Class 07 - Chapter 01 - Integers (50)

Posted in Class VII

Q.1. Represent the following integers on the number line.

a) 5

b) -6

c) 4

d) 10

e) -7

f) 9

g) -3

h) -9

i) 7

Q.2. Arrange the numbers -7, 0, 2, -6, 10, -11 in the ascending order and then mark them on number line to verify your answer.

Q.3. Arrange the numbers 10, -2, 8, -4 ,9, -3 in the descending order and then mark them on number line to verify your answer.

Q.4. State whether the following statements are correct or incorrect. Correct those which are wrong.

a) On a number line, we move right when we add a number.

b) On a number line, we move left when we subtract a number.

c) When two positive numbers are added we get a positive number.

d) When a positive number is added to a negative number we get a positive number.

e) When a negative number is added to a positive number we get a negative number.

f) Additive inverse of 9 is (-9) and additive inverse of (-9) is 9.

g) For subtraction we add the additive inverse of the integer that is being subtracted to the other integer.

Q.5. Solve the following:

a) + 10 - 17 + 6

b) - 20 + 2 - 7

c) 100 - 20 - 50

d) 45 - 90

e) - 89 - 21 + 100

Q.6. Solve the following:

a) ____ + 10 = - 20

b) - 20 + 11 = ______

c) - 12 - 24 = 36 - ______

d) -12 + ______ = 40 - 60

e) ____ + 15 = - 56 + 72

Q.7. Write at least two pairs of integers whose sum is:

a) a negative integer

b) a positive integer

c) zero

d) -5

Q.8. Arrange the following in the decreasing (descending) order:

a) -100, -1000, -10, 110

b) 100, -10, -100, 110

c) -111, 1, -11, -1

d) 9999, 999, 99999, 9

e) -9999, -999, -99999, -9

Q.9. Arrange the following in the increasing order (ascending) order:

a) 23, -45, -78, 53

b) 119, -378, 38, -837

c) -4673, 9377, 0982, -9388

d) 765, -837, 983, -958

e) -009, -09, -0009, -9 

Q.10. Write at least two pairs of integers whose difference gives:

a) a positive integer

b) a negative integer

c) zero

d) -5


 Q.11. Solve the following:

a) (+17) + (-17) = _______

b) (-19) + (12) = ______

c) (+10) - (+12) = ______

d) (15) - (-25) = ____ + 12

Q.12. Solve the following:

(a) (-5) + [(-12) + (20)] = ______

(b) [ - 20 + 10 ] - 3 = ______

(c) 11 - ( - 20 + 10 ) = _____

(d) - 92 - ( 12 - 30) + 121 = ____

Q.13. Fill in the blanks, to satisfy the equation:

(a) ____ - 12 + [ 17 - 54 ] = 12 + 100

(b) 98 + ____  - 7 = 12 - [ 12 - ( 7 + 20 - 21 ) ]

(c) 839 + [ - 1000 + 836 ] = ______ - 3525

(d) [ 98 - 1000 + 456 ] 

Q.14. Solve the following:

(a) \( 10 \times 10 \)  

(b) \( 10 \times (-10) \)

(c) \( 10 \times 10 \times (-100) \)  

(d) \( (-1) \times 12 \)

(e) \( (-12) \times (+12) \times (-2) \)  

(f) \( 5 \times (-5) \times 0 \)

Q.15. Solve the following:

(a) 3 + 2 [ - 12 + 10 ] = _____

(b) 3546 x ( - 1 ) - 3 [ 12 + 6 x 3 - 100 ] = ____

(c) [ - 2 ( 21 - 7 x 2 + 7 ) - 100 ] + 12 = ___

(d) 767 + 2 [ 387 - 874 + 8 x 2 ] = ___

Q.16. Verify the following:

(a) 67 x [ 12 + ( - 3 ) ] = [ 67 x 12 ] + [ 67 x ( - 3 ) ]

(b) ( - 30 ) x [ ( - 5 ) + ( - 7 )]  = [ ( - 30 ) x ( - 5 ) ] + [ ( - 30 ) x ( - 7 ) ]

(c) 10 x 80 + 10 x 20 = 10 x ( 80 + 20 )

(d) 10 x 120 - 10 x 20 = 10 x ( 120 - 20 )

Q.17. Find the product, using suitable properties:

(a) 12 x ( - 50 ) + ( - 50 ) x 38

(b) 4 x ( -23 ) x 25

(c) ( - 25 ) x 78 x ( - 4 )

(d) 101 x ( - 32 )

(e) 67 x ( - 17 ) + 17 x ( - 33 )

Q.18. Suraj has two different size of glasses. Bigger glass can contain 300 ml of water and smaller one can contain 150 ml of water. Suraj poured water in a bigger vessel. He used big glass three times and small glass two times. Find how much water is poured in the vessel.

