Page 16 - Maths Skills - 7

14 Maths

Example 3: Evaluate: (– 6) × (– 5) × 2 × (– 1) × (– 3)
Solution: We have, [(– 6) × (– 5)] × [2 × (– 1)] × (– 3)

= 30 × (– 2) × (– 3) = [30 × (– 2)] × (– 3) = (– 60) × (– 3) = 180
Since the number of negative integers is even (i.e. 4), therefore the product is positive.
Example 4: In a class test containing 20 questions, 4 marks are awarded for every correct answer, 1 mark
is deducted for every incorrect answer and 0 is given for questions not attempted. Answer the
following questions.
(i) Manish gets four correct and six incorrect answers. What is his score?

(ii) Divya gets five correct and five incorrect answers. What is her score?
Solution: (i) Manish’s score = 4 × 4 + 6 × (– 1) = 16 – 6 = 10
(ii) Divya’s score = 5 × 4 + 5 × (– 1) = 20 – 5 = 15

Example 5: A cement company earns a profit of ` 8 per bag of white cement sold and a loss of ` 5 per bag of
grey cement sold.
(i) The company sells 3,000 bags of white cement and 5,000 bags of grey cement in a month.
What is its profit or loss?
(ii) What is the number of white cement bags it must sell to have neither profit nor loss, if the
number of grey bags sold is 6,400?
Solution: (i) Profit or loss of the company = [` 3,000 × 8] + [` 5,000 × (– 5)]
= ` 24,000 – ` 25,000 = – ` 1,000

\ There is net loss of ` 1,000.
(ii) Let the number of white cement bags sold for neither profit nor loss be n.
Now, 8 × n + (– 5) × 6,400 = 0

× 400,
56
⇒ 8n = 5 × 6,400 ⇒ n = 8
⇒ n = 5 × 800 = 4,000 bags

Therefore, the company must sell 4,000 bags of white cement to have neither profit nor loss.

Exercise 1.3

1. Multiply.
(i) – 9 × 7 (ii) 0 × 0 (iii) (– 29) × 0 (iv) 62 × (– 8) (v) (– 138) × (– 3)

2. Use the distributive law to simplify the following.
(i) 52 × 27 – 32 × 52 (ii) (– 13) × (– 22) + (– 13) × (–11)
(iii) (– 4) × 20 + 20 × (– 5) (iv) 200 × 2543 – 100 × 2543

3. Find the value of ‘x’ for the following.
(i) 5 × [(– 4) – x] = 5 × (– 4) – 5 × 10 (ii) x × [(– 10) – (– 8)] = (– 5) × (– 10) – (– 5) × (– 8)

(iii) 2 × (3 + x) = 2 × 3 + 6 × 2 (iv) 3 × (0 – x) = 3 × 0 – 3 × 3
4. State the sign of the products without multiplying.
(i) (– 2) × (– 5) × (– 3) × 2 × (– 4) (ii) (– 11) × 0 × (11)

(iii) 3 × (– 7) × (– 5) × 2 × (– 3) × (– 2) × (– 1) (iv) (– 1) × 1 × 3 × 2 × (– 3)