NCERT Class 7 Mathematics First Chapter Integers Exercise 1.1 Solutions
EXERCISE 1.1
(1) Following number line shows the temperature in degree celsius (°C) at different places on a particular day
(a) Observe this number line and write the temperature of the places marked on it.
Solution: Lahulspiti = – 8o C
Srinagar = – 2o C
Shimla= 5o C
Ooty = 14o C
Bengaluru = 22o C
(b) What is the temperature difference between the hottest and the coldest places among the above?
Solution: Temperature at the hottest place, that is Bengaluru = 22o C.
Temperature at coldest place, that is Lahulspiti = – 8o C
Temperature difference = 22o C – (- 8o C) = 30o C
Hence, the temperature difference between the hottest and coldest places among the above is 30o C.
(c) What is the temperature difference between Lahulspiti and Srinagar?
Solution: Temperature of Lahulspiti = – 8o C
Temperature of Srinagar = – 2o C
Difference between Lahulspiti and Srinagar = (- 2o C) – (- 8o C) = 6o C.
(d) Can we say temperature of Srinagar and Shimla taken together is less than the temperature at Shimla? Is it also less than the temperature at Srinagar?
Solution: Temperature at Srinagar = – 2o C
Temperature at Shimla = 5o C
Temperature of Srinagar and Shimla taken together = – 2o C + 5o C = 3o C
3o C < 5o C
3o C < Temperature at Shimla
Yes, the temperature of Srinagar and Shimla taken together is less than the temperature of Shimla. However, 3o C > – 2o C.
Hence, the temperature of Srinagar and shimla taken together is not less than the temperature of Srinagar.
(2) In a quiz, positive marks are given for correct answers and negative marks are given for incorrect answers. If Jack’s scores in five successive rounds were 25, – 5, – 10, 15 and 10, what was his total at the end?
Solution: Jack’s total score at the end = 25 + (- 5) + (- 10) + 15 + 10
= 25 + 15 + 10 – (5 + 10)
= 50 – 15 = 35
(3) At Srinagar temperature was – 5°C on Monday and then it dropped by 2°C on Tues day. What was the temperature of Srinagar on Tuesday? On Wednesday, it rose by 4°C. What was the temperature on this day?
Solution: Temperature at Srinagar on Tues day = (- 5 – 2)o C = (- 7)o C.
On Wednesday the temperature was = {(- 7) + 4}o C = (- 3)o C.
(4) A plane is flying at the height of 5000 m above the sea level. At a particular point, it is exactly above a submarine floating 1200 m below the sea level. What is the vertical distance between them?
Solution: Height of the plane = 5000 m
Depth of the submarine = (- 1200) m
The vertical distance between them,
{5000 – (- 1200)} m = (5000 + 1200) m = 6200 m
(5) Mohan deposits Rs 2,000 in his bank account and withdraws Rs 1,642 from it, the next day. If withdrawal of amount from the account is represented by a negative integer, then how will you represent the amount deposited? Find the balance in Mohan’s account after the withdrawal.
Solution: Mohan deposits = Rs 2000
Mohan withdraws (represented negative integers) = Rs (- 1642)
The required balance = Rs {2000 + (-1642)} = Rs 358
(6) Rita goes 20 km towards east from a point A to the point B. From B, she moves 30 km towards west along the same road. If the distance towards east is represented by a positive integer then, how will you represent the distance traveled towards west? By which integer will you represent her final position from A?
Solution: Distance towards east = 20 km
Distance towards west = (- 30) km
Distance travelled from A = 20 + (- 30) = (20 – 30) km = (- 10) km
Hence, Rita from point A by a negative integer that is (- 10) km in west direction.
(7) In a magic square each row, column and diagonal have the same sum. Check which of the following is a magic square.
Solution: (ii) is a magic square, because in square (ii) each row, column and diagonal give up to – 9.
(8) Verify a – (– b) = a + b for the following values of a and b.
(i) a = 21, b = 18
Solution: a – (- b) = a + b
- H. S. = 21 – (- 18) = 21 + 18 = 39
- H. S. = 21 + 18 = 39
∴ L. H. S. = R. H. S (proved)
(ii) a = 118, b = 125
Solution: L.H.S. = a – (- b) = 118 – (- 125) = 118 + 125 = 243
- H.S. = a + b = 118 + 125 = 243
∴ L. H. S. = R. H. S (proved)
(iii) a = 75, b = 84
Solution: L. H.S. = a – (- b) = 75 – (- 84) = 75 + 84 = 159
R.H.S. = a + b = 75 + 84 = 159
∴ L. H. S. = R. H. S (proved)
(iv) a = 28, b = 11
Solution: L. H.S. = a – (- b) = 28 – (- 11) = 28 +11 = 39
R.H.S. = a + b = 28 + 11 = 39
∴ L. H. S. = R. H. S (proved)
(9) Use the sign of >, < or = in the box to make the statements true.
(a) (– 8) + (– 4) (–8) – (– 4)
Solution: – 12 < – 4
(b) (– 3) + 7 – (19) 15 – 8 + (– 9)
Solution: 4 – 19 7 – 9
= – 15 < – 2
(c) 23 – 41 + 11 23 – 41 – 11
Solution: – 18 +11 – 18 – 11
= – 7 > – 29
(d) 39 + (– 24) – (15) 36 + (– 52) – (– 36)
Solution: 39 – 39 36 – 88
= 0 < – 52
(e) – 231 + 79 + 51 –399 + 159 + 81
Solution: – 231 + 130 – 399 + 240
= – 101 > -159
(10) A water tank has steps inside it. A monkey is sitting on the topmost step (i.e., the first step). The water level is at the ninth step.
(i) He jumps 3 steps down and then jumps back 2 steps up. In how many jumps will he reach the water level?
Solution: The monkey was at step = 1
After 1st jump = 1 + 3 = 4
After 2nd jump = 4 + (- 2) = 2
After 3rd jump = 2 + 3 = 5
After 4th jump = 5 + (- 2) = 3
After 5th jump = 3 + 3 = 6
After 6th jump = 6 + (- 2) = 4
After 7th jump = 4 + 3 = 7
After 8th jump = 7 + (- 2) = 5
After 9th jump = 5 + 3 = 8
After 10th jump = 8 + (- 2) = 6
After 11th jump = 6 + 3 = 9
Hence, the monkey will be at water level after 11 jumps.
(ii) After drinking water, he wants to go back. For this, he jumps 4 steps up and then jumps back 2 steps down in every move. In how many jumps will he reach back the top step?
Solution: The monkey was step = 9
After 1st jump = 9 + (- 4) = 5
After 2nd jump = 5 + 2 = 7
After 3rd jump = 7 + (- 4) = 3
After 4th jump = 3 + 2 = 5
After 5th jump = 5 + (- 4) = 1
Hence, the monkey will reach back at the top step after 5th jumps.
(iii) If the number of steps moved down is represented by negative integers and the number of steps moved up by positive integers, represent his moves in part (i) and (ii) by completing the following; (a) – 3 + 2 – … = – 8 (b) 4 – 2 + … = 8. In (a) the sum (– 8) represents going down by eight steps. So, what will the sum 8 in (b) represent?
Solution: Moves in part (i),
– 3 + 2 – 3 + 2 – 3 + 2 – 3 + 2 – 3 + 2 – 3 = – 8
Moves in part (ii),
4 – 2 + 4 – 2 + 4 = 8
Moves in part (ii) represent going up 8 steps.
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