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Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, interactive explorations.

Used and loved by over 7 million people

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.

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Properties of Arithmetic

Intro

Concept Quizzes

Warmup
Order of Operations
Power of Parentheses
Associative and Commutative Properties
Zero Product Property
Distributive Property
Distributive Property Misconception
Problem Solving

Challenge Quizzes

Level 1
Level 2

Zero Product Property

If \( ab = 0 \), which of the following statements MUST be true?

\( a = 0 \text{ and } b = 0 \) \( b = 0 \) \( a = 0 \) \( a = 0 \text{ or } b = 0 \)

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by Brilliant Staff

If \( b \neq c \) and \( ab = ac \), which of the following statements must be true?

\( b= -c \) \( b= c \) \( a= b-c \) \( a= 0 \)

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by Brilliant Staff

Solve \(x^2-5x=0\).

\[ x = 0 \text{ or } x=5 \] \[ x = 5 \] \[ x = 0 \] \[ x = 1 \text{ or } x=5 \]

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by Brilliant Staff

What are the solutions to \((x-3)(x-5)=0\)?

\[ x = -3, -5 \] \[ x = 3, 5 \] \[ x = 5 \] \[ x = 3 \]

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by Brilliant Staff

If \( a \neq 5 \) and

\[ a x = 5 x ,\]

then what is the value of \(x\)?

\( x = -1 \) \( x = 0 \) \( x = 1 \) \( x \) cannot be determined

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by Brilliant Staff

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