Properties of Operations

Math ⇒ Number and Operations

Properties of Operations starts at 6 and continues till grade 12. QuestionsToday has an evolving set of questions to continuously challenge students so that their knowledge grows in Properties of Operations. How you perform is determined by your score and the time you take. When you play a quiz, your answers are evaluated in concept instead of actual words and definitions used.

See sample questions for grade 11

Explain why division does not have an identity element.

Explain why the distributive property is important when simplifying algebraic expressions.

Given the expression 2(x + 3y), use the distributive property to expand it.

If a = 2, b = 3, and c = 4, show that addition is commutative for these values.

If a = 5, b = 2, and c = 7, verify the distributive property for a(b + c).

If a = 7, b = 3, and c = 2, verify the associative property of multiplication for these values.

If a = 8, b = 0, what is a × b? Which property does this illustrate?

If x = 4 and y = 5, use the distributive property to expand x(y + 2).

State the commutative property of multiplication.

State the identity property of multiplication.

Which property is being used in the following scenario? Context: A student calculates 4 + 7 + 3 by first adding 4 + 7 to get 11, then adding 3 to get 14. Another student adds 7 + 3 to get 10, then adds 4 to get 14. Both get the same result.

Which property is illustrated by the equation: (a × b) × c = a × (b × c)?

Which property is illustrated by the equation: 5 + (3 + 2) = (5 + 3) + 2?

Which property is used in the following calculation: 6 × (2 + 3) = 6 × 2 + 6 × 3?

Context: A student is simplifying the expression 2x + 3x + 4x. The student first adds 2x and 3x to get 5x, then adds 4x to get 9x. Another student adds 3x and 4x to get 7x, then adds 2x to get 9x. Which property of operations justifies that both students get the same result?

Given the expression (x + 2)(x - 3), use the distributive property to expand and simplify the expression.

Let a, b, and c be real numbers. If a(b + c) = ab + ac, explain why this property is essential when expanding algebraic expressions involving polynomials.

Prove or disprove: The distributive property holds for division over addition, i.e., a ÷ (b + c) = (a ÷ b) + (a ÷ c) for all real numbers a, b, and c (where b, c ≠ 0).

Prove that the distributive property holds for real numbers by showing that for any real numbers a, b, and c, a(b - c) = ab - ac.