Chapter 10 · Class 7 CBSE · MCQ Test
Integer Operations MCQ Test — Class 7 CBSE
Practice 10 multiple-choice questions with instant answer reveal and explanations.
Integer Operations — MCQ Questions
1Which of the following statements is true regarding the product of a positive integer and a negative integer?
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Answer: The product is always a negative integer.
Hint: Remember the rule for multiplying integers with different signs.
Solution:
When multiplying two integers with different signs (one positive and one negative), the product is always negative.
For example, 5 × (-3) = -15 or (-2) × 7 = -14. The sign of the product is consistently negative.
2What is the product of (-9) and (-7)?
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Answer: 63
Hint: Recall the rule for multiplying two negative integers.
Solution:
When multiplying two negative integers, the product is always positive.
First, multiply their absolute values: 9 × 7 = 63.
Since both integers are negative, the product is positive. So, (-9) × (-7) = 63.
3A temperature change of -3°C occurs every hour. If this change continues for 4 hours, what will be the total change in temperature?
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Answer: -12°C
Hint: A decrease or drop is represented by a negative integer. Multiply the rate of change by the number of hours.
Solution:
The temperature change per hour is -3°C.
For 4 hours, the total change will be 4 × (-3°C).
Multiplying a positive integer (4) by a negative integer (-3) gives a negative product: 4 × (-3) = -12°C.
4Rohan calculated (-8) × 6 as -48. His friend, Priya, argued that the answer should be 48 because 'two negatives make a positive'. Who is correct and why?
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Answer: Rohan is correct because when multiplying a negative integer by a positive integer, the product is always negative.
Hint: Remember the rules for multiplying integers with *different* signs versus *same* signs.
Solution:
Rohan is correct. When multiplying a negative integer (-8) by a positive integer (6), the product is always negative.
The rule 'two negatives make a positive' applies only when multiplying two negative integers. Here, one integer is negative and the other is positive.
So, (-8) × 6 = -48.
5Consider the product of several negative integers. Which of the following statements is true?
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Answer: If the number of negative integers is even, the product is positive.
Hint: Think about what happens when you multiply two negative integers, then three, then four, and observe the pattern of the sign.
Solution:
When multiplying an even number of negative integers, pairs of negatives cancel out their signs, resulting in a positive product. For example, (-2) × (-3) = 6.
When multiplying an odd number of negative integers, there will always be one negative sign left over after pairing, resulting in a negative product. For example, (-2) × (-3) × (-4) = -24.
Therefore, if the number of negative integers is even, the product is positive.
6For any integer 'a', a × ___ = a. The number that fills the blank is called the multiplicative identity for integers.
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Answer: 1
Hint: What number, when multiplied by any integer, leaves the integer unchanged?
Solution:
The multiplicative identity for integers is the number that, when multiplied by any integer 'a', results in 'a' itself.
This number is 1. So, a × 1 = a.
7Ravi says that (-5) × 8 is the same as 8 × (-5). Kavya says they are different because the order of numbers is changed. Who is correct and why?
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Answer: Ravi is correct because multiplication of integers is commutative.
Hint: Recall the property of commutativity for multiplication of integers.
Solution:
Ravi is correct. The multiplication of integers is commutative, which means that changing the order of the integers does not change the product.
The property states that for any two integers 'a' and 'b', a × b = b × a.
In this case, (-5) × 8 = -40 and 8 × (-5) = -40. Both expressions yield the same result.
8Find the integer that must be multiplied by (-6) to get 42.
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Answer: -7
Hint: Think about what sign the missing integer must have to make the product positive, and what number when multiplied by 6 gives 42.
Solution:
Let the missing integer be 'x'. The problem can be written as: (-6) × x = 42.
To find 'x', we need to perform the inverse operation, which is division: x = 42 ÷ (-6).
When dividing a positive integer by a negative integer, the quotient is negative. Also, 42 ÷ 6 = 7.
Therefore, x = -7.
9What is the value of (-15) × (20 - 20)?
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Answer: 0
Hint: First, evaluate the expression inside the parenthesis according to the order of operations (BODMAS/PEMDAS).
Solution:
According to the order of operations, first evaluate the expression inside the parenthesis.
20 - 20 = 0.
Now, substitute this value back into the expression: (-15) × 0.
Any integer multiplied by zero results in zero. So, (-15) × 0 = 0.
10Which of the following statements correctly describes the closure property for multiplication of integers?
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Answer: When you multiply two integers, the product is always an integer.
Hint: The closure property asks if the result of an operation on elements of a set always stays within that set.
Solution:
The closure property for multiplication of integers states that if you multiply any two integers, the result will always be another integer.
For example, 3 × (-4) = -12 (which is an integer), and (-2) × (-5) = 10 (which is an integer). The product always remains within the set of integers.
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Tips for Integer Operations MCQs
- 1Read each question carefully and identify what is being asked before looking at the options.
- 2Try to solve the problem mentally or on paper first, then match your answer with the options.
- 3Use elimination — rule out clearly wrong options to improve your chances even when unsure.
- 4Check units, signs, and edge cases — these are common traps in Integer Operations MCQs.
- 5Review your mistakes after completing the test to build lasting understanding.
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