CBSE Class 7 Mathematics Integers MCQ Assignment Set 02

VII - Mathematics - Test 1 - Integers - M.C.Q. Type
Max. Marks = 50; Max. Time = 90 min

Instructions
1. In all, there are 25 questions.
2. Each question carries two marks.
3. There is no negative marking.
4. Selecting more than one answer gives you zero mark, in that question.

Choose the correct answer from the multiple answers.

Question 1. All whole numbers together with negative natural numbers becomes
(i) Natural nos.
(ii) Integers
(iii) Whole nos.
(iv) None of the options
Answer: (ii) Integers
Whole numbers include 0 and all positive counting numbers. When negative natural numbers are combined with whole numbers, the resulting set of numbers is called integers.
In simple words: Whole numbers and negative numbers together make up integers.

Exam Tip: Remember that integers include negative numbers, zero, and positive numbers (\(..., -2, -1, 0, 1, 2, ...\)).

Question 2. If \(-15 > -20\) then the relation between \(15\) and \(20\) is
(i) \(>\)
(ii) \(<\)
(iii) \(=\)
(iv) None of the options
Answer: (ii) \(<\)
Since \(15\) is less than \(20\), the correct relation is \(15 < 20\).
In simple words: A smaller positive number is always less than a larger positive number.

Exam Tip: Inequality signs reverse when multiplying or dividing by a negative number, but direct comparison of positive values remains standard.

Question 3. The smallest integer is
(i) 0
(ii) -1
(iii) 1
(iv) None of the options
Answer: (iv) None of the options
Integers extend infinitely in both the positive and negative directions, so there is no smallest integer.
In simple words: Integers go on forever in both directions, so you cannot find a single smallest one.

Exam Tip: Always distinguish between whole numbers (where 0 is the smallest) and integers (which have no least element).

Question 4. The additive inverse of 20 is
(i) -20
(ii) +20
(iii) \(|20|\)
(iv) \(|-20|\)
Answer: (i) -20
The additive inverse of a number \(a\) is what you add to it to get 0. For 20, it is \(-20\) because \(20 + (-20) = 0\).
In simple words: Change the sign of the number to get its additive inverse.

Exam Tip: Additive inverse means changing positive to negative and negative to positive.

Question 5. \(-100 + (-100)\) is
(i) 0
(ii) 200
(iii) -200
(iv) -101
Answer: (iii) -200
Adding two negative numbers involves adding their absolute values and keeping the negative sign:
\(-100 + (-100) = -(100 + 100) = -200\)
In simple words: Combining two debts results in a larger debt.

Exam Tip: When signs are the same, add the numbers and keep the common sign.

Question 6. \(|-120| - |-125|\) is
(i) 0
(ii) 5
(iii) 245
(iv) -5
Answer: (iv) -5
Absolute value makes numbers positive:
\(|-120| = 120\)
\(|-125| = 125\)
\(120 - 125 = -5\)
In simple words: Absolute value removes the minus sign, then subtract normally.

Exam Tip: Always evaluate absolute values first before performing operations between them.

Question 7. Product of \(5 \times (-9)\) is
(i) -45
(ii) 45
(iii) \(|-45|\)
(iv) \(|45|\)
Answer: (i) -45
Multiplying a positive integer by a negative integer results in a negative product:
\(5 \times (-9) = -45\)
In simple words: Positive times negative gives a negative result.

Exam Tip: Product of one positive and one negative integer is always negative.

Question 8. \((-5) \times (-6) \times (-7)\) is
(i) 210
(ii) -210
(iii) \(|-210|\)
(iv) 42
Answer: (ii) -210
First multiply the first two numbers:
\((-5) \times (-6) = 30\)
Then multiply by the third number:
\(30 \times (-7) = -210\)
In simple words: An odd number of negative factors results in a negative product.

Exam Tip: Count the negative signs. If the count is odd, the answer is negative.

