Class 6 - Mathematics
Chapter - Integers : Exercise 1.1
Top Block 1
Question: 1.Following number line shows the temperature in degree Celsius {∘C} at different places on a particular day:
(b) What is the temperature difference between the hottest and the coldest places among the above?
(c) What is the temperature difference between Lahulspiti and Srinagar?
(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?
Answer:
(a) The temperature of the places marked on it is:
| Places | Temperature |
|---|---|
| 1. Bangalore | A. 22oC |
| 2. Ooty | B. 13oC |
| 3. Shimla | C. 5oC |
| 4. Srinagar | D. -2oC |
| 5. Lahulspiti | E. -8oC |
(b) The temperature of the hottest place Bangalore = 22oC
The temperature of the coldest place Lahulspiti = –8oC
Difference = 22oC – (–8oC) = 22oC + 8oC = 30oC
(c)The temperature of Srinagar = –2oC
The temperature of Lahulspiti =–8oC
Difference = –2oC + (–8oC) = –2oC –8oC =6oC
(d)The temperature of Srinagar and Shimla = 5oC + (–2oC) = 5oC –2oC =3oC
The temperature at Shimla =5oC
Therefore, 3oC < 5oC
Thus, temperature of Srinagar and Shimla taken together is less than the temperature at Shimla.
Now, Temperature of Srinagar = –2oC
Therefore, 3oC > –2oC
No, it is not less than the temperature at Srinagar.
Question: 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,–10,15and 10, what was his total at the end?
Answer :
Jack’s scores in five successive rounds are 25,–5,–10,15 and 10.
Total marks got by Jack = 25+(–5)+(–10)+15+10
= 25 – 15 + 25 = 35
Thus, 35 marks are got by Jack in a quiz.
Question: 3.At Srinagar temperature was –5oC on Monday and then it dropped by 2oC on Tuesday. What was the temperature of Srinagar on Tuesday? On Wednesday, it rose by 4oC. What was the temperature on this day?
Answer :
On Monday, temperature at Srinagar = –5oC
On Tuesday, temperature dropped = 2oC
∴∴ Temperature on Tuesday = –5oC – 2oC = –7oC
On Wednesday, temperature rose up = 4oC
∴∴ Temperature on Wednesday = ––7oC + 4oC = –3oC
Thus, temperature on Tuesday and Wednesday was –7oCand –3oCrespectively.
Question: 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?
Mddle block 1
Answer :
Height of a place above the sea level = 5000 m
Floating a submarine below the sea level = 1200 m
∴ The vertical distance between the plane and the submarine = 5000 + 1200 = 6200 m
Thus, the vertical distance between the plane and the submarine is 6200 m.
Question: 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 accounts after the withdrawal?
Answer :
Deposit amount = Rs. 2,000 and Withdrawal amount = Rs. 1,642
∴ Balance = 2,000 – 1,642 = Rs. 358
Thus, the balance in Mohan’s account after withdrawal is Rs. 358.
According to the number line, Rita moves towards east is represented by a positive integer. But she moves in opposite direction means Rita moves west, is represented by negative integer.
Distance from A to B = 20 km
Distance from B to C = 30 km
Distance from A to C = 20 – 30 = –10 km
Thus, Rital is at final position from A to C is –10 km.
Question: 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?
Answer :
(i) Taking rows 5 + (–1) + (–4) = 5 – 5 = 0
(–5) + (–2) + 7 = –7 + 7 = 0
0 + 3 + (–3) = 3 – 3 = 0
Taking columns 5 + (–5) + 0 = 5 – 5 = 0
(–1) + (–2) + 3 = –3 + 3 = 0
(–4) + 7 + (–3) = 7 – 7 = 0
Taking diagonals 5 + (–2) + (–3) = 5 – 5 = 0
(–4) + (–2) + 0 = –6
This box is not a magic square because all the sums are not equal.
(ii) Taking rows 1 + (–10) + 0 = 1 – 10 = –9
(–4) + (–3) + (–2) = –7 – 2 = –9
(–6) + 4 + (–7) = –2 – 7 = –9
Taking columns 1 + (–4) + (–6) = 1 – 10 = –9
(–10) + (–3) + 4 = –13 + 4 = –9
0 + (–2) + (–7) = 0 – 9 = –9
Taking diagonals 1 + (–3) + (–7) = 1 – 10 = –9
0 + (–3) + (–6) = –9
This box is magic square because all the sums are equal.
