Title Class 7 Math.docx ✅

LESSON 1: INTEGERS  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: (a) Lahulspiti: –8°C, Srinagar: –2°C, Shimla: 5°C, Ooty: 14°C, Bangalore: 22°C (b) 30°C (c) 6°C (d) Yes; No.  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 score obtained by Jack = 25 +(- 5) + (-10) + 15 + 10 = 35.  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? Solution: The temperature of Srinagar on Tuesday is -7°C. It’s temperature on Wednesday is  -3°C.  4.  A plane is flying at a 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: The vertical distance between the plane and submarine is 5000 + 1200 = 6200m.
 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: The amount deposited is represented by a positive integer. The balance in Mohan’s account after withdrawal = 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 travelled towards west? By which integer will you represent her final position from A? Solution: The distance travelled towards west is represented by a negative integer.  The final position from A = 20 – 30 = -10 km.  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 each row, column and diagonal have the same sum -9.  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. Solution: (i) a = 21 , b = 18  a – (-b) = 21 – (- 18)             = 21 + 18             = 39     a + b = 21 + 18             = 39 a–(- b)= a + b (ii)a= 118, b = 125 a – (-b) = 118 – (- 125 )            = 118 + 125            = 243            
  a + b = 118 + 125            = 243 a – (- b) = a + b (iii)a = 75, b = 84  a – (-b) = 75 – (- 84 )             = 75 + 84             = 159    a + b = 75 + 84             = 159 a – (- b) = a + b (iv)a = 28, b = 11 a – (-b) = 28 – (- 11 )             = 28 + 11             = 39    a + b = 28 + 11             = 39 a – (- b) = a + b.  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. Solution: (a) < (b) < (c) > (d) < (e) >  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? Solution: (i) From the 1 st  step it jumps three steps down(-) and then two steps up( +) and so on… (i.e.,) 1-[ (- 3 + 2)+( – 3 + 2)+( – 3 + 2)+( – 3 + 2)+( – 3 + 2)+ - 3] . So it continues to reach the water level after 11 jumps. (ii) After drinking water, when he jumps 4 steps up (+), and jumps 2 steps down(-). (i.e.,) 9 –[ (4 – 2) + (4 – 2) + 4] . Here nine denotes the 9 th step to reach the top step 5 jumps are required. (iii) (a) –3 + 2 –3 + 2 – 3 + 2 – 3 + 2 –3 + 2 –3 = – 8 (b) 4 – 2 + 4 – 2 + 4 = 8 8 in (b) represents going up 8 steps.  11.  Write down a pair of integers whose: (a) sum is –7 (b) difference is –10 (c) sum is 0. Solution: One such pair could be : (a)–4, -3 (b)–4, 6 ( because –4 –(6) = -10) (c) –3, 3 (because –3 +(3) = 0).  12.  (a) Write a pair of negative integers whose difference gives 8. (b) Write a negative integer and a positive integer whose sum is –5. (c) Write a negative integer and a positive integer whose difference is -3. Solution: One such pair could be : (a)-4, -12;[-4 - (-12) = 8] (b)-7, 2; [-7+ 2 = -5]