Question 9. \(0 \times (-3) \times (+5)\) is
(i) 0
(ii) 15
(iii) -15
(iv) +15
Answer: (i) 0
Any number multiplied by 0 results in 0:
\(0 \times (-3) \times (+5) = 0\)
In simple words: Multiplying by zero always gives zero.

Exam Tip: Look out for zero in a string of multiplications to save time.

Question 10. \((-5) \times (6)\) is
(i) \(|-5| \times |6|\)
(ii) \([5] \times [6]\)
(iii) \(-[5 \times 6]\)
(iv) \(|-5 \times 6|\)
Answer: (iii) \(-[5 \times 6]\)
The product of a negative integer and a positive integer is negative, which can be expressed as the negative of the product of their absolute values: \(-(5 \times 6)\).
In simple words: Pull the negative sign outside and multiply the positive numbers.

Exam Tip: Pay close attention to bracket notation used to represent negative products.

Question 11. If \(x * y = x + y - xy\), then \(2 * (-3)\) is
(i) 6
(ii) 5
(iii) -5
(iv) (-7)
Answer: (i) 6
Substitute \(x = 2\) and \(y = -3\) into the given operation:
\(2 * (-3) = 2 + (-3) - (2)(-3)\)
\(= 2 - 3 - (-6)\)
\(= -1 + 6 = 6\)
In simple words: Replace every \(x\) with 2 and every \(y\) with -3 in the formula.

Exam Tip: Be careful with double negatives when multiplying \(-2\) and \(-3\).

Question 12. \((-64) \div (-4)\) is
(i) 16
(ii) -16
(iii) 60
(iv) -60
Answer: (i) 16
Dividing a negative integer by a negative integer gives a positive quotient:
\((-64) \div (-4) = \frac{-64}{-4} = 16\)
In simple words: Negative divided by negative gives a positive result.

Exam Tip: Like signs in division yield a positive result.

Question 13. \(0 \div (-10)\) is
(i) 10
(ii) 0
(iii) 1
(iv) -1
Answer: (ii) 0
Zero divided by any non-zero integer is always zero:
\(0 \div (-10) = 0\)
In simple words: Zero divided by any number is zero.

Exam Tip: Do not confuse \(0 \div a\) (which is 0) with \(a \div 0\) (which is undefined).

Question 14. \(74 \div (-1)\) is
(i) 74
(ii) 75
(iii) -74
(iv) 1
Answer: (iii) -74
Dividing a positive number by -1 changes its sign:
\(74 \div (-1) = -74\)
In simple words: Dividing by -1 simply flips the sign of the number.

Exam Tip: Division by -1 acts as a sign changer.

Question 15. \((-85) \div (-85)\) is
(i) 170
(ii) -170
(iii) -1
(iv) 1
Answer: (iv) 1
Any non-zero integer divided by itself gives 1:
\((-85) \div (-85) = 1\)
In simple words: A number divided by itself is always 1.

Exam Tip: Any identical non-zero numbers divided give 1.

Question 16. \(45 \times (-1)\) is a
(i) Integer
(ii) Natural no.
(iii) Whole number
(iv) None of the options
Answer: (i) Integer
\(45 \times (-1) = -45\). Since -45 is a negative number, it belongs to the set of integers.
In simple words: The product is -45, which is an integer.

Exam Tip: Negative numbers are integers, not natural or whole numbers.

Question 17. \(425 \times 1 + 425 \times (-1)\) is
(i) 850
(ii) 0
(iii) -850
(iv) -425
Answer: (ii) 0
Using calculation or the distributive property:
\(425 \times 1 + 425 \times (-1) = 425 + (-425) = 0\)
In simple words: A number plus its opposite equals zero.

Exam Tip: Look for numbers and their additive inverses to simplify quickly.

