NCERT Solutions For Class 7 Maths Chapter 1 Integers Exercise 1.1

Table of Contents

Class 7, Maths, Chapter 1, Exercise 1.1 Solutions

Q.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.

(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?

Q.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?

Q.3. At Srinagar temperature was – 5°C on Monday and then it dropped by 2°C on Tuesday. What was the temperature of Srinagar on Tuesday? On Wednesday, it rose by 4°C. What was the temperature on this day?

Q.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?

Q.5. Mohan deposits ₹ 2,000 in his bank account and withdraws ₹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.

Q.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?

Q.7. In a magic square each row, column and diagonal have the same sum. Check which of the following is a magic square.

Q.8. Verify a – (– b) = a + b for the following values of a and b.

(i) a = 21, b = 18

(ii) a = 118, b = 125

(iii) a = 75, b = 84

(iv) a = 28, b = 11

Q.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

Q.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?

(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 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?

Ans:

(i) He jumps 3 steps down and then jumps back 2 steps up. In how many jumps will he reach the water level?

Let us consider steps moved down are represented by positive integers and then, steps

moved up are represented by negative integers.

Initially monkey is sitting on the top most step i.e., first step

In 1^st jump monkey will be at step =1+ 3 = 4 steps

In 2^nd jump monkey will be at step = 4 + (-2) = 4 – 2 = 2 steps

In 3^rd jump monkey will be at step = 2 + 3 = 5 steps

In 4^th jump monkey will be at step = 5 + (-2) = 5- 2 = 3 steps

In 5^th jump monkey will be at step = 3 + 3 = 6 steps

In 6^th jump monkey will be at step = 6 + (-2) = 6- 2 = 4 steps

In 7^th jump monkey will be at step = 4 + 3 = 7 steps

In 8^th jump monkey will be at step = 7 + (-2) = 7- 2 = 5 steps

In 9^th jump monkey will be at step = 5 + 3 = 8 steps

In 10^th jump monkey will be at step = 8 + (-2) = 8- 2 = 6 steps

In 11^th jump monkey will be at step = 6 + 3 = 9 steps

∴ Monkey will reach 9^th step in 11 jumps at the water level.

(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?

Let us consider steps moved down are represented by positive integers and then, steps

moved up are represented by negative integers.

Initially monkey is sitting on the 9^th step i.e., at the water level

In 1^st jump monkey will be at step = 9 + (-4) = 9- 4 = 5 steps

In 2^nd jump monkey will be at step = 5 + 2 = 7 steps

In 3^rd jump monkey will be at step = 7 + (-4) = 7- 4 = 3 steps

In 4^th jump monkey will be at step = 3 + 2 = 5 steps

In 5^th jump monkey will be at step = 5 + (-4) = 5- 4 =1step

∴ Monkey reach back on the 1^st step in 5^th jump.

(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?

According to question, it is given that

If the number of steps moved down is represented by negative integers and the number

of steps moved up by positive integers.

Monkey moves in part (i)

Then, LHS = = – 3 + 2 – 3 +2 – 3 +2 – 3 +2 – 3 + 2 – 3 = – 8

= – 18 + 10

= – 8

RHS = -8