Page 19 - Start Up Mathematics_7

2. Find each of the following products:
(a) 2 × 3 × (–8) (b) (–5) × 7 × (–4) (c) (–6) × (–7) × (–9)
(d) (–11) × (21) × 0 × (–34) (e) (–2) × (–5) × (–4) × (–10)

3. Simplify using suitable properties of multiplication of integers:
(a) (–3) × 5 + (–3) × 3 (b) 7 × (–13) + 7 × (–10) (c) 10 × (–4) + 5 × (–4)

(d) (–12) × (–7) + (–12) × (–3) (e) 16 × (–68) + 16 × (–32)
4. 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.
(a) Nishi 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?

(b) Rohan attempted 7 questions correctly and 9 questions incorrectly. He did not attempt
4 questions. What will be his score?
5. A company is producing two products A and B. The company makes a profit of ` 52 per
unit on A and a loss of ` 10 per unit on B. If the company sells 3,600 units of product A and

4,000 units of product B, find the profit or loss of the company due to the sale.

Division of Integers
Division is inverse process of multiplication, i.e., 4 × 7 = 28 implies 28 ÷ 4 = 7 or 28 ÷ 7 = 4.
Also, 5 × (–4) = –20 implies –20 ÷ 5 = –4 and –20 ÷ (–4) = 5.

Important Rules for Division of Integers

• When we divide two integers having the same sign (either both positive or both negative),
we divide them regardless of their sign as whole numbers and then assign a positive sign to
the quotient.
• When we divide two integers having different signs (one positive and other negative), we
divide them regardless of their sign as whole numbers and then assign a negative sign to the
quotient.

Properties of Division of Integers
Closure property does not hold good

The closure property is not valid for integers. If a and b are two integers, then a ÷ b is not
necessarily an integer.
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For example, 7 and 3 are integers but is not an integer.
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Not commutative
If a and b are two different integers, then (a ÷ b) ≠ (b ÷ a), i.e., division of integers is not commutative.

For integers 3 and 6, (3 ÷ 6) ≠ (6 ÷ 3).
Not associative
If a, b and c are three integers such that b ≠ 0 and c ≠ 0, then (a ÷ b) ÷ c ≠ a ÷ (b ÷ c).

The result is true only for c equal to 1.

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