Question: 7.In a magic square each row, column and diagonal have the same sum. Check which of the following is a magic square.
(i)| 5 | -1 | -4 |
| -5 | -2 | 7 |
| 0 | 3 | -3 |
| 1 | -10 | 0 |
| -4 | -3 | -2 |
| -6 | 4 | -7 |
Answer :
(i) Given: a=21,b=18
We have a–(–b)=a+b
Putting the values in L.H.S. = a–(–b)=21–(–18) = 21 + 18 = 39
Putting the values in R.H.S. = a+b = 21 + 19 = 39
Since, L.H.S. = R.H.S Hence, verified.
(ii) Given: a=118,b=125
We have a–(–b)=a+b
Putting the values in L.H.S. = a–(–b)=118–(–125) = 118 + 125 = 243
Putting the values in R.H.S. = a+b = 118 + 125 = 243
Since, L.H.S. = R.H.S Hence, verified.
(iii) Given: a=75,b=84
We have a–(–b)=a+b
Putting the values in L.H.S. = a–(–b)=75–(–84) = 75 + 84 = 159
Putting the values in R.H.S. = a+b = 75 + 84 = 159
Since, L.H.S. = R.H.S Hence, verified.
(iv) Given: a=28,b=11
We have a–(–b)=a+b
Putting the values in L.H.S. = a–(–b)=28–(–11) = 28 + 11 = 39
Putting the values in R.H.S. = a+b = 28 + 11 = 39
Since, L.H.S. = R.H.S Hence, verified.
Question: 8.Verifya–(–b)=a+b for the following values of aa and b:b:
(i) a=21,b=18
(ii) a=118,b=125
(iii) a=75,b=84
(iv) a=28,b=11
Answer :
(a) (–8)+(–4) (–8)–(–4) ⇒⇒ –8–4 –8+4
⇒–12 –4 ⇒⇒ –12 < –4
(b) (–3)+7–(19) 15–8+(–9) ⇒–3+7–19 15–8–9
⇒–19 15–17 ⇒–15 –2
⇒–15 > –2
(c)23–41+11 23–41–11 ⇒–18+11 23–52
⇒–7 –29 ⇒–7 > –29
(d)39+(–24)–(15) 36+(–52)–(–36) ⇒ 39–24–15 36–52+36
⇒39–39 72–52 ⇒0 20
⇒0 < 20
(e)(–231)+79+51 (–399)+159+81 ⇒–231+130 –399+240
⇒–101 –159 ⇒–101 > –159
Question: 9.Use the sign of >, < or = in the box to make the statements true:
(a)(–8) + (–4) (–8)–(–4)
(b)(–3) + 7 – (19) 15 – 8 + (–9)
(c)23 – 41 + 11 23 – 41 – 11
(d)39 + (–24) – (15) 36 + (–52) – (–36)
(e)(–231) + 79 + 51 (–399) + 159 + 81
Answer :
(a)(–8) + (–4) < (–8)–(–4)
⇒ -12 < –4
(b)(–3) + 7 – (19) > 15 – 8 + (–9)
⇒(–15) < (–2)
(c)23 – 41 + 11 > 23 – 41 – 11
⇒–7 > -29
(d)39 + (–24) – (15) < 36 + (–52) – (–36)
⇒ 0 > (–52)
(e)(–231) + 79 + 51 > (–399) + 159 + 81
⇒(–101) > (–159)
Question: 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:
(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?
(iii)If the number of steps moved down is represented by negative integers and the number of steps move 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) represent going down by eight steps. So, what will the sum 8 in (b) represent?
Answer :
(i) He jumps 3 steps down and jumps back 2 steps up. Following number ray shows the
jumps of monkey:
Third jump = 2 + 3 = 5 steps Fourth jump = 5 – 2 = 3 steps
Fifth jump = 3 + 3 = 6 steps Sixth jump = 6 – 2 = 4 steps
Seventh jump = 4 + 3 = 7 steps Eighth jump = 7 – 2 = 5 steps
Ninth jump = 5 + 3 = 8 steps Tenth jump = 8 – 2 = 6 steps
Eleventh jump = 6 + 3 = 9 steps
He will reach ninth steps in 11 jumps.
(ii) He jumps four steps and them jumps down 2 steps. Following number ray shows the jumps of monkey:
(iii) (a)–3+2–3+2–3+2–3+2–3+2–3+2–3+2–3+2=–8
(b) 4–2+4–2+4–2+4–2=8
Thus, sum 8 in (b) represents going up by eight steps.