (iv) (– 2) × (– 2) × (– 2) × (– 2) × (– 2)
6. A cooling machine requires that room temperature be lowered from 50°C at the rate of 6°C every hour.
What will be the room temperature 7 hours after the process begins?
7. In a competitive examination, 5 marks are awarded for each correct answer, 2 marks are deducted for
each incorrect answer and no marks are given for a question which is not attempted.
(i) Pinky appeared in the examination and attempted 12 questions correctly and 5 questions incorrectly.
However she did not attempt 3 questions. What will be her score?

(ii) Daksh attempted 7 questions correctly and 9 questions incorrectly. He did not attempt 4 questions.
What will be his score?

DIVISION OF INTEGERS
We know that division is the ‘Reverse process of multiplication’.
For example; (i) 6 × (– 8) = – 48 implies – 48 ÷ 6 = – 8 (ii) (– 5) × (– 3) = 15 implies 15 ÷ (– 5) = – 3
and – 48 ÷ (– 8) = 6. and 15 ÷ (– 3) = – 5.

Rules for Division of Integers
1. If the divisor and dividend are of the same signs, the quotient is positive.
2. If the divisor and dividend are of the different signs, the quotient is negative.

PROPERTIES OF DIVISION OF INTEGERS

1. Closure Property: If an integer is divided by another integer, the result is not always an integer.
In other words, if a and b (b ≠ 0) are any two integers, then a ÷ b is not always an integer.

For example; (i) (– 4) ÷ 2 = – 2, which is an integer. (ii) (– 21) ÷ 4, the result is not an integer.
Hence, the closure property does not hold good for integers.
2. Commutative Property: For any two integers a and b, a ÷ b ≠ b ÷ a. The division of integers is not
commutative.
1
For example; (i) (– 4) ÷ 2 = – 2, which is an integer. (ii) 2 ÷ (– 4) = – , which is not an integer.
2
Hence, commutative property does not hold good for integers.
3. Associative Property: If a, b and c are any three integers, then a ÷ (b ÷ c) ≠ (a ÷ b) ÷ c

For example; (– 8) ÷ [(– 4) ÷ 2] = ( – 8) ÷ (– 2) = 4 and [(– 8) ÷ (– 4)] ÷ 2 = 2 ÷ 2 = 1
\ (– 8) ÷ [(– 4) ÷ 2] ≠ [(– 8) ÷ (– 4)] ÷ 2
Hence, associative property not hold good for integers.

4. Identity Property: When any integer is divided by 1, the quotient is the integer itself.
In other words, if a is any integer, then a ÷ 1 = a

For example; (i) (– 3) ÷ 1 = – 3 (ii) 27 ÷ 1 = 27 (iii) 31 ÷ 1 = 31
5. Zero Property: When zero is divided by any non-zero integer, the
quotient is zero. In other words, if a is any integer, then 0 ÷ a = 0 Absorbing Facts
For example; (i) 0 ÷ (– 5) = 0 (ii) 0 ÷ 3 = 0 Division by 0 is not defined.