Exercise 1.4
1. Fill in the blanks.
(i) (-100) × (-6) = ?
Solution:
(ii) (-3) × ? = 3
Solution:
(iii) 100 × (-6) = ?
Solution:
(iv) (-20) × (-10) = ?
Solution:
+
(v) 15 × (-3) = ?
Solution:
1. Find each of the following products.
(i) 3 × (-1)
Solution:
(ii) (-1) × 225
Solution:
(iii) (-21) × (-30)
Solution:
(iv) (-316) × (-1)
Solution:
(v) (-12) × (-11) × (10)
Solution:
3. A Certain freezing process requires that the room temparature be lowered from 40°C at the rate of 5°C every hour. What will be the room temparature 10 hours after the process begins?
Solution:
The room temperature starts at 40°C and decreases at a rate of
After 10 hours, the temperature change is: 10 × 5 =
Now, subtract this from the initial temperature: 40°C − 50°C =
So, the room temperature 10 hours after the process begins will be -10°C.
4. In a class test containing 10 questions, '3' marks are awarded for every correct answer and (-1) mark is for every incorrect answer and '0' for questions not attempted.
(i)
(i) Gopi gets 5 correct and 5 incorrect answers. What is his score?
Gopi's score can be calculated as follows:
Gopi gets 5 correct answers, and each correct answer gives 3 marks.
5 × 3 =
Gopi gets 5 incorrect answers, and each incorrect answer deducts 1 mark.
5 × (−1) =
Total score: 15 + (−5) = 15−5 =
So, Gopi's final score is 10 marks.
(ii)
(ii) Reshma gets 7 correct answers and 3 incorrect answers. What is her score?
Solution:
Reshma's score can be calculated as follows:
Reshma gets 7 correct answers, and each correct answer gives 3 marks.
7 × 3 =
Reshma gets 3 incorrect answers, and each incorrect answer deducts 1 mark.
3 × (−1) =
Total score: 21 + (−3) = 21 −
So, Reshma's final score is 18 marks.
(iii)
(iii) Rashmi gets 3 correct and 4 incorrect answers out of seven questions she attempts. What is her score?
Solution:
Rashmi's score can be calculated as follows:
Rashmi gets 3 correct answers, and each correct answer gives 3 marks.
3 × 3 =
Rashmi gets 4 incorrect answers, and each incorrect answer deducts 1 mark.
4 ×(−1) =
Total score: 9 + (−4) = 9 − 4 =
So, Rashmi's final score is 5 marks.
5. A merchant on selling rice earns a profit of ₹10 per bag of basmati rice sold and a loss of ₹5 per bag of non-basmati rice
(i)
(i) He sells 3,000 bags of basmati rice and 5,000 bags of non-basmati rice in a month. What is his profit or loss in a month?
Solution:
Calculate total profit from basmati rice
Total Profit = 3,000 × 10 =
Calculate total loss from non-basmati rice
Total Loss = 5,000 × 5 =
Find net profit or loss
= 30,000 − 25,000 =
Since the result is positive, the merchant makes a profit of ₹5,000 in a month.
(ii)
(ii) What is the number of basmati rice bags he must sell to have neither profit nor loss, if the number of bags of non-basmati rice sold is 6,400.
Solution:
Calculate total loss from non-basmati rice
Total Loss = 6,400 × 5 =
Find the required number of basmati rice bags
Let X be the number of basmati rice bags needed to make the total profit equal to ₹32,000.
Total Profit = X * 10
Since there is no profit or loss, the total profit must equal the total loss:
x * 10 = 32,000
Solve for X
X =
The merchant must sell 3,200 bags of basmati rice to have neither profit nor loss.
6. Replace the blank with an integer to make it a true statement.
(i) (-3) × _ = 27
Solution:
(ii) 5 × _ = -35
Solution:
(iii) _ × (-8) = -56
Solution: +