Properties & operations — Class 8 CBSE Mathematics MCQs with Solutions
Free Class 8 CBSE Mathematics Properties & operations 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 — 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 — Properties & operations · medium · theory
The set of natural numbers is closed under which pair of operations?
A. Addition and multiplication ✓ Correct
B. Subtraction and division
C. Addition and subtraction
D. Multiplication and division
Solution: Natural numbers are closed only under addition and multiplication; subtraction (e.g. 2 - 5 = -3) and division (e.g. 2 ÷ 3) can give results that are not natural numbers.
Q12 — Properties & operations · medium · theory
For any two rational numbers a and b, which one of these operations is commutative (always gives the same result if a and b are swapped)?
A. Addition ✓ Correct
B. Subtraction
C. Division
D. Both subtraction and division
Solution: Addition (and multiplication) satisfy a + b = b + a, but subtraction and division are not commutative.
Q13 — Properties & operations · medium · theory
What should be added to (-3/8) to obtain the additive identity?
A. 3/8 ✓ Correct
B. -3/8
C. 8/3
D. -8/3
Solution: The additive identity is 0, so we need the additive inverse of -3/8, which is 3/8: (-3/8) + (3/8) = 0.
Q14 — Properties & operations · medium · theory
The equation 2/5 × (3/7 + 1/4) = (2/5 × 3/7) + (2/5 × 1/4) illustrates which property of rational numbers?
A. Distributivity of multiplication over addition ✓ Correct
B. Commutativity of multiplication
C. Associativity of addition
D. Closure under multiplication
Solution: Multiplying a sum by spreading the multiplication over each term, a×(b+c) = a×b + a×c, is the distributive property.
Q15 — Properties & operations · medium · theory
Evaluate (-3/4) + (5/6).
A. 1/12 ✓ Correct
B. -1/12
C. 1/5
D. 19/12
Solution: Using LCM 12: -3/4 = -9/12 and 5/6 = 10/12, so -9/12 + 10/12 = 1/12.
Q16 — Properties & operations · medium · theory
Evaluate (-2/3) × (9/10).
A. -3/5 ✓ Correct
B. 3/5
C. -5/3
D. 7/13
Solution: Multiply numerators and denominators: (-2×9)/(3×10) = -18/30, which simplifies to -3/5.
Q17 — Properties & operations · medium · theory
The statement [(-1/2) × (3/5)] × (4/7) = (-1/2) × [(3/5) × (4/7)] is an example of which property?
A. Associativity of multiplication ✓ Correct
B. Commutativity of multiplication
C. Distributivity of multiplication over addition
D. Multiplicative identity
Solution: Only the grouping of the three factors changes while their order stays the same, which is associativity of multiplication, a×(b×c) = (a×b)×c.
Q18 — Properties & operations · medium · theory
Which one of the following sets of numbers is NOT closed under subtraction?
A. Whole numbers ✓ Correct
B. Integers
C. Rational numbers
D. All of these are closed under subtraction
Solution: Whole numbers are closed only under addition and multiplication; e.g. 3 − 5 = -2 is not a whole number, whereas integers and rationals are closed under subtraction.
Q19 — Properties & operations · medium · theory
Using the distributive property, evaluate 7/9 × (-3/5) + 7/9 × (-2/5).
A. -7/9 ✓ Correct
B. 7/9
C. -7/18
D. -35/9
Solution: Take 7/9 common: 7/9 × (-3/5 + -2/5) = 7/9 × (-5/5) = 7/9 × (-1) = -7/9.
Q20 — Properties & operations · medium · theory
By suitably regrouping, evaluate 3/7 + (-5/9) + 4/7.
A. 4/9 ✓ Correct
B. -4/9
C. 14/9
D. 2/23
Solution: Group the like denominators: 3/7 + 4/7 = 7/7 = 1, then 1 + (-5/9) = 4/9.
Q21 — Properties & operations · hard · theory
Evaluate (-5/6) + (2/3) + (-7/12), writing the answer in lowest terms.
A. -3/4 ✓ Correct
B. 3/4
C. -1/4
D. -9/4
Solution: Using LCM 12: -10/12 + 8/12 - 7/12 = -9/12 = -3/4.
Q22 — Properties & operations · hard · theory
By using a suitable rearrangement of the factors, evaluate (-4/7) × (5/9) × (7/4).
A. -5/9 ✓ Correct
B. 5/9
C. -20/63
D. 5/63
Solution: Using commutativity and associativity of multiplication, group (-4/7) × (7/4) = -1 first, then -1 × 5/9 = -5/9.
Q23 — Properties & operations · hard · theory
Which one of the following statements is TRUE?
A. Integers are closed under subtraction. ✓ Correct
B. Rational numbers are closed under division.
C. Whole numbers are closed under subtraction.
D. Natural numbers are closed under subtraction.
Solution: The difference of any two integers is always an integer; rationals fail closure under division (÷0 is undefined) and whole/natural numbers can give negatives on subtraction (e.g. 2-5=-3).
Q24 — Properties & operations · hard · theory
Evaluate [(-2/5) + (2/5)] × [(-3/7) × (-7/3)].
A. 0 ✓ Correct
B. 1
C. -1
D. 6/35
Solution: (-2/5) + (2/5) = 0 (a number plus its additive inverse), and (-3/7) × (-7/3) = 1 (a number times its reciprocal), so the product is 0 × 1 = 0.
Q25 — Properties & operations · hard · theory
By rearranging using commutativity and associativity, evaluate (-3/11) + (5/7) + (3/11) + (2/7).
A. 1 ✓ Correct
B. 0
C. 1/2
D. 5/7
Solution: Group as ((-3/11) + (3/11)) + ((5/7) + (2/7)) = 0 + 7/7 = 1.
Q26 — Properties & operations · hard · theory
By what rational number must (-8/15) be multiplied to obtain the multiplicative identity?
A. -15/8 ✓ Correct
B. 15/8
C. 8/15
D. -8/15
Solution: The multiplicative identity is 1, so the required number is the reciprocal of -8/15, which is -15/8.
Q27 — Properties & operations · hard · theory
For all rational numbers a, b and c, which of the following statements is NOT true?
A. a - (b - c) = (a - b) - c ✓ Correct
B. a + (b + c) = (a + b) + c
C. a × (b × c) = (a × b) × c
D. a × (b - c) = a×b - a×c
Solution: Subtraction is not associative, so a - (b - c) generally does not equal (a - b) - c, while the other three properties always hold.
Q28 — Properties & operations · hard · theory
Evaluate ((-2/3) + (3/5)) × ((-2/3) - (3/5)).
A. 19/225 ✓ Correct
B. -19/225
C. 19/15
D. 181/225
Solution: The factors are -1/15 and -19/15, whose product is (-1/15)×(-19/15) = 19/225.
Q29 — Properties & operations · hard · theory
What is the additive inverse of the reciprocal of (-3/7)?
A. 7/3 ✓ Correct
B. -7/3
C. 3/7
D. -3/7
Solution: The reciprocal of -3/7 is -7/3, and its additive inverse is 7/3.
Q30 — Properties & operations · hard · theory
Using distributivity, evaluate (-4/9) × (3/7) + (-4/9) × (11/7).
A. -8/9 ✓ Correct
B. 8/9
C. -56/9
D. -8/63
Solution: Take out -4/9: (-4/9) × ((3/7) + (11/7)) = (-4/9) × (14/7) = (-4/9) × 2 = -8/9.