NCERT Solution : Integers Chapter 1 Class 7 Mathematics Exercise 1.1
1. Following number line shows the temperature in degree celsius (℃) at different places on a particular day.
Solution :
Temperature of the places are :
- Lahulspiti : -8℃
- Srinagar : -2℃
- Shimla : 5℃
- Ooty : 14℃
- Banglore : 22℃
(b) What is the temperature difference between the hottest and the coldest places among the above ?
Solution :
Hottest place : Bengaluru (22℃)
Coldest place : Lahulspiti (-8℃)
Temperature difference between hottest and coldest place :
= 22℃ - (-8℃)
= 22℃ + 8℃
= 30℃
(c) What is the temperature difference between Lahulspiti and Srinagar ?
Solution :
Temperature of Lahulspiti : -8℃
Temperature of Srinagar : -2℃
Difference : -2℃ - (-8℃)
= -2℃ + 8℃
= 6℃
(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 of Srinagar : -2℃
Temperature of Shimla : 5℃
If temperature of Srinagar and Shimla is taken together then,
-2℃ + 5℃ = 3℃
Yes, it is less than the temperature of Shimla.
No, it 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 :
Total marks at the end = 25 + (-5) + (-10) + 15 + 10
= 25 - 5 - 10 + 15 + 10
= 50 - 15
= 35
3. At Srinagar temperature was -5℃ on Monday and then it dropped by 2℃ on Tuesday. What was the temperature of Srinagar on Tuesday ? On Wednesday, it rose by 4℃ . What was the temperature on this day ?
Solution :
Temperature of Srinagar on Monday : -5℃
Temperature dropped : 2℃ = -2℃
So, Temperature of Srinagar on Tuesday
= -5℃ -2℃
= -7℃
Now,
Temperature rose on Wednesday : 4℃ = +4℃
Therefore,
Temperature on this day
= -7℃ + 4℃
= -3℃
4. A plane is flying at the height of 5000m above the sea level. At a particular point, it is exactly above a submarine floating 1200m below the sea level. What is the vertical distance between them ?
Height of plane from the sea level
= 5000m = +5000m
Height of submarine from the sea level
= 1200m = -1200m
Vertical distance between them
= 5000m - (-1200m)
= 5000m + 1200m
=6200m
5. Mohan deposits ₹2,000 in his bank account and withdraws ₹1,642 from it, the next day. If withdrawl 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 withdrawl.
Solution :
By a positive integer.
Now,
Balance in Mohan's account
= ₹2,000 - ₹1,642
= ₹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 travelled towards west ? By which integer will you represent her final position from A ?
Solution :
By a negative integer.
Her final position from A
= 20 - 30
= -10
7. In a magic square each row, column and diagonal have the same sum. Check which of the following is a magic square.
Solution :
(i) Row one R1
= 5 + (-1) + (-4)
= 5 - 1 - 4
= 5 - 5
= 0
Row two, R2
= -5 + (-2) + 7
= -5 - 2 + 7
= -7 + 7
= 0
Row three, R3
= 0 + 3 + (-3)
= 0 + 3 - 3
= 0
Column one, C1
= 5 + (-5) + 0
= 5 - 5 + 0
= 0
Column two, C2
= -1 + (-2) + 3
= -1 -2 + 3
= -3 + 3
= 0
Column three, C3
= -4 + 7 + (-3)
= -4 + 7 -3
= -7 + 7
= 0
Diagonal one, D1
= 5 + (-2) + (-3)
= 5 -2 -3
= 5 - 5
= 0
Diagonal two, D2
= (-4) + (-2) + 0
= -4 -2 + 0
= -6
Here, the sum of the diagonal two, D2 is different from others. Hence, it is not magic square.
(ii) Row one, R1
= 1 + (-10 + 0
= 1 - 10
= -9
Row two, R2
= (-4) + (-3) + (-2)
= -4 -3 -2
= -9
Row three, R3
= (-6) + 4 + (-7)
= -6 + 4 -7
= -13 + 4
= -9
Column one, C1
= 1 + (-4) + (-6)
= 1 -4 -6
= 1 -10
= -9
Column two, C2
= (-10) + (-3) + 4
= -10 - 3 + 4
= -13 + 4
= -9
Column three, C3
= 0 + (-2) + (-7)
= -2 -7
= -9
Diagonal one, D1
= 1 + (-3) + (-7)
= 1 -3 -7
= 1 -10
= -9
Diagonal two, D2
= 0 + (-3) + (-6)
= -3 -6
= -9
Here, sum of the integers column wise, row wise and diagonally is same i.e., -9. So, (ii) is a magic sqaure.
