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Solving Integer Operations, Quizzes of Mathematics

Mathematics

Various problems related to operations on integers, including addition, subtraction, multiplication, and division. It provides solutions to questions on finding the sum of two integers, identifying patterns in consecutive numbers, and performing calculations with negative integers. The document also discusses the properties of integers, such as the additive inverse and the multiplicative identity. By studying this document, students can develop a deeper understanding of integer operations and improve their problem-solving skills in this fundamental area of mathematics.

Typology: Quizzes

2023/2024

Available from 09/19/2024

rajjatt-sabhrwal
rajjatt-sabhrwal 🇮🇳

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Q1. The sum of two integers is 93. If one of them is -59, the other one is:
1. 34
2. -34
3. 152
4. -152
1 Mark
Ans: 3. 152
Soluon:
Sum of two integers = 93
One integer = -59
Second = 93 - (-59) = 93 + 59 = 152
Q2. Next three consecuve numbers in the paern 11, 8, 5, 2, --, --, -- are:
1. 0, -3, -6
2. -1, -5, -8
3. -2, -5, -8
4. -1, -4, -7
1 Mark
Ans: 4. -1, -4, -7
Soluon:
By observing the series, difference between two consecuve numbers is 3
i.e, 11 - 8 = 3
8 - 5 = 3
5 - 2 = 3
So, next number will be
2 - 3 = -1
Similarly, next two number are
-1 - 3 = -4
-4 - 3 = -7.
Q3. (-10) × (-5) + (-7) is equal to:
1. -57
2. 57
3. -43
4. 43
1 Mark
Ans: 4. 43
Soluon:
(-10) × (- 5) + (-7)
= {(-10) × (-5)} + (-7)
= 50 + (-7)
= 50 - 7
= 43.
Q4. Encircle the odd one of the following:
1. (-9) × 5 × 6 × (-3)
2. 9 × (-5) × 6 × (-3)
3. (-9) × (-5) × (-6) × 3
4. 9 × (-5) × (-6) × 3
1 Mark
Ans: 3. (-9) × (-5) × (-6) × 3
Soluon:
1. (-9) × 5 × 6 × (-3) = (-45) × (-18) = 810
2. 9 × (-50 × 6 × (-3) = (-45) × (-18) = 810
3. (-9) × (-50 × (-6) × 3 = 45 × (-18) = 810
4. 9 × 9-50 × (-60 × (-3) = (-45) × (-18) = 810
So, odd one is opon (c).
Q5. The next number in the paern -62, -37, -12 _____ is.
1. 25
2. 13
3. 0
4. -13
1 Mark
Ans: 2. 13
Soluon:
pf3
pf4
pf5
pf8
pf9
pfa
pfd

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Q1. The sum of two integers is 93. If one of them is -59, the other one is:

  1. 34
  3. 152

1 Mark

Ans: 3. 152 Soluon: Sum of two integers = 93 One integer = - Second = 93 - (-59) = 93 + 59 = 152

Q2. Next three consecuve numbers in the paern 11, 8, 5, 2, --, --, -- are:

  1. 0, -3, -
  2. -1, -5, -
  3. -2, -5, -
  4. -1, -4, -

1 Mark

Ans: 4. -1, -4, - Soluon: By observing the series, difference between two consecuve numbers is 3 i.e, 11 - 8 = 3 8 - 5 = 3 5 - 2 = 3 So, next number will be 2 - 3 = - Similarly, next two number are -1 - 3 = - -4 - 3 = -7.

Q3. (-10) × (-5) + (-7) is equal to:

  2. 57
  4. 43

1 Mark

Ans: 4. 43 Soluon: (-10) × (- 5) + (-7) = {(-10) × (-5)} + (-7) = 50 + (-7) = 50 - 7 = 43.

