INTEGERS. Question Bank. Class - VI Mathematics

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1 3 INTEGERS 1. Write the opposite of each of the following statements : (i) Gain of Rs 6 (ii) 5 m above sea-level (iii) 2 m due west (iv) 25% increase. (v) 1 C below freezing point (vi) 2 m to the left (vii) Below average (viii) Gaining a weight of 2 kg Ans. (i) Loss of Rs 6 (ii) 5 m below sea level (iii) 2 m due east (iv) 25% decrease (v) 1 C above freezing point (vi) 2 m to the right (vii) Above average (viii) Losing a weight of 2 kg 2. Indicate the following using negative sign : (i) Loss of Rs 3 (ii) Spending Rs 7 (iii) 6 m below sea-level (v) 2 C below freezing point Ans. (i) Gain of Rs ( 3) (iii) Earning Rs ( 7) (iv) 6 m above sea-level (v) 2 C above freezing point 3. Write all integers between : (i) + 2 and + 6 (ii) 3 and 4 (iii) 6 and (iv) 5 and + 5 (v) 1 and 3 Ans. (i) + 3, + 4, + 5 (ii) 2, 1,, 1, 2, 3 (iii) 5, 4, 3, 2, 1, (iv) 4, 3, 2, 1,, 1, 2, 3, 4 (v) 9, 8, 7, 6, 5, 4 4. Mark each of the following on a number line : (i) + 6 (ii) (iii) 7 (iv) 1 Ans. (i) (ii) (iii) (iv) Fill in each of the place holders with < or > sign : (i) (ii) 15 1 (iii) 8 8 (iv) 13 2 Ans. (i) 2 < (ii) 15 < 1 (iii) 8 < 8 (vi) 13 > 2 1

2 6. Write the following integers in ascending order : (i) 4, 7, 1,, 6, 13 (ii) 37, 28, 15, 6, 23, 19 Ans. (i) 13 < 7 < < 1 < 4 < 6 (ii) 28 < 19 < 15 < 6 < 23 < Write the following integers in descending order : (i), 4, 31, 41, 35, 6 (ii) 61,, 3, 3, 6, 6 Ans. (i) 31 > 6 > > 4 > 35 > 41(ii) 6 > 3 > 3 > 6 > > Write the value of : (i) 3 (ii) (iii) (iv) 9 2 Ans. (i) 3 (ii) (iii) 12 (iv) 7 9. Find the sum : (i) (+ 37) + (+ 68) (ii) ( 85) + ( 76) Ans = + 15 Ans = 161 (iii) = 9 (iv) (+43) + ( 11) Ans = 9 Ans = Write the additive inverse of : (i) 17 (ii) 39 (ii) (iv) 143 Ans. (i) 17 (ii) 39 (iii) (iv) Find the difference : (i) (+15) (+17) (ii) (+13) (+78) Ans = 2 Ans = 25 (iii) ( 56) (+173) (iv) (+216) () Ans = 229 Ans. 216 = Subtract : (i) 186 from 186 (ii) 276 from 276 Ans. = 186 ( 186) Ans. = 276 (276) = = = 52 (iii) 659 from 78 Ans. 78 ( 659) = = The sum of two integers is 17. If one of them is 6, find the other. Ans. Let the other integer be is x 6 + x = 17 x = 17 6 = 23 The other integer is What must be added to 26 to get 14? Ans. Let x be the number to be added 2

3 26 + x = 14 x = = 4 4 must be added. 15. A car travelled east of Delhi by 1 km and then to the west of it by 13 km. How far from Delhi was the car finally? Ans. Finally = (13 1) km = 3 km to the west of Delhi. 16. While playing cards Amit lost Rs 7 in the first game, Rs 5 in the second game and Rs 35 in the third game. Also, he gained Rs 6 in the fourth game and Rs 8 in the fifth game. What was his net loss or gain? Ans. Amount Amit lost in first three games. = Rs ( ) = Rs 155 Amit gain in fourth and fifth games = Rs (6 + 8) = Rs 14 Net loss = Rs (155 14) = Rs Find the product : (i) (+21) (+ 19) (ii) () ( 35) Ans. + (21 19) = Ans. + (12 35) = 42 (iii) ( 16) ( 245) (iv) (+ 21) ( 4) Ans. + (16 245) = Ans. (21 4) = 84 (v) () ( 15) (vi) () (+ 6) Ans. (36 15) = 54 Ans. 6 = On a certain day at a certain time in Ladakh, the temperature was 21 C. On the same day at the same time, the temperature in Kolkata was 21 C. What is the difference between these two temperatures? Ans. Temperature in Ladakh = 21 C. Temperature in Kolkata = 21 C Difference = 21 C ( 21 C) = 21 C + 21 C = 42 C. 19. Evalute the following : (i) 5 7 (ii) Ans. 5 7 = 5 7 = 2 Ans = = 8 (iii) 6 = 6 (iv) Ans. 6 = 6 Ans. = = = 6 (v) 11 1 (viii) = 11 1 = 1 = 1 Ans = 13 1 =13 1 = 3 Ans = = 8 (vi) 9 4 Ans. = 9 4 = 9 4 = 5 2. If a rise in temperature by 3 C is represented by + 3 ; what does each of the following represent : (i) + 5 (ii) (iii) 3 (iv) 2 3