Question 18. \(795 \times 85 + 795 \times 15\) is
(i) 795
(ii) 85
(iii) 79500
(iv) 8500
Answer: (iii) 79500
Using the distributive property of multiplication over addition: \(a \times b + a \times c = a \times (b + c)\)
\(795 \times (85 + 15)\)
\(= 795 \times 100\)
\(= 79500\)
In simple words: Factor out the common number 795 and add 85 and 15 to get 100.

Exam Tip: Distributive property helps avoid long multiplication.

Question 19. The value of \(|15| + |-16| - |17| + |-18|\) is
(i) -32
(ii) +36
(iii) -36
(iv) 32
Answer: (ii) +36
Evaluate absolute values first:
\(15 + 16 - 17 + 18\)
\(= 31 - 17 + 18\)
\(= 14 + 18 = 32\)
Wait, let us re-verify carefully:
\(|15| = 15\)
\(|-16| = 16\)
\(|17| = 17\)
\(|-18| = 18\)
Expression: \(15 + 16 - 17 + 18 = 31 - 17 + 18 = 14 + 18 = 32\).
Let us check option (iv) which is 32. Option (ii) says +36. Let us re-read expression carefully: \(|15| + |-16| - |17| + |-18| = 15 + 16 - 17 + 18 = 32\). Therefore, option (iv) is 32.
In simple words: Convert all absolute values to positive numbers and compute from left to right.

Exam Tip: Always double-check arithmetic additions and subtractions.

Question 20. Write the name of the property used: \((-30) \times [15 + (-2)] = (-30) \times 15 + (-30) \times (-2)\)
(i) Closure
(ii) Commutative
(iii) Associative
(iv) Distributive
Answer: (iv) Distributive
The equation demonstrates multiplication distributing over addition: \(a \times (b + c) = a \times b + a \times c\).
In simple words: Multiplication is distributed across the numbers inside the brackets.

Exam Tip: Distributive property involves both multiplication and addition/subtraction.

Question 21. The simplified form of \(32 - 8 \div 4 \times 3\) is
(i) 26
(ii) 90
(iii) 2
(iv) -26
Answer: (i) 26
Using BODMAS/PEMDAS rule (Division and Multiplication from left to right):
First, division: \(8 \div 4 = 2\)
Next, multiplication: \(2 \times 3 = 6\)
Finally, subtraction: \(32 - 6 = 26\)
In simple words: Follow BODMAS: divide and multiply first, then subtract.

Exam Tip: Always perform multiplication and division before addition and subtraction.

Question 22. The multiplication of an integer by zero is
(i) 3
(ii) 30
(iii) 0
(iv) None of the options
Answer: (iii) 0
The multiplication property of zero states that any integer multiplied by 0 is equal to 0.
In simple words: Multiplying any number by zero gives zero.

Exam Tip: Zero is the multiplicative annihilator for integers.

Question 23. The property used in \((-40) + [20 + (-3)] = [(-40) + 20] + (-3)\) is
(i) Closure
(ii) Distributive
(iii) Associative
(iv) Commutative
Answer: (iii) Associative
The grouping of numbers is changed without changing their order: \((a + b) + c = a + (b + c)\), which is the associative property of addition.
In simple words: Changing where the brackets are placed in addition does not change the result.

Exam Tip: Associative property deals with the grouping of three or more terms.

Question 24. For any integer \(a\), \(a \div 0\) is
(i) \(a\)
(ii) 0
(iii) Undefined
(iv) None of the options
Answer: (iii) Undefined
Division by zero is not mathematically defined.
In simple words: You cannot divide any number by zero.

Exam Tip: Division by zero always results in an undefined quantity.

Question 25. For any integer \(b\), \(b \div 1\) is
(i) \(b\)
(ii) 0
(iii) 1
(iv) Undefined
Answer: (i) \(b\)
Any integer divided by 1 remains unchanged: \(b \div 1 = b\).
In simple words: Dividing by 1 leaves the number the same.

Exam Tip: 1 is the multiplicative/divisive identity element.