NCERT Solutions Class 6 MathsChapter  6: IntegersExercise 6.11. Write opposites of the following: (a) Increase in weight Answer: Decrease in weight Explanation: Decrease is the opposite of increase (b) 30 km north Answer: 30 km South Explanation: South is the opposite direction of North (c) 80 m east Answer: 80 m west Explanation: West is the opposite direction of East (d) Loss of Rs 700 Answer: Gain of Rs 700 Explanation: Gain is the opposite of loss (e) 100 m above sea level Answer: 100 m below sea level Explanation: Below is the opposite of above 2. Represent the following numbers as integers with appropriate signs. (a) An aeroplane is flying at a height two thousand metre above the ground. Answer: + 2000 Explanation: Ground level is considered at level 0. The level above the ground level is positive, while the level below the ground level is negative. Hence, 2000 m above the ground can be represented as +2000. (b) A submarine is moving at a depth, eight hundred metre below the sea level. Answer:  800 Explanation: Sea level is considered at level 0. The level above the sea level is positive, while the level below the sea level is negative. Hence, 800 m below the ground can be represented as 800. (c) A deposit of rupees two hundred. Answer: +200 Explanation: Deposit means to submit the amount in the respective account. The value deposited is added to the total amount. Hence, it represented as positive. (d) Withdrawal of rupees seven hundred. Answer: 700 Explanation: Withdraw means to take out the amount from the respective account. The value taken is subtracted from the total amount. Hence, it represented as negative. 3. Represent the following numbers on a number line: (a) + 5 (b)  10 (c) + 8 (d)  1 (e)  6 4. Adjacent figure is a vertical number line, representing integers. Observe it and locate the following points: The equivalent diagram showing the numbers on the number line is shown below: (a) If point D is + 8, then which point is  8? Answer: F The above diagram shows that F is the point that has the value equivalent to 8. (b) Is point G a negative integer or a positive integer? Answer: Negative G has the value equivalent to 6. Hence, it is a negative integer. (c) Write integers for points B and E. Answer: 4, 10 B has the value equivalent to 4 and E has the value equivalent to 10. (d) Which point marked on this number line has the least value? Answer: E E has the least value of 10. (e) Arrange all the points in decreasing order of value. Answer: D, C, B, A, H, G, F, E D has the highest value of 8 and E has the lowest value of 100. Thus, the decreasing order from highest integer to the lowest integer is D, C, B, A, H, G, F, E. 5. Following is the list of temperatures of five places in India on a particular day of the year. Siachin 10°C below 0°C Shimla 2°C below 0°C Ahmedabad 30°C above 0°C Delhi 20°C above 0°C Srinagar 5°C below 0°C a) Write the temperatures of these places in the form of integers in the blank column.
The temperatures below 0°C are represented with the negative sign, while the temperatures above 0°C are represented with the positive sign. (b) Following is the number line representing the temperature in degree Celsius. Plot the name of the city against its temperature. The cities with positive temperature are represented on the right side of the number line, while the cities with negative temperatures are represented on the left side of the number line. Answer: (c) Which is the coolest place? Answer: Siachin The city with the lowest temperature is considered as the coolest place. (d) Write the names of the places where temperatures are above 10°C. Answer: Delhi and Ahmedabad Delhi has the temperature of 20 degrees Celsius, while Ahmedabad has the temperature of 30 degrees Celsius. 6. In each of the following pairs, which number is to the right of the other on the number line? Positive number is always represented on the right side of the number line, while negative numbers are represented on the left side. 0 is the centre of the number line. (a) 2, 9 Answer: 9 9 is to the right of the number 2 (b)  3,  8 Answer: 3 3 is to the right of the number 8 (c) 0,  1 Answer: 0 0 is to the right of the number 1 (d)  11, 10 Answer: 10 10 is the right of the number 11 (e)  6, 6 Answer: 6 6 is the right of the number 6 (f) 1,  100 Answer: 1 1 is the right of the number 100 7. Write all the integers between the given pairs (write them in the increasing order.) (a) 0 and  7 Answer: 6, 5, 4, 3, 2, 1 These numbers on the number line will appear as: (b)  4 and 4 Answer: 3, 2, 1, 0, 1, 2, 3 These numbers on the number line will appear as: (c)  8 and  15 Answer: 14, 13, 12, 11, 10, 9 (d)  30 and  23 Answer: 29, 28, 27, 26, 25, 24 8. (a) Write four negative integers greater than  20. Answer: 19, 18, 17, 16 Note: In the case of negative numbers, the numbers starting from 1 to 2, 3, and so on are in the decreasing order. It means that 2 is smaller than 1. The same is reverse in case of the positive numbers. The numbers starting from 1 to 2, 3, 4 and so on are in the increasing order. It means that 2 is greater than 1.