4 Ans. (i) + 5, A rise in temperature by 5 C (ii), No change in temperature (iii) 3 Fall in temperature by 3 C (iv) 2, Fall in temperature by 2 C. 21. If moving of 16 m due West is given by + 16; what is given by : (i) 1 (ii) 5 Ans. (i) 1 Moving of 1 m due East (ii) 5 Moving of 5 m due West. 22. A speed of 2 m/s towards North is represented by + 2 ; what is represented by : (i) + 5 (ii) 3 Ans. (i) + 5 Speed of 5 m/s towards North. (ii) 3 Speed of 3 m/s towards South. 23. Walking 8 km towards South is denoted by 8 ; what is denoted by : (i) + 2 (ii) 3 Ans. (i) + 2 Walking 2 km towards North (ii) 3 Walking 3 km towards m below the earth s surface is given by 28; state, what is given by : (i) 5 (ii) (iii) + 34 Ans. (i) 5, represents, 5 m below the earth surface (ii) ; 12 m above the earth s surface (iii) + 34; 34 m above the earth s surface. 25. A boy walks 8 m due North and then 63 m due South. Find his position with respect to his starting point. Ans. Let 8 m due North is represented by + 8, then 63 represents 63 m due South. On adding + 8 and 63 we get (+ 8) + ( 63) = = + 17; which is positive The position of the man with respect to his starting point is 17 m due North 26. The temperature of a body first rises by 18 C and then falls by 23 C. Find the final temperature of the body, if its initial temperature is : (i) 3 C (ii) C (iii) 27 C Ans. Let the rise in temperature be denoted by positive sign (+), then the fall in temperature will denoted by negative sign ( ) (i) Final temperature = 3 C + (+ 18 C) + ( 23 C) = 3 C + 18 C 23 C = 35 C. (ii) Final temperature = C + (+ 18 C) + ( 23 C) = C + 18 C 23 C = 5 C. (iii) Final temperature = 27 C + (+ 18 C) + ( 23 C) = 22 C. 27. Complete the following multiplication table : Second Number x First Number

5 Hence state true or false : (i) ( 3) ( 4) = ( 4) ( 3) (ii) ( 12) < (iii) ( 1) = 1 (iv) 3 ( 4) > First Number 4 x Second Number Ans. (i) ( 3) ( 4) = ( 4) ( 3) True (ii) ( 12) < < False (iii) ( 1) = 1 = 1 False (iv) 3 ( 4) > = > False 28. (i) 7 8 ( 2) + 3 ( 4) (ii) 9 {724 ( } Ans () = 11 = 1 Ans. = 9 {7 24 (8 16) = 9 {7 24 (2 16} = 9 {7 24 4}= 9 {7 6} = 9 (+1) = 9 1 = 8 (iii) 5 2 [3 {5 (7 + 2 of 4 19)}] Ans. = 5 2 [3 {5 ( )}] = 1 [3 {5 ( )}] = 1 [3 {5 ( 4)}] = 1 [3 {5 + 4}] = 1 {3 9} = 1 [ 6} = = 16 (iv) 11 [ 6 {3 5 (8 4 1)}] Ans. = 11 [ 6 {3 5 (2 1)}] = 11 [ 6 {3 5 (1}] = 11 [ 6 { 2}] = 11 [ 4] = 7. (v) ( 7) ( 5) + 6 ( 3) ( 9) 8 Ans ( 18) ( 72) = = = 89 (vi) ( 6) ( 11) 5 () + ( 16) 4 Ans. = ( 16) 4 = ( 64) = 6 64 = To get a closer finish in a 1 m race, the runners are given different starting positions, depending upon how fast they can run. A starting position of + 1 means 5

6 that the runner starts 1 m in front of the start line and 5 means that the runner starts 5 m behind the start line. The competitors starting positions are : Arnav Tushar 3 Nakul 2 Anshul + 1 Tarush + 15 Ankita + 5 (i) Who starts farthest from the finish line? Ans. Nakul starts the farthest from finish line i.e., 2 is least. (ii) How far does Tarush have to run to reach the finish line? Ans. Starting position + 15; Race = 1 m Difference = 1 ( + 15) = 1 15 = 85 m. (iii) How many metres are there between the starting positions of Tushar and Anshul? Ans. Starting position of Tushar = 3; Starting position of Anshul = + 1 Difference = + 1 ( 3) = 13. 6

Directed Numbers. +5 x -3 = Mathletics Instant Workbooks. Copyright

Directed Numbers. +5 x -3 = Mathletics Instant Workbooks. Copyright Directed Numbers Student Book - Series H- +5-3 = Mathletics Instant Workbooks Copright Student Book - Series H Contents Topics Topic - Plotting on number lines Topic 2 - Opposite directions negative numbers