Q4. Encircle the odd one of the following:

  1. (-9) × 5 × 6 × (-3)
  2. 9 × (-5) × 6 × (-3)
  3. (-9) × (-5) × (-6) × 3
  4. 9 × (-5) × (-6) × 3

1 Mark

Ans: 3. (-9) × (-5) × (-6) × 3 Soluon:

  1. (-9) × 5 × 6 × (-3) = (-45) × (-18) = 810
  2. 9 × (-50 × 6 × (-3) = (-45) × (-18) = 810
  3. (-9) × (-50 × (-6) × 3 = 45 × (-18) = 810
  4. 9 × 9-50 × (-60 × (-3) = (-45) × (-18) = 810 So, odd one is opon (c).

Q5. The next number in the paern -62, -37, -12 _____ is.

  1. 25
  2. 13
  3. 0

1 Mark

Ans: 2. 13 Soluon:

By observing the series, difference between two consecuve numbers is 25, i.e. -37 - (-62) = -37 + 62 = 25 -12 - (-37) = -12 + 37 = 25 So, next number will be -12 + 25 = 13.

Q6. By how much less than -3 is -7?

  1. 4
  3. 10

1 Mark

Ans: 1. 4 Soluon: Difference between -3 and -7 = (-3) - (-7) = -3 + 7 = 4 Thus, -7 is less than -3 by 4

Q7. On subtracng -14 from -18, we get:

  1. 4
  4. 32

1 Mark

Ans: 2. - Soluon: -14 subtracted from - = -18 - (-14) = -18 + 14 = -

Q8. The Sum of two integers is -8. If one of the integers is 2, then the other is:

  1. 20
  2. 4

1 Mark

Ans: 4. - Soluon: Sum of two integers = - One of the integers = 12 Other integer = Sum of two integers - One of the integers = -8 - 12 = -8 + (-12) = -

Q9. The addive inverse of -7 is:

1 Mark

Ans: 3. 7 Soluon: We know that, for every integer a, there exists integer -a such that a + (-a) = 0 = -a + a Here, -a is the addive inverse of a and a is the addive inverse of -a. Now, 7 + (-7) = 0 = -7 + 7 7 is the addive inverse of -

Q10. By how much does 2 exceed -3?

  2. 1
  4. 5

1 Mark

Ans: 4. 5 Soluon: -3 + 5 = 2

Q11. (-15) × 8 + (-15) × 2 =?

  1. 150

1 Mark

1 7

  1. None of these.

Ans: 3. - Soluon: -5 - (6) = -5 - 6 = -

Q18. The sum of two integers is 24. is one them is -9, then the other is:

  1. 43
  3. 5

1 Mark

Ans: 1. 43 Soluon: Sum of two integers = 24 One of the integers = - Other integer = Sum of two integers - One of the integers = 24 - (-19) = 24 + 19 = 43

Q19. 0 ÷ (-5) =?

  2. 0
  3. 1
  4. Not defined.

1 Mark

Ans: 2. 0 Soluon: 0 ÷ (-5) = 0 (Zero divided by any integer other than zero, is zero)

Q20. (-27) × (-16) + (-27) × (-14) =?

  2. 810
  4. 54

1 Mark

Ans: 2. 810 Soluon: (-27) × (-16) + (-27) × (-14) = (-27){-16 - 14} = (-27) × (-30) = 810

Q21. 30 × (-23) + 30 × 14 =?

  2. 270
  3. 1110

1 Mark

Ans: 1. - Soluon: 30 × (-23) + 30 × 14 = 30 × (-23 + 14) = 30 × (-9) = -

Q22. For a non-zero integer a which of the following is not defined?

  1. a ÷ 0
  2. 0 ÷ a
  3. a ÷ 1
  4. 1 ÷ a

1 Mark

Ans: 1. a ÷ 0 Soluon: Division of any number by zero is not defined, a + 0 = not defined.

Q23. By how much does -3 exceed -5?

  2. 2
  3. 8

1 Mark

Ans: 2. 2 Soluon: -3 - (-5) = -3 + 5 = 2

Q24. When the integers 10, 0, 5, -5, -7 are arranged in descending or ascending order, them find out which of the following integers always remains in the middle of the arrangement.

