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The Distributive Property is easy to remember, if you recall that "multiplication distributes over addition". Formally, they write this property as "a(b + c) = ab + ac". In numbers, this means, that 2(3 + 4) = 2×3 + 2×4. Any time they refer in a problem to using the Distributive Property, they want you to take something through the parentheses (or factor something out); any time a computation depends on multiplying through a parentheses (or factoring something out), they want you to say that the computation used the Distributive Property.
Since they distributed through the parentheses, this is true by the Distributive Property.
The Distributive Property either takes something through a parentheses or else factors something out. Since there aren't any parentheses to go into, you must need to factor out of. Then the answer is "By the Distributive Property, 4x – 8 = 4(x – 2)"
"But wait!" you say. "The Distributive Property says multiplication distributes over addition, notsubtraction! What gives?" You make a good point. This is one of those times when it's best to be flexible. You can either view the contents of the parentheses as the subtraction of a positive number ("x – 2") or else as the addition of a negative number ("x + (–2)"). In the latter case, it's easy to see that the Distributive Property applies, because you're still adding; you're just adding a negative.
The other two properties come in two versions each: one for addition and the other for multiplication. (Note that the Distributive Property refers to both addition and multiplication, too, but to both within just one rule.)
The word "associative" comes from "associate" or "group";the Associative Property is the rule that refers to grouping. For addition, the rule is "a + (b + c) = (a + b) + c"; in numbers, this means
They want you to regroup things, not simplify things. In other words, they do not want you to say "6x". They want to see the following regrouping: (2×3)x
In this case, they do want you to simplify, but you have to tell why it's okay to do... just exactly what you've always done. Here's how this works:
Since all they did was regroup things, this is true by the Associative Property.
The word "commutative" comes from "commute" or "move around", so the Commutative Property is the one that refers to moving stuff around. For addition, the rule is "a + b = b + a"; in numbers, this means 2 + 3 = 3 + 2. For multiplication, the rule is "ab = ba"; in numbers, this means 2×3 = 3×2.Any time they refer to the Commutative Property, they want you to move stuff around; any time a computation depends on moving stuff around, they want you to say that the computation uses the Commutative Property.
They want you to move stuff around, not simplify. In other words, the answer is not "12x"; the answer is any two of the following:
4 × 3 × x, 4 × x × 3, 3 × x × 4, x × 3 × 4, and x × 4 × 3
Since all they did was move stuff around (they didn't regroup), this is true by the Commutative Property.
I'm going to do the exact same algebra I've always done, but now I have to give the name of the property that says its okay for me to take each step. The answer looks like this:
The only fiddly part was moving the "– 5b" from the middle of the expression (in the first line of the table above) to the end of the expression (in the second line). If you need help keeping your negativesstraight, convert the "– 5b" to "+ (–5b)". Just don't lose that minus sign!
All they did was move stuff around: Commutative Property
All they did was regroup: Associative Property
They factored: Distributive Property
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PRE ALGEBRA: Here are some great videos for you also!
Ordered Pairs - Interactive Site: Click Here
Understanding Whole Numbers Click Here
U.S. Customary Measurement: Click Here
The Metric System: Click Here
All About Geometry: Click Here
Multiplying Fractions: Click Here
Finding the Average: Click Here
Mode, Median, and Range Examples: Click Here
Eqivalent Fractions: Click Here
Fraction Word Problems: Click Here
Equivalent Fractions Interactive Quiz: Click Here
Fractions by Zeebo(King of the Fractions!):Click Here
Geometry Worksheets: Click Here
Long Division Videos Click Here
Fact Families Game: Click Here
Multiplication.com Click Here
Adding with Regrouping Click Here
Fractions Help: Click Here
Multiplying by 100's: Click Here
Division With Remainders: Click Here
Printable Flash Cards: Click Here
Math Cats...Really cool math games! Click Here
Telling Time Game: Click Here
Decimals - Tenths and Hundredths: Click Here
Subtraction Across Zeros Video: Click Here
Prime and Composite Battleship Game: Click Here
Baseball Math: Click Here
Cool Math 4 Kids: Click Here
Elapsed Time Matching Game: Click Here
The Best Math Practice Page on the Net!: Click Here
2 Digit X 2 Digit Multiplication: Click Here
Place Value Game: Click Here
Place Value: Click Here
Bar Graphs: Click Here
Line Graphs: Click Here
Line Plots: Click Here
Basic Addition: Click Here
Basic Subtraction: Click Here