(b) Write four integers less than  10. Answer: 11, 12, 13, 14 9. For the following statements, write True (T) or False (F). If the statement is false, correct the statement. (a)  8 is to the right of  10 on a number line. Answer: True (b)  100 is to the right of  50 on a number line. Answer: False Correct statement:  50 is to the right of  100 on a number line. (c) Smallest negative integer is  1. Answer: False Correct statement: Largest negative integer is  1. (d)  26 is greater than  25. Answer: False Correct statement:  25 is greater than  26. 10. Draw a number line and answer the following: (a) Which number will we reach if we move 4 numbers to the right of  2. Answer: 2 Number line: (b) Which number will we reach if we move 5 numbers to the left of 1. Answer: 4 Number line: (c) If we are at  8 on the number line, in which direction should we move to reach  13? Answer: left Explanation: The numbers smaller than 8 are present on its left side. 13 is smaller than 8. (d) If we are at  6 on the number line, in which direction should we move to reach  1? Answer: Right Explanation: The numbers greater than 6 are present on its right side. 1 is greater than 6. Exercise 6.21. Using the number line write the integer which is: (a) 3 more than 5 Answer: 8 (b) 5 more than 5 Answer: 0 (c) 6 less than 2 Answer: 4 (d) 3 less than 2 Answer: 5 2. Use number line and add the following integers: (a) 9 + ( 6) Answer: 3 (b) 5 + ( 11) Answer: 6 (c) ( 1) + ( 7) Answer: 8 (d) ( 5) + 10 Answer: 5 (e) ( 1) + ( 2) + ( 3) Answer: 6 (f) ( 2) + 8 + ( 4) Answer: 2 3. Add without using number line: (a) 11 + ( 7) Answer: 11  7 = 4 Adding + and  is equal to  (b) ( 13) + (+ 18) Answer: 13 + 18 = 5 Adding + and + is equal to + (c) ( 10) + (+ 19) Answer: 10 + 19 = 19  10 = 9 (d) ( 250) + (+ 150) Answer: 250 + 150 = 150  250 = 100 The sign of the greater integer comes with the answer. If the greater number is positive, the answer is positive. If the greater number is negative, the answer is negative. Here, the number 250 is greater than 150. (e) ( 380) + ( 270) Answer: 380  270 = 650 Same sign numbers are always added. Both the numbers are added because of the same negative sign. The answer will be an added number with the negative sign. (f) ( 217) + ( 100) Answer: 217  100 = 317 4. Find the sum of: (a) 137 and  354 Answer: 217 137 + (354) = 137  354 = 217 (b)  52 and 52 Answer: 0 52 + 52 = 0 (c)  312, 39 and 192 Answer: 81 312 + 39 + 192 = 312 + 231 = 231  312 = 81 (d)  50,  200 and 300 Answer: 50 50 + (200) + 300 = 50  200 + 300 = 250 + 300 = 300  250 = 50 5. Find the sum: (a) ( 7) + ( 9) + 4 + 16 Answer: 4  7  9 + 4 + 16 = 16 + 20 (Adding the numbers with same sign first) = 20  16 = 4 (b) (37) + ( 2) + ( 65) + ( 8) Answer: 38 = 37  2  65  8 (Adding the numbers with same sign first) = 37  75 = 38 Exercise 6.31. Find (a) 35  (20) Answer: 15 35  20 = 15 (b) 72  (90) Answer: 18 72  90 = 18 (c) ( 15)  ( 18) Answer: 3 15 + 18 = 18  15 = 3 Adding  and  is equal to  (d) (20)  (13) Answer: 33 20  13 = 33 (e) 23  ( 12) Answer: 35 23 + 12 = 35 (f) (32)  ( 40) Answer: 8 32 + 40 = 40  32 = 8 2. Fill in the blanks with >, < or = sign. (a) ( 3) + ( 6) < ( 3)  ( 6) Explanation: LHS (Left Hand Side) ( 3) + ( 6) = 3  6 = 9 RHS (Right Hand Side) ( 3)  ( 6) = 3 + 6 = 3 Thus, LHS < RHS (b) ( 21)  ( 10) > ( 31) + ( 11) Explanation: LHS ( 21)  ( 10) 21 + 10 = 11 RHS ( 31) + ( 11) 31  11 = 42 Thus, LHS > RHS (c) 45  ( 11) > 57 + ( 4) Explanation: LHS 45  ( 11) 45 + 11 = 56 RHS 57 + ( 4) = 57  4 = 53 Thus, LHS > RHS (d) ( 25)  ( 42) > ( 42)  ( 25) Explanation: LHS ( 25)  ( 42) = 25 + 42 = 42  25 = 17 RHS ( 42)  ( 25) = 42 + 25 = 17 Thus, LHS > RHS 3. Fill in the blanks. (a) ( 8) + 8 = 0 (b) 13 + ( 13) = 0 (c) 12 + ( 12) = 0 (d) ( 4) + ( 8) =  12 (e) 5  15 =  10 4. Find (a) ( 7)  8  ( 25) Answer: 10 7 8 + 25 = 15 + 25 = 10 (b) ( 13) + 32  8  1 Answer: 10 13 + 32  8  1 = 32  13  8  1 Adding numbers with the same negative sign first = 32  22 = 10 (c) ( 7) + ( 8) + ( 90) Answer: 105 7 8  90 Adding numbers with the same negative sign =  105 (d) 50  ( 40)  ( 2) Answer: 92 50 + 40 + 2 = 92
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