8. Verify a-(-b)=a+b for the following values of a and b.
(i) a = 21, b = 18
Solution :
a - (-b) = a + b
21 - (-18) = 21 + 18
21 + 18 = 21 + 18
39 = 39
LHS = RHS. Hence, verified
(ii) a = 118, b = 125
Solution :
a - (-b) = a + b
118 - (-125) = 118 + 125
118 + 125 = 118 + 125
243 = 243
LHS = RHS. Hence, verified
(iii) a = 75, b = 84
Solution :
a - (-b) = a + b
75 - (-84) = 75 + 84
75 + 84 = 75 + 84
159 = 159
LHS = RHS. Hence, verified
(iv) a = 28, b = 11
Solution :
a - (-b) = a + b
28 - (-11) = 28 + 11
28 + 11 = 28 + 11
39 = 39
LHS = RHS. Hence, Verified
9. Use the sign of >, < or = in the box to make the statement true.
(a) (-8) + (-4) ⬜ (-8) - (-4)
Solution :
LHS : (-8) + (-4)
= -8 -4
= -12
RHS : (-8) - (-4)
= -8 + 4
= -4
Here, -12 < -4
(b) (-3) + 7 - (19) ⬜ 15 - 8 + (-9)
Solution :
LHS : (-3) + 7 - (19)
= -3 + 7 -19
= -22 + 7
= -15
RHS : 15 - 8 + (-9)
= 15 -8 -9
= 15 -17
= -2
Here, -15 < -2
(c) 23 -41 + 11 ⬜ 23 -41 - 11
Solution :
LHS : 23 - 41 + 11
= 34 - 41
= -7
RHS : 23 - 41 - 11
= 23 - 52
= -29
Here, -7 > -29
(d) 39 + (-24) - (15) ⬜ 36 + (-52) - (-36)
Solution :
LHS : 39 + (-24) - (15)
= 39 - 24 - 15
= 39 - 39
= 0
RHS : 36 + (-52) - (-36)
= 36 - 52 + 36
= 72 - 52
= 20
Here, 0 < 20
(e) -231 + 79 + 51 ⬜ -399 + 159 + 81
Solution :
LHS : -231 + 79 + 51
= -231 + 130
= -101
RHS : -399 + 159 + 81
= -399 + 240
= -159
Here, -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 position of monkey after the
1st jump J1
is at 4th step ↓
2nd jump J2
is at 2nd step ↑
3rd jump J3
is at 5th step ↓
4th jump J4
is at 3rd step ↑
5th jump J5
is at 6th step ↓
6th jump J6 is at 4th step ↑
7th jump J7
is at 7th step ↓
8th jump J8 is at 5th step ↑
9th jump J9
is at 8th step ↓
10th jump J10
is at 6th step ↑
11th jump J11
is at 9th step ↓ (water level)
Hence the required number of jumps = 11
(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 :
Monkey's position after the
1st jump J1 is at 5th step ↑
2nd jump J2 is at 7th step ↓
3rd jump J3 is at 3rd step ↑
4th jump J4 is at 5th step ↓
5th jump J5 is at 1st step ↑
Hence, the required number of steps jumps = 5
(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 :
According to the given conditions we have the following tables
| Jumps | J1 | J2 | J3 | J4 | J5 | J6 | J7 | J8 | J9 | J10 | J11 |
| Number of steps | -3 | +2 | -3 | +2 | -3 | +2 | -3 | +2 | -3 | +2 | -3 |
= -3 + 2 -3 + 2 -3+2-3+2 -3+2-3
= -8 which represents the money goes down by 8 steps.
In case (ii) , we get
| Jumps | J1 | J2 | J3 | J4 | J5 |
| Number of steps | +4 | -2 | +4 | -2 | +4 |
= +4 -2 +4 -2 +4
= 8
Here, the monkey is going up by 8 steps.