  1. 0
  2. 5

1 Mark

Ans: 1. 0 Soluon: To arrange these integers in ascending or descending order, first we locate these points on number line.

As we know, if a point or number lies on the right side to the other number, then the number is greater. Then, Ascending order -7, -5, 0, 5, 10 Middle term = 0 Descending order → 10, 5, 0, -5, - Middle term = 0 Hence, zero always remains in the middle of the arrangement.

Q25. Which of the following statements is not true?

  1. When two posive integers are added, we always get a posive integer.
  2. When two negave integers are added we always get a negave integer.
  3. When a posive integer and a negave integer is added we always get a negave integer.
  4. Addive inverse of an integer 2 is (-2) and addive inverse of (-2) is 2.

1 Mark

Ans: 3. When a posive integer and a negave integer is added we always get a negave integer. Soluon:

  1. True, when two posive integers are added, the resultant number is also a posive integer.
  2. True, while adding integers, if both the numbers have same sign, the resultant number also get that sign.
  3. False, while adding the integers of different signs, the resultant number get the sign of greater number.
  4. True, addive inverse of an integer is the same integer value, with opposite sign.

Q26. If x = (-1) × (-1) × (-1) × (-1) × ...... 25 mes, y = (-3) × (-3) × (-3), then xy =

  2. 27
  3. 26

1 Mark

Ans: 2. 27 Soluon: x = (-1) × (-1) × (-1) × (-1) × ..... 25 mes The number of integers in the given product is odd. x = (-1) × (-1) × (-1) × (-1) × ...... 25 mes = -(1 × 1 × 1 × ...... 25 mes) = - y = (-3) × (-3) × (-3) The number of integers in the given product is odd. y = (-3) × (-3) × (-3) = -(3 × 3 × 3) = - So, xy = (-1) × (-27) = 27 (Product of two negave integers is always posive)

Q27. If a and b are two integers, then which of the following may not be an integer?

  1. a + b
  2. a - b
  3. a × b
  4. a ÷ b

1 Mark

Ans: 4. a ÷ b Soluon: Addion, subtracon and mulplicaon of two or more integers is always an integer. But, division of integers may or may not be an integer. e.g.

Q28. By observing the number line (Fig.), state which of the following statements is not true. 1 Mark

2 + 3 = 23 not an integer

3 + 3 = 1(integer)

Q33. (-11) × 7 is not equal to:

  1. 11 × (-7)
  2. -(11 × 7)
  3. (-11) × (-7)
  4. 7 × (-11)

1 Mark

Ans: 3. (-11) × (-7) Soluon: (-11) × 7 = (-77) (we know, in mulplicaon, if sign of both numbers are different, then the sign of the resultant is negave and if sign of both numbers are same, then the sign of the resultant is posive.)

  1. 11 × (-7) = -
  2. -(11 × 7) = -
  3. (-11) × (-7) = 77
  4. 7 × (-11) = -

Q34. The modulus of an integer x is 9, then:

  1. x = 9 only.
  2. x = -9 only.
  4. None of these.

1 Mark

Ans: 3. Soluon: The modulus (or absolute value) of an integer is its numerical value regardless of its sign. The absolute value of an integer is always non-negave. It is given that, Modulus of x = |x| = 9 Now, |-9| = 9 and |9| = 9 x = -9 or x = 9

Q35. The sum of two integers is 10. If one of them is negave, then the other has to be:

  1. Negave.
  2. Posive.
  3. May be posive or negave.
  4. None of these.

1 Mark

Ans: 2. Posive. Soluon: It is given that the sum of two integers is 10, which is a posive integer. But, we know that the sum of two negave integers is always a negave integer. So, if the sum of two integers is posive and one of them is negave, then the other has to be posive. For example, ⇒ -2 + 12 = 10 ⇒ -5 + 15 = 10 Thus, the other integer has to be posive.

Q36. Which of the following does not represent an integer?

