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Commutative Associative Distributive Laws

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Commutative Associative Distributive Laws

Study Guide

Key Definition

Commutative, Associative, and Distributive Laws are fundamental properties in mathematics that dictate how numbers behave in specific operations.

Important Notes

The Commutative Law applies to addition and multiplication, but not to subtraction and division.
The Associative Law applies to addition and multiplication, but not to subtraction and division.
The Distributive Law applies to the distribution of multiplication over addition or subtraction within a parenthesis.

Mathematical Notation

$a + b = b + a$ and $a \times b = b \times a$ illustrate the Commutative Law

$(a + b) + c = a + (b + c)$ and $(a \times b) \times c = a \times (b \times c)$ illustrate the Associative Law

$a \times (b + c) = a \times b + a \times c$ and $a \times (b - c) = a \times b - a \times c$ illustrate the Distributive Law

Remember to use proper notation when solving problems

Why It Works

These laws are based on the consistent behaviors of real numbers under the operations of addition and multiplication.

Remember

Remembering these laws can simplify many algebraic expressions and equations.

Quick Reference

Commutative Law:$a + b = b + a$ and $a \times b = b \times a$

Associative Law:$(a + b) + c = a + (b + c)$ and $(a \times b) \times c = a \times (b \times c)$

Distributive Law:$a \times (b + c) = a \times b + a \times c$ and $a \times (b - c) = a \times b - a \times c$

Understanding Commutative Associative Distributive Laws

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Video explanation of this concept

Beginner

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Beginner Explanation

The Commutative Law states that changing the order of numbers in addition or multiplication does not change the result: a + b = b + a and a × b = b × a.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

Which of the following represents the Commutative Law for addition?

Real-World Problem

Question Exercise

Intermediate

Shopping Scenario

John bought 2 apples and 3 oranges, each costing $2. Calculate the total cost using the Distributive Law.

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

What does the Associative Law for multiplication tell us?

Challenge Quiz

Single Choice Quiz

Advanced

Which of the following represents the Distributive Law?

Recap

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Review key concepts and takeaways