(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?

Answer :

(i) 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 1st jump monkey will be at step = 1 + 3 = 4 steps

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

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

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

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

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

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

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

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

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

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

?\(\therefore \) Monkey took 11 jumps (i.e., 9th step) to reach the water level

(ii) 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 ninth step i.e., at the water level

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

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

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

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

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

?Monkey took 5 jumps to reach back the top step i.e., first step.

(iii) From the 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

RHS = -8

\(\therefore \) Moves in part (i) represents monkey is going down 8 steps. Because negative integer.

Now,

Monkey moves in part (ii)

Then LHS = 4 – 2 + 4 – 2 + 4

= 8

RHS = 8

\(\therefore \) Moves in part (ii) represents monkey is going up 8 steps. Because positive integer.

- 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? Solution:
- 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 Rs.2,000 in a 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.
- 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 her final position from A?
- Q.7 In a magic square each row, column and the 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, 6 = 11
- Q.9 Use the sign of >, (a) (-8) +(-4) \(\square \) (-8)-(-4) (b) (-3) + 7 – (19) \(\square \) 15 – 8 + (-9) (c) 23 – 41 + 11 \(\square \) 23 – 41 – 11 (d) 39 + (-24) – (15) \(\square \) 36 + (-52) – (-36) (e) -231 + 79 + 51 \(\square \)-399 + 159 + 81

- NCERT solutions for class 7 maths chapter 1 Integers
- NCERT solutions for class 7 maths chapter 2 Fractions and Decimals
- NCERT solutions for class 7 maths chapter 3 Data Handling
- NCERT solutions for class 7 maths chapter 4 Simple Equations
- NCERT solutions for class 7 maths chapter 5 Lines and Angles
- NCERT solutions for class 7 maths chapter 6 The Triangle and its Properties
- NCERT solutions for class 7 maths chapter 7 Congruence of Triangles
- NCERT solutions for class 7 maths chapter 8 Comparing Quantities
- NCERT solutions for class 7 maths chapter 9 Rational Numbers
- NCERT solutions for class 7 maths chapter 10 Practical Geometry
- NCERT solutions for class 7 maths chapter 11 Perimeter and Area
- NCERT solutions for class 7 maths chapter 12 Algebraic Expressions
- NCERT solutions for class 7 maths chapter 13 Exponents and Powers
- NCERT solutions for class 7 maths chapter 14 Symmetry
- NCERT solutions for class 7 maths chapter 15 Visualising Solid Shapes

- NCERT solutions for class 7 science chapter 1 Nutrition in Plants
- NCERT solutions for class 7 science chapter 2 Nutrition In Animals
- NCERT solutions for class 7 science chapter 3 Fibre to Fabric
- NCERT solutions for class 7 science chapter 4 Heat
- NCERT solutions for class 7 science chapter 5 Acids Bases and Salts
- NCERT solutions for class 7 science chapter 6 Physical and Chemical Changes
- NCERT solutions for class 7 science chapter 7 Weather, Climate and Adaptations of Animals to Climate
- NCERT solutions for class 7 science chapter 8 Winds, Storms and Cyclones
- NCERT solutions for class 7 science chapter 9 soil
- NCERT solutions for class 7 science chapter 10 Respiration in Organisms
- NCERT solutions for class 7 science chapter 11 Transportation in Animals and Plants
- NCERT solutions for class 7 science chapter 12 Reproduction In Plant
- NCERT solutions for class 7 science chapter 13 Motion and Time
- NCERT solutions for class 7 science chapter 14 Electric Current and Its Effects
- NCERT solutions for class 7 science chapter 15 Light
- NCERT solutions for class 7 science chapter 16 Water: A Precious Resource
- NCERT solutions for class 7 science chapter 17 Forests: Our Lifeline
- NCERT solutions for class 7 science chapter 18 Waste Water Story