Q.19. A truck can carry 12 tons of material and a mini-truck can carry 8 tons of material. Shyam shifted his material from Chennai to Delhi. He required 7 trucks and 12 mini-trucks to carry the material. Find the total quantity of material shifted.

Q.20. In a class test containing 20 questions, 10 marks are awarded for every correct answer and (-5) marks are awarded for every incorrect answer and 0 for questions not attempted.

(a) Raju gets five correct and 6 incorrect answers. What is his score?

(b) Seema gets 10 correct and 10 incorrect answers. What is her score?

(c) Reshma gets 12 correct and 3 incorrect answers out of 15 questions she attempts. What is her score?


Q.21. Evaluate each of the following:

(a) \( 100 \div 10 \)                  (b) \( (-100) \div 10 \)

(c) \( 84 \div 3\)                 (d) \( 84 \div (-3) \)

(e) \( (-84) \div (-3) \)                     (f) \( ( 100 \times (-84)) \div (-3) \)

Q.22. Evaluate each of the following:

(a) \(1240 \div 10 \)       (b) \(12500 \div 100 \)

(c) \(75 \div 3 \)     (d) \(75 \div 25 \)

(e) \( -25 \div 5 \)     (f) \( 25 \div -5 \)

(g) \( 25 \div 5 \)      (h) \( -25 \div -5 \)

Q.23. Evaluate each of the following:

(a) \( \frac{5 \times (-5)}{5} \)

(b) \(\frac{(-5) \times (-5)}{5} \)

(c) \( \frac{(-5) \times (-5)}{-5} \)

(d) \(\frac{(-5) \times (5)}{-5} \)

Q.24. Divide:

(a) 27 by 3

(b) 81 by 9

(c) 72 by (-12) 

(d) 0 by -75

(e) 11 by 1

(f) (-25) by 25

(g) 27 by (-27)

(h) 7 by 7

(i) (-88) by (-11)

Q.25. Evaluate each of the following:

(a) \( \frac{ 3 \times (-2) \times 12}{-4} \)

(b) \( \frac{ (-5) \times (-3) \times (-10) }{ (-2) \times (3) } \)

(c) \( 7 \times \frac{(-2) \times (-3)}{14} \)

(d) \( 3 + 25 \times \frac{(2) \times (12)}{(-20)} \)

Q.26. What will be the sign of the product if we multiply together:

(a) 2 negative integers and 1 positive integer

(b) 3 positive integers and 3 negative integers

(c) 197 negative integers and 5 positive integers

Q.27. What will be the sign of the expression which is as follows:

(a) ( product of 2 negative integers and 1 positive integer ) divided by ( 1 negative integer)

(b) ( product of 3 positive integers and 3 negative integers) divided by ( 2 positive integers and 3 negative integers)

Q.28. Determine the integer whose product with '-1' is:

(a) 7    (b) 25     (c) -7      (d) 2898      (e) -898      (f) 0

Q.29. Write True or False for the following statements:

(a) For all non-zero integers p and q, p x q is always greater than either p or q.

(b) The product of a positive integer and negative integer is negative.

(c) The product of five negative integers is a negative integer.

(d) The product of even number of negative integers is a negative integer.

(e) The product of odd number of negative integers is a negative integer.

Q.30. Simplify each of the following:

(a) \( 25 - 14 \div 7 + 13 \)

(b) \( 10 + 25 \times 10 \div 2 - 27 \)

(c) \( -(7) - (-10) \div (-2) + 7 \times (-3) \)

(d) \( -(-20) \div 10 \times 12 - (-20) \)

 


Q.31. Represent the following integers on the number line.

(a) 11   (b) 14   (c) -12 
(d) 15  (e) -15   (f) -8
(g) -4  (h) 0  (i) -1

Q.32. Arrange the numbers 11, 14, -14, 12, -7, -6 in the ascending order and then mark them on number line to verify your answer.

Q.33. Arrange the number 6, 7, -8, 4, 9, -3 in the descending order and then mark them on the number line to verify your answer.

