Difficulty
Calculator
Interactive practice · 15 questions on equivalent expressions and naming the real-number properties (commutative, associative, distributive, identity, inverse), with step-by-step solutions.
Press Check answer on each question to see whether you got it right — every check is timestamped and recorded in your Activity log below.
Each attempt is saved under its own name — load, rename, or delete them below. Difficulty / calculator tags are shared across all attempts. Numeric answers accept equivalent forms (e.g. 4/3 or 1.333).
The timer is stopped. Questions are hidden until you resume.
Easy Which property is shown? \(a+b=b+a\)
Answer: B — Commutative Property of Addition
Easy Which property is shown? \((2\cdot3)\cdot4=2\cdot(3\cdot4)\)
Answer: D — Associative Property of Multiplication
Easy Which expression is equivalent to \(5(x+3)\)?
Answer: D — \(5x+15\)
Easy Which property is shown? \(x+0=x\)
Answer: C — Additive Identity
Medium Which property is shown? \(4+(6+x)=(4+6)+x\)
Answer: D — Associative Property of Addition
Medium Which is equivalent to \(\dfrac{a+b}{c}\)?
Answer: A — \(\dfrac{a}{c}+\dfrac{b}{c}\)
Medium Simplify: \(-2(3x-5)\).
Answer: B — \(-6x+10\)
Medium Simplify: \(\dfrac{12x-8}{4}\).
Answer: B — \(3x-2\)
Medium Which is equivalent to \(2x+2y\)?
Answer: B — \(2(x+y)\)
Medium What is the multiplicative inverse (reciprocal) of \(5\)? (fraction or decimal)
\(=\)Answer: \(\tfrac15=0.2\)
Medium What is the additive inverse (opposite) of \(-7\)?
\(=\)Answer: \(7\)
Medium Which property is shown? \(7\cdot 1=7\)
Answer: D — Multiplicative Identity
Hard Which property justifies rewriting \(3+(x+9)\) as \(3+(9+x)\)?
Answer: A — Commutative Property of Addition
Hard Which statement is NOT true for all real numbers?
Answer: A — \(a-b=b-a\)
Hard Which is equivalent to \(4(x+2)+3x\)?
Answer: C — \(7x+8\)