Additive & multiplicative identity — Class 8 CBSE Mathematics MCQs with Solutions
Free Class 8 CBSE Mathematics Additive & multiplicative identity MCQs with step-by-step solutions (30 questions). Part of Rational Numbers. Practise online on Prepizo — no login needed.
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Questions with solutions
Q1 — Additive & multiplicative identity · easy · theory
Which of the following rational numbers is the additive identity?
A. 0 ✓ Correct
B. 1
C. -1
D. 10
Solution: For every rational a, a + 0 = 0 + a = a, so 0 is the additive identity.
Q2 — Additive & multiplicative identity · easy · theory
What is the value of (-5/7) + 0?
A. -5/7 ✓ Correct
B. 5/7
C. 0
D. -7/5
Solution: Adding 0 (the additive identity) leaves the number unchanged, so (-5/7) + 0 = -5/7.
Q3 — Additive & multiplicative identity · easy · theory
Which of the following rational numbers is the multiplicative identity?
A. 1 ✓ Correct
B. 0
C. -1
D. 10
Solution: For every rational a, a × 1 = 1 × a = a, so 1 is the multiplicative identity.
Q4 — Additive & multiplicative identity · easy · theory
What is the value of (3/8) × 1?
A. 3/8 ✓ Correct
B. 8/3
C. 1
D. 3
Solution: Multiplying by 1 (the multiplicative identity) leaves the number unchanged, so (3/8) × 1 = 3/8.
Q5 — Additive & multiplicative identity · easy · theory
What is the additive inverse of -3/5?
A. 3/5 ✓ Correct
B. -3/5
C. 5/3
D. -5/3
Solution: The additive inverse of -3/5 is 3/5 because (-3/5) + (3/5) = 0.
Q6 — Additive & multiplicative identity · easy · theory
What is the reciprocal (multiplicative inverse) of -7/4?
A. -4/7 ✓ Correct
B. 4/7
C. 7/4
D. -7/4
Solution: The reciprocal of a/b is b/a keeping the sign, so the reciprocal of -7/4 is -4/7 (their product is 1).
Q7 — Additive & multiplicative identity · easy · theory
Which of the following rational numbers has NO reciprocal?
A. 0 ✓ Correct
B. 1
C. -1
D. 1/2
Solution: Zero has no reciprocal because there is no number that multiplied by 0 gives 1.
Q8 — Additive & multiplicative identity · easy · theory
What is the value of (2/7) × (7/2)?
A. 1 ✓ Correct
B. 0
C. 4/49
D. 49/4
Solution: A non-zero rational multiplied by its reciprocal always gives 1, so (2/7) × (7/2) = 1.
Q9 — Additive & multiplicative identity · easy · theory
What is the value of 1 × (-6/13)?
A. -6/13 ✓ Correct
B. 6/13
C. -13/6
D. 1
Solution: Multiplying by 1 (the multiplicative identity) leaves the number unchanged, so 1 × (-6/13) = -6/13.
Q10 — Additive & multiplicative identity · easy · theory
What is the value of (-2/3) + (2/3)?
A. 0 ✓ Correct
B. -4/3
C. 4/3
D. 1
Solution: A rational number plus its additive inverse gives 0, so (-2/3) + (2/3) = 0.
Q11 — Additive & multiplicative identity · medium · theory
Find the additive inverse of the rational number (2/5 + (-7/5)).
A. 1 ✓ Correct
B. -1
C. 5
D. -1/5
Solution: 2/5 + (-7/5) = -5/5 = -1, and the additive inverse (negative) of -1 is 1, since -1 + 1 = 0.
Q12 — Additive & multiplicative identity · medium · theory
What is the reciprocal (multiplicative inverse) of the product (-3/4 × 8/9)?
A. -3/2 ✓ Correct
B. -2/3
C. 3/2
D. 2/3
Solution: (-3/4 × 8/9) = -24/36 = -2/3, and the reciprocal of -2/3 is -3/2, since -2/3 × -3/2 = 1.
Q13 — Additive & multiplicative identity · medium · theory
By which number must -6/7 be multiplied so that the product is the multiplicative identity (1)?
A. -7/6 ✓ Correct
B. 7/6
C. 6/7
D. -6/7
Solution: The number giving product 1 is the reciprocal of -6/7, which is -7/6, since -6/7 × -7/6 = 1.
Q14 — Additive & multiplicative identity · medium · theory
For any rational number a, the sum a + (additive inverse of a) equals ___, and for any non-zero rational b, the product b × (reciprocal of b) equals ___.
A. 0 and 1 ✓ Correct
B. 1 and 0
C. 1 and 1
D. 0 and 0
Solution: A rational plus its additive inverse gives 0 (the additive identity), while a non-zero rational times its reciprocal gives 1 (the multiplicative identity).
Q15 — Additive & multiplicative identity · medium · theory
What number must be added to -5/6 so that the sum equals the multiplicative identity (1)?
A. 11/6 ✓ Correct
B. 5/6
C. 1/6
D. -11/6
Solution: We need x with x + (-5/6) = 1, so x = 1 + 5/6 = 6/6 + 5/6 = 11/6.
Q16 — Additive & multiplicative identity · medium · theory
The additive inverse of a rational number is 4/9. What is the reciprocal of that rational number?
A. -9/4 ✓ Correct
B. 9/4
C. -4/9
D. 4/9
Solution: If the additive inverse is 4/9 the number itself is -4/9, and the reciprocal of -4/9 is -9/4.
