Properties of operations on integers Quiz - ICSE Class 7 Mathematics

Free practice quiz: Properties of operations on integers (ICSE Class 7 Mathematics). 55 multiple-choice questions with answers and explanations. Play online, no sign-up needed.

This ICSE Class 7 Mathematics practice quiz has 55 multiple-choice questions on Properties of operations on integers, and 55 of them come with an explanation. Try the 5 sample questions below (tap an option to check yourself), then play the full quiz online. No sign-up needed.

Sample questions

1. If a = -5 and b = 3, what is the value of a - b?

   1. -8
   2. -2
   3. 2
   4. 8
   Show answer

   Answer: A. -8

   To find a - b, substitute the given values: -5 - 3. When subtracting integers with the same sign, you add their absolute values and keep the sign. So, |-5| + |3| = 5 + 3 = 8. Since both numbers are negative (or we are subtracting a positive from a negative), the result is negative: -8.

2. Calculate: (-25) ÷ 5 - (-10) × 3

   1. -25
   2. 25
   3. -35
   4. 35
   Show answer

   Answer: B. 25

   Following the order of operations (PEMDAS/BODMAS): First, perform the division: (-25) ÷ 5 = -5. Next, perform the multiplication: (-10) × 3 = -30. Finally, perform the subtraction: -5 - (-30). Subtracting a negative is the same as adding a positive: -5 + 30. When adding integers with different signs, find the difference between their absolute values: |30| - |5| = 30 - 5 = 25. The result takes the sign of the integer with the larger absolute value, which is 30. Therefore, -5 + 30 = 25.

3. What is the smallest positive integer?

   1. 0
   2. 1
   3. -1
   4. None of the above
   Show answer

   Answer: B. 1

   Positive integers are integers greater than zero. The set of positive integers is {1, 2, 3, ...}. The smallest number in this set is 1.

4. If a number is multiplied by 0, what is the result?

   1. The number itself
   2. The additive inverse of the number
   3. Zero
   4. Undefined
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   Answer: C. Zero

   Multiplying any integer by zero always results in zero. This is a fundamental property of multiplication.

5. Which property guarantees that the product of two integers is always an integer?

   1. Commutative property
   2. Associative property
   3. Closure property under multiplication
   4. Distributive property
   Show answer

   Answer: C. Closure property under multiplication

   The closure property under multiplication for integers means that when you multiply any two integers, the result is always another integer. For example, -3 × 5 = -15, and both -3, 5, and -15 are integers.

More questions in this quiz

Answers and explanations are in the full quiz.

1. What is the additive inverse of -17?
2. Which property of integers is demonstrated by the equation: (-7) + 5 = 5 + (-7)?
3. Calculate: (-15) × (-3) ÷ (-5)
4. Which of the following expressions is equivalent to -10 - (-5)?
5. What is the value of the expression: 5 × (-2 + 7) - 3?
6. The product of three integers is -48. If two of the integers are -3 and 4, what is the third integer?
7. Which property ensures that for any two integers 'a' and 'b', a × b = b × a?
8. Calculate: -100 ÷ 10 + (-5) × 2
9. The sum of two integers is -15. If one of the integers is -8, what is the other integer?
10. Which property of addition of integers is illustrated by the equation 0 + (-12) = -12?
11. Which of the following is NOT a property of integers?
12. What is the smallest integer that is greater than -10?
13. Calculate the value of 15 + (-8) - 7.
14. Which of the following is the multiplicative inverse of -4?
15. If a = 6, b = -3, calculate a - b.
16. What is the result of (-9) × (-8) ÷ (-6)?
17. The distributive property states that a × (b + c) = (a × b) + (a × c). If a = -5, b = 2, and c = -4, which expression is equivalent to a × (b + c)?
18. What is the value of -20 - (-15) + 10?
19. If a number is divided by -1, what happens to the number?
20. Which property of multiplication is illustrated by the equation: 7 × (3 × 5) = (7 × 3) × 5?
21. What is the result of -8 × (-6) + (-10) ÷ 2?
22. Which operation on integers is commutative?
23. What is the largest integer that is less than -5?
24. Calculate: 10 - 12 + 8 - 6.
25. What is the value of (-7) + (-7) + (-7) + (-7)?
26. Which property is demonstrated by the equation (-6) × 1 = -6?
27. What is the value of (-12) × (-3) ÷ (-4)?
28. If a = -9, b = 3, and c = -1, what is the value of a + b - c?
29. Which of the following is an example of the additive inverse property?
30. What is the result of (-5) × (-4) + 10?
31. Calculate: -18 ÷ (-3) × 2.
32. Which property states that adding zero to an integer does not change its value?
33. What is the value of -5 - (8 - 12)?
34. The product of two integers is 64. If one of the integers is -8, what is the other integer?
35. Which property of operations on integers states that a + b = b + a?
36. Calculate: (-10) × (-5) - 20.
37. What is the value of -50 + 25 - (-10)?
38. Which integer has no additive inverse?
39. Calculate the value of (-6) × (4 - (-2)).
40. The sum of three integers is -18. If two of the integers are -7 and 5, what is the third integer?
41. What is the value of -1 × (-1) × (-1) × (-1)?
42. If a = 10, b = -5, and c = 2, what is the value of a ÷ (b ÷ c)?
43. What is the smallest integer that is not positive and not negative?
44. Which property is demonstrated by the equation 9 × (5 + 3) = 9 × 5 + 9 × 3?
45. Calculate: (-10 + 5) × (-2 - 3).
46. If a = -15 and b = -3, what is the value of a - b?
47. What is the largest integer that is greater than -100?
48. Calculate: -20 × 3 + (-15) ÷ 5.
49. What is the integer identity element for addition?
50. If a = -4, b = -5, and c = -2, what is the value of a - b - c?

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