  1. 0 ÷ (-7)
  2. 20 ÷ (-4)
  3. (-9) ÷ 3
  4. (-12) ÷ 5

1 Mark

Ans: 4. (-12) ÷ 5 Soluon: An integer is a whole number (not a fraconal number) that can be posive, negave or zero. So,

Q37. On subtracng 4 from -4, we get:

  1. 8
  3. 0
  4. None of these

1 Mark

Ans: 2. - Soluon: -4 - (+4) = -4 - 4 = -

Q38. On subtracng -13 from -8, we get:

  2. 21

1 Mark

x = ±

x = ±

x = ±

−7^0 = 0

−4^20 = −

−12 5 (not an integer)

Ans: 3. 5 Soluon: -8 - (-13) = -8 + 13 = 5

Q39. Encircle the odd one of the following:

  1. (-1) × (-1)
  2. (-1) × (-1) × (-1)
  3. (-1) × (-1) × (-1) × (-1)
  4. (-1) × (-1) × (-1) × (-1) × (-1) × (-1)

1 Mark

Ans: 4. (-1) × (-1) × (-1) × (-1) × (-1) × (-1) Soluon:

  1. (-1) × (-1) = 1
  2. (-1) × (-1) × (-1) = - 1
  3. (-1) × (-1) × (-1) × (-1) = 1
  4. (-1) × (-1) × (-1) × (-1) × {-1) × (-1) = 1 Hence, value of opons (a), (c), (d) are same but value of opon (b) is different.

Q40. (-1) × (-1) × (-1) × (-1) × .......... 500 mes =

  2. 1
  3. 500

1 Mark

Ans: 2. 1 Soluon: The number of integers in the given product is even. (-1) × (-1) × (-1) × (-1) × ........ 500 mes = 1 × 1 × 1 × 1 × ..... 500 mes = 1

Q41. Which of the folllowing is not the addive inverse of a?

  1. -(-a)
  2. a × (-1)
  3. -a
  4. a ÷ (-1)

1 Mark

Ans: 1. -(-a) Soluon: Addive inverse of a is (-a). [addive inverse of an integer is the same integer value, with opposite sign] So,

  1. -(-a) = a
  2. a × (-1) = -a
  3. -a
  4. a + (-1) = -a

Q42. If ⊗, O, and • represent some integers on number line, then descending order of these numbers is. 1 Mark

Ans:

Soluon: Descending order in number line, is from right to le. Accordingly.

Q48. (-36) - (-9) =?

  1. None of these.

1 Mark

Ans: 1. 4 Soluon: (-36) ÷ (-9) = 4

Q49. (-1) + (-1) + (-1) + (-1) + .......... 500 mes =

  1. 500
  2. 1

1 Mark

Ans: 4. - Soluon: (-1) + (-1) + (-1) + (-1) + .......... 500 mes = -(1 + 1 + 1 + 1 + ..... 500 mes) = -

Q50. The sum of two integers is 14. If one of them is -8, then the other is:

  1. 22
  3. 6

1 Mark

Ans: 1. 22 Soluon: Sum = 14 One integer = - Second = 14 - (-8) = 14 + 8 = 22

Q51. What should be divided by 6 to get -18?

  2. 3
  4. 108

1 Mark

Ans: 3. - Soluon:

Pung x = -108, we get

Thus, -108 should be divided by 6 to get -

Q52. (-16) ÷ 4 is not same as:

  1. (-4) ÷ 16
  2. -( 16 ÷ 4)
  3. 16 ÷ (-4)

1 Mark

Ans: 1. (-4) ÷ 16 Soluon:

But division is not commutave hence

Q53. (-12) × 6 - (-12) × 4 =?

1 Mark

Ans: 2. - Soluon: (-12) × 6 - (-12) × 4 = (-12)(6 - 4) = -12 × 2 = -

∴ x ÷ 6 = −

⇒ x 6 = −

L.H.S = −108 6 = −|−108| 6

= − 1086 = −18 = R.H.S

(−16) + 4 = −(16 ÷ 4)

= −16 + 4 ÷ (−4) = −4^16 = −

−16 + 4 ≠ (−4) ÷ 16

Q54. Water level in a well was 20m below ground level. During rainy season, rain water collected in different water tanks was drainedinto the well and the water level rises 5m above the previous level. The wall of the well is 1m 20cm high and a pulley is fixed at a height of 80cm. Raghu wants to draw water from the well. The minimum length of the rope that he can use is:

  1. 17m
  2. 18m
  3. 96m
  4. 97m

1 Mark

Ans: 1. 17m Soluon: Details given in the queson, can be described in the figure shown below.

From the above figure, it is clear that. Minimum length of the rope required to draw the water during the rainy season = Distance between pulley and wall of + Height of wall of wall + Distance between

Q55. Encircle the odd one of the following:

  1. (-100) ÷ 5
  2. (-81) ÷ 9
  3. (-75) ÷ 5
  4. (-32) ÷ 9

1 Mark

Ans: 4. (-32) ÷ 9 Soluon:

Here, opon (a), (b) and (c) are the negave integers, but opon (d) is not the negave integer. So, odd one is opon (d).

Q56. (-35) × 2 + (-35) × 8 =

  4. 350

1 Mark

Ans: 1. - Soluon: (-35) × 2 + (-35) × 8 = (-35) × (2 + 8) [a × b + a × c = a × (b + c)] = (-35) × 10 = -

Q57. If x = (-10) + (-10) + ..... 15 mes and y = (-2) × (-2) × (-2) × (-2) × (-2) then x - y =

  1. 118
  4. 182

1 Mark

Ans: 2. - Soluon: x = (-10) + (-10) + ..... 15 mes = - (10 + 10 + .... 15 mes) = - y = (-2) × (-2) × (-2) × (-2) × (-2) = -(2 × 2 × 2 × 2 × 2) (When the number of negave integers in a product is odd, the product is negave) = -

= 80cm + 1m20cm + 15m

= (0.8 + 1.2 + 15)m[ ∵ 1cm = 1001 m ⇒ 80cm = 10080 m = 0.80m and 1cm = 120m]

= 17m

− 9

  1. a
  2. 1
  3. 0

Ans: 2. 1 Soluon: Mulplicave identy for an integer a is 1. [ a mulplicave identy is that identy in which any number is mulplied by that identy, it gives out the same number]

Q64. Which of the following shows the maximum rise in temperature?

  1. 23° to 32°
  2. -10° to + 1°
  3. -18° to -11°
  4. -5° to 5°

1 Mark

Ans: 2. -10° to + 1° Soluon: Rise in temperature,

  1. 32° - 23° = 9°
  2. 1° - (-10)° = 1° + 10° = 11°(maximum)
  3. -11° - (-18)° = -11° + 18° = 7°
  4. 5° - (-5°) = 5° + 5° = 10°

Q65. If a = (-1) × (-1) × (-1) ..... 100 mes and b = (-1) × (-1) × (-1) ..... 95 mes, then a + b =

  3. 0
  4. 1

1 Mark

Ans: 3. 0 Soluon: a = (-1) × (-1) × (-1) × ...... 100 mes Here, the number of integers in the product is even. a = (-1) × (-1) × (-1) × ...... 100 mes = 1 × 1 × 1 × ...... 100 mes = 1 b = (-1) × (-1) × (-1) × ..... 95 mes Here, the number of integers in the product is odd. b = (-1) × (-1) × (-1) × ... 95 mes = − (1 × 1 × 1 × ... 95 mes) = − So, a + b = 1 + (-1) = 0

Q66. By observing the above number line (Fig.), state which of the following statements is true.

  1. B is 2
  2. A is -
  3. B is -
  4. B is -

1 Mark

Ans: 4. B is - Soluon: Since, 8 lies at the le side of 0, so it will be negave and it is at 4th place. So, 8 = - Similarly, A lies at the right side of 0, so it will be posive and it is at 7th place. So, A = 7 Hence, the value of A - 7 and value of 8 = -4.