Q17 — Additive & multiplicative identity · medium · theory
Using the roles of 0 and 1, the value of (-7/12 + 0) × 1 + (0 × 8/9) is:
A. -7/12 ✓ Correct
B. 7/12
C. 0
D. 8/9
Solution: Adding 0 keeps -7/12, multiplying by 1 keeps -7/12, and 0 × 8/9 = 0, so the total is -7/12 + 0 = -7/12.
Q18 — Additive & multiplicative identity · medium · theory
The reciprocal of a rational number is -12/5. What is the additive inverse of that rational number?
A. 5/12 ✓ Correct
B. -5/12
C. 12/5
D. -12/5
Solution: If the reciprocal is -12/5 the number is -5/12, and the additive inverse of -5/12 is 5/12.
Q19 — Additive & multiplicative identity · medium · theory
Evaluate: [(-4/5) + 4/5] × (9/13) + 1.
A. 1 ✓ Correct
B. 0
C. 9/13
D. 13/9
Solution: (-4/5) + 4/5 = 0 (additive inverses), then 0 × 9/13 = 0, and 0 + 1 = 1.
Q20 — Additive & multiplicative identity · medium · theory
What is the additive inverse of the reciprocal of -5/8?
A. 8/5 ✓ Correct
B. -8/5
C. 5/8
D. -5/8
Solution: The reciprocal of -5/8 is -8/5, and the additive inverse of -8/5 is 8/5.
Q21 — Additive & multiplicative identity · hard · theory
Using the identity properties, the value of ((-5/8) × 1) + (0 + (7/12)) is:
A. -1/24 ✓ Correct
B. 1/24
C. 1/10
D. -29/24
Solution: Since a×1 = a and 0+a = a, the expression becomes -5/8 + 7/12 = -15/24 + 14/24 = -1/24.
Q22 — Additive & multiplicative identity · hard · theory
What rational number must be added to ((-2/9) + (5/6)) to obtain the additive identity?
A. -11/18 ✓ Correct
B. 11/18
C. -1/6
D. 7/18
Solution: (-2/9)+(5/6) = -4/18 + 15/18 = 11/18, and the number giving sum 0 is its additive inverse, -11/18.
Q23 — Additive & multiplicative identity · hard · theory
The reciprocal (multiplicative inverse) of ((-4/5) × (10/3)) is:
A. -3/8 ✓ Correct
B. 3/8
C. -8/3
D. 8/3
Solution: (-4/5)×(10/3) = -40/15 = -8/3, whose reciprocal is -3/8.
Q24 — Additive & multiplicative identity · hard · theory
The reciprocal of ((2/3) + (3/4)) is:
A. 12/17 ✓ Correct
B. 17/12
C. 17/6
D. 5/7
Solution: First add: 2/3 + 3/4 = 8/12 + 9/12 = 17/12, and its reciprocal is 12/17 (you must add first, not reciprocate each term).
Q25 — Additive & multiplicative identity · hard · theory
For x = -7/9, the value of (x × reciprocal of x) + (additive inverse of x) is:
A. 16/9 ✓ Correct
B. 2/9
C. -16/9
D. 9/16
Solution: A number times its reciprocal is 1 and the additive inverse of -7/9 is 7/9, so 1 + 7/9 = 16/9.
Q26 — Additive & multiplicative identity · hard · theory
Which of the following statements about rational numbers is FALSE?
A. Every rational number has a reciprocal ✓ Correct
B. Adding 0 to any rational number leaves it unchanged
C. Multiplying any rational number by 1 leaves it unchanged
D. The additive inverse of 0 is 0
Solution: The statement is false because 0 is a rational number that has no reciprocal, while the other three correctly describe the identities and inverses.
Q27 — Additive & multiplicative identity · hard · theory
If a × 1 = -4/7 and b + 0 = 5/14, then the reciprocal of (a + b) is:
A. -14/3 ✓ Correct
B. 14/3
C. -3/14
D. -14/9
Solution: By the identities a = -4/7 and b = 5/14, so a+b = -8/14 + 5/14 = -3/14, whose reciprocal is -14/3.
Q28 — Additive & multiplicative identity · hard · theory
The product of two rational numbers is the multiplicative identity. If one of them equals ((-2/3) × (9/4)), the other number is:
A. -2/3 ✓ Correct
B. 2/3
C. -3/2
D. 3/2
Solution: (-2/3)×(9/4) = -18/12 = -3/2, and since the product is 1 the other number is its reciprocal, -2/3.
Q29 — Additive & multiplicative identity · hard · theory
The reciprocal of a rational number x is -5/8, and the additive inverse of a rational number y is 3/4. The value of x + y is:
A. -47/20 ✓ Correct
B. -17/20
C. 47/20
D. -23/20
Solution: x is the reciprocal of -5/8, so x = -8/5, and y = -3/4 (its additive inverse is 3/4); thus x+y = -32/20 - 15/20 = -47/20.
Q30 — Additive & multiplicative identity · hard · theory
Simplify: (((-9/11) + (9/11)) × (5/7)) + ((4/9) × 1).
A. 4/9 ✓ Correct
B. 0
C. 73/63
D. 5/7
Solution: (-9/11)+(9/11) = 0 (a number plus its additive inverse), so 0×(5/7) = 0, leaving (4/9)×1 = 4/9.