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Rational Numbers — Class 8 CBSE Mathematics MCQs with Solutions
Free Class 8 CBSE Mathematics Rational Numbers MCQs with step-by-step solutions covering Properties & operations, Additive & multiplicative identity, Distributivity, Representation on the number line, Rationals between two rationals. Practise online on Prepizo — no login needed.
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Sample questions with solutions
Q1 — Properties & operations · easy · theory
Which property is illustrated by (-2/3) + (5/7) = (5/7) + (-2/3)?
A. Commutativity of addition ✓ Correct
B. Associativity of addition
C. Distributivity
D. Closure under addition
Solution: Swapping the order of the two rationals being added leaves the sum unchanged, which is the commutative property of addition.
Q2 — Properties & operations · easy · theory
Rational numbers are NOT closed under which of the following operations?
A. Division ✓ Correct
B. Addition
C. Subtraction
D. Multiplication
Solution: Rationals are closed under +, - and ×, but not under division because dividing by 0 is not defined.
Q3 — Properties & operations · easy · theory
For every rational number a, a × 1 = 1 × a = a. The number 1 is therefore called the:
A. Multiplicative identity ✓ Correct
B. Additive identity
C. Multiplicative inverse
D. Additive inverse
Solution: A number that leaves every rational unchanged under multiplication is the multiplicative identity, which is 1.
Q4 — Properties & operations · easy · theory
Compute (3/7) + (2/7).
A. 5/7 ✓ Correct
B. 5/14
C. 6/7
D. 1/7
Solution: With equal denominators, add only the numerators: (3+2)/7 = 5/7.
Q5 — Properties & operations · easy · theory
For rational numbers, which of these operations IS commutative?
A. Multiplication ✓ Correct
B. Subtraction
C. Division
D. None of these
Solution: Only addition and multiplication are commutative for rationals (a × b = b × a); subtraction and division are not.
Q6 — Properties & operations · easy · theory
Compute (2/3) × (3/5).
A. 2/5 ✓ Correct
B. 5/8
C. 6/5
D. 5/6
Solution: Multiply numerators and denominators: (2×3)/(3×5) = 6/15 = 2/5.
Q7 — Properties & operations · easy · theory
For every rational number a, a + 0 = 0 + a = a. The number 0 is called the:
A. Additive identity ✓ Correct
B. Multiplicative identity
C. Reciprocal
D. Multiplicative inverse
Solution: A number that leaves every rational unchanged under addition is the additive identity, which is 0.
Q8 — Properties & operations · easy · theory
Which property is shown by (1/2 + 1/3) + 1/4 = 1/2 + (1/3 + 1/4)?
A. Associativity of addition ✓ Correct
B. Commutativity of addition
C. Distributivity
D. Additive identity
Solution: Changing only how the three rationals are grouped, without changing their order, is the associative property of addition.
Q9 — Properties & operations · easy · theory
For rational numbers, which operation is NOT commutative?
A. Subtraction ✓ Correct
B. Addition
C. Multiplication
D. Both addition and multiplication
Solution: Subtraction is not commutative because a - b is generally not equal to b - a, while addition and multiplication are commutative.
Q10 — Properties & operations · easy · theory
Compute (5/7) - (2/7).
A. 3/7 ✓ Correct
B. 3/14
C. 7/3
D. 7/7
Solution: With equal denominators, subtract only the numerators: (5-2)/7 = 3/7.
Q11 — 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.
Q12 — 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.
Q13 — 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.
Q14 — 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.
Q15 — 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.
Q16 — 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).
Q17 — 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.
Q18 — 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.
Q19 — 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.
Q20 — 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.
Q21 — Distributivity · easy · theory
The equation (-3/7) × (1/2 + 1/5) = (-3/7) × 1/2 + (-3/7) × 1/5 is an example of which property of rational numbers?
A. Distributivity of multiplication over addition ✓ Correct
B. Commutativity of addition
C. Associativity of multiplication
D. Closure under multiplication
Solution: Multiplying a single number by a sum and spreading it over each term, a×(b+c)=a×b+a×c, is exactly the distributive law.
Q22 — Distributivity · easy · theory
Which of the following statements shows the distributive property?
A. 4 × (5 + 6) = 4 × 5 + 4 × 6 ✓ Correct
B. 4 × 5 = 5 × 4
C. 4 + (5 + 6) = (4 + 5) + 6
D. 4 × 1 = 4
Solution: Only 4 × (5 + 6) = 4 × 5 + 4 × 6 matches the form a×(b+c)=a×b+a×c; the others show commutativity, associativity and the multiplicative identity.
Q23 — Distributivity · easy · theory
For rational numbers a, b and c, the distributive law states that a × (b − c) = ?
A. a×b − a×c ✓ Correct
B. a×b − c
C. a − b×c
D. a×b + a×c
Solution: Distributivity over subtraction spreads the multiplier over both terms, giving a×b − a×c.
Q24 — Distributivity · easy · theory
The property a × (b + c) = a × b + a × c is called the distributivity of multiplication over ______.
A. addition ✓ Correct
B. subtraction
C. division
D. multiplication
Solution: Because the bracket contains a sum (b + c), this is distributivity of multiplication over addition.
Q25 — Distributivity · easy · theory
Using the distributive law, 7 × (10 + 2) = 7 × 10 + 7 × 2 = ?
A. 84 ✓ Correct
B. 72
C. 74
D. 90
Solution: 7 × 10 = 70 and 7 × 2 = 14, and 70 + 14 = 84.
Q26 — Distributivity · easy · theory
Complete using distributivity: 3/5 × (4/7 + 2/9) = 3/5 × 4/7 + 3/5 × ____
A. 2/9 ✓ Correct
B. 3/5
C. 4/7
D. 2/5
Solution: The multiplier 3/5 is distributed over each term of the bracket, so the second term must be 3/5 × 2/9.
Q27 — Distributivity · easy · theory
Taking out the common factor, (2/5 × 3/4) + (2/5 × 1/4) = 2/5 × (3/4 + 1/4). Its value is:
A. 2/5 ✓ Correct
B. 4/5
C. 2/25
D. 5/2
Solution: Inside the bracket 3/4 + 1/4 = 1, so 2/5 × 1 = 2/5.
Q28 — Distributivity · easy · theory
Using distributivity, 6 × (1/2 + 1/3) = 6 × 1/2 + 6 × 1/3 = ?
A. 5 ✓ Correct
B. 6
C. 1
D. 4
Solution: 6 × 1/2 = 3 and 6 × 1/3 = 2, and 3 + 2 = 5.
Q29 — Distributivity · easy · theory
By distributivity, (−2) × (3 + 4) = (−2) × 3 + (−2) × 4 = ?
A. −14 ✓ Correct
B. −2
C. 14
D. −1
Solution: (−2) × 3 = −6 and (−2) × 4 = −8, and −6 + (−8) = −14.
Q30 — Distributivity · easy · theory
Using the distributive law, 2/3 × (1/2 + 1/4) = ?
A. 1/2 ✓ Correct
B. 3/4
C. 1/3
D. 2/9
Solution: Since 1/2 + 1/4 = 3/4, we get 2/3 × 3/4 = 6/12 = 1/2.