Check out this Video about Multiplication, Commutativity and Distribution properties.
From Purple Math:
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, not subtraction! 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
2 + (3 + 4) = (2 + 3) + 4. For multiplication, the rule is "a(bc) = (ab)c"; in numbers, this means 2(3×4) = (2×3)4. Any time they refer to the Associative Property, they want you to regroup things; any time a computation depends on things being regrouped, they want you to say that the computation uses the Associative Property. Copyright © Elizabeth Stapel 2000-2011 All Rights Reserved
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.
Your brain likes repitition to move information into long term memory.
Watch, Review and Look Over your Math Notes from our whole group math lesson.
factor: a number that is multiplied by another number to get a product
product: the answer when 2 factors are multiplied
Greatest Common Divisor: 4 example problems of determining the greatest common factor of two numbers by factoring the 2 numbers first
Least Common Multiple (LCM): U02_L3_T1_we6 Least Common Multiple (LCM)
Least Common Multiple: Example of figuring out the least common multiple of two numbers
Finding Factors of a Number: U02_L1_T3_we2 Finding Factors of a Number
Click here for an interactive Decimal/ Estimation Activity:
Math 6 Spy Guys
SET E: Number Properties
Commutative Law of Multiplication: U01_L4_T1_we4 Commutative Law of Multiplication
SET D: Number PropertiesCommutative Law of Addition: U01_L4_T1_we3 Commutative Law of AdditionSet C: Adding integers with different signs: U09_L2_T1_we2 Adding integers with different signs
Rounding Whole Numbers 2: U01_L1_T2_we2 Rounding Whole Numbers 2
SET A: Multiplication 5: 2-digit times a 2-digit number: Multiplying a 2-digit number times a 2-digit number
Click on a corresponding link below:
Mega Math: Ice Station Exploration: Arctic Algebra: Level N: Divisibility Rules - 4, 6
Mega Math: Ice Station Exploration: Arctic Algebra: Level M: Divisibility Rules - 2, 3, 5, 9, 10
Mega Math: Ice Station Exploration: Arctic Algebra: Level H: Value of Expressions- Multiply/ Divide
Mega Math: Ice Station Exploration: Arctic Algebra: Level E: Relate Mulitplication and Division
Mega Math: Fