The commutative, associative, and distributive properties
▶ Associative and commutative properties of addition with negatives
The commutative and associative properties apply to addition, but not to subtraction. Rewriting subtraction as addition of the opposite is a superpower that suddenly lets us use the commutative and associative properties (without changing the value of the expression) in expressions that previously had subtraction involved.
▶ Equivalent expressions with negative numbers
Understand that we can commute and associate terms as long as we keep the signs with the terms. We can also apply the additive identity property and the additive inverse property.
▶ Equivalent expressions
In this math lesson, we learn how to find equivalent expressions by combining like terms and factoring. We start with an expression like x + 2 - y + x + 2 and simplify it by adding the x terms and factoring out common factors. This helps us compare expressions and solve problems more easily.
▶ Combining like terms with negative coefficients
This example of combining like terms in an expression gets a little hairy. Pay attention.
▶ Combining like terms with negative coefficients & distribution
We've learned about order of operations and combining like terms. Let's layer the distributive property on top of this.
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