Q.34. Solve the following:

(a) - 22 + 7 

(b) 35 - 20

(c) - 40 - 30 

(d) 70 + 45

(e) - 90 + 45

Q.35. Solve the following:

(a) 100 - _____ = 80

(b) - 100 + 70 = ______

(c) _____ - 40 = 11

(d) - 10 + 10 = ____

(e) 76 - 0 = ____

Q.36. Write at least two pairs of integers whose sum is:

(a) a negative integer

(b) a positive integer

(c) zero

(d) - 7

Q.37. Arrange the following in the descending ( decreasing ) order:

(a) 1, 0, -1, -2, 3

(b) 1000, -1000, 100, -100, 10

(c) 78, -88, 98, 108, -48

(d) 2345, -1345, 7345, -6345, 8345

(e) 345, -645, 745, -845, 945

Q.38. Arrange the following in the ascending ( increasing ) order:

(a) 9000, -900, 900, -90, 90

(b) -25,75,-45, -75, 65

(c) 11, -111, 111, -1, 1111

(d) 78, -78, 68, -68, 58, 58

(e) 178, -1278, 1178, 278, -378

Q.39. Write at least two pairs of integers whose difference gives:

(a) a positive integer

(b) a negative integer

(c) zero

(d) - 11

Q.40. Solve the following:

(a) (-117) + (117) = ____

(b) 25 - (9) = ____

(c) (-25) + (-9)  = ____

(d) 109 - (+17) = ____

 


Q.41. Solve the following:

(a) [( -10 ) + 10 ] - 0 = ________

(b) 1 - [ 11 - 12 ] = ________

(c) - 25 + [ 7 - ( 12 + 7 - 23 )] = _______

(d) - 26 + 25 - 36 - 76 + 83 + 20 - 47 = ________

Q.42. Solve the following:

(a) \( 12 \times 10 \)

(b) \( 243 \times 10 \)

(c) \( 4647 \times 10\)

(d) \( 980 \times 10 \)

Q.43. Solve the following:

(a) \( 12 \times 100 \)

(b) \( 234 \times 1000 \)

(c) \(4848 \times 10000 \)

(d) \( 20 \times 1000 \)

Q.44. Solve the following:

(a) \( 466 \times (-100) \)

(b) \( 45 \times (10) \times (-10) \)

(c) \( 11 \times (1) \times (-1) \)

(d) \( (-93) \times 1 \times 0 \)

Q.45. Solve the following:

(a) \( (2) \times (-2) \times (2) \times (-2) \times (1) \times (-2) \)

(b) \( (1) \times (-1) \times (1) \times (-1) \times (1) \times (-1) \)

(c) \( (3) \times (-3) \times (-0) \times(3) \times (-3) \)

(d) \( (-2) \times (1) \times (-1) \times (2) \times (-1) \)

Q.46. Solve the following:

(a) \( (-2) ( 75 - 12 ) \)

(b) \( 17 + 3 ( 5 - 6 ) \)

(c) \( 4 ( 7 - 12)  + 8 \)

(d) \( 5 ( 12 - 10 ) + 3 ( 56 - 60 ) \)

Q.47. Verify the following:

(a) \( 12 \times [ 10 + ( - 5 ) ] = [ 12 \times 10 ] + [ 12 \times ( - 5) ] \) 

(b) \( 11 \times [ 5 + ( - 7)  + 2 ] = [ 11 \times 5 ] + [ 11 \times ( - 7 ) ] + [ 11 \times 2 ] \)  

(c) \( 7 \times 13 + 7 - 7 \times 2 = 7 \times [ 13 + 1 - 2 ] \)

(d) \( 10 \times [ 11 - 9 ] = ( 10 \times 11 ) + ( 10 \times - 9 ) \) 

Q.48. Find the product using suitable properties:

(a) \( 1001 \times 48 \)

(b) \( 10 \times 48 + 10 \times 2 \)

(c) \( 7 \times 59 - 59 \times 107 \)

(d) \( 25 \times (-14) \times 4 \)

Q.49. Find the product using suitable properties:

(a) \( 17 \times 27 + 15 \times 17 + 17 \times 8 \)

(b) \( (1002 \times 34 \)

(c) \( 50 \times 987 \times 2 \)

(d) \( 23 \times 92 + 11 \times 23 - 3 \times 23 \)

Q.50. Ajay has two boxes of different sizes. Bigger box can contain 500 ml of oil and smaller one can contain 300 ml of oil. Ajay poured oil in a bigger vessel. He used big box 5 times and small box 10 times. Find how much oil was poured in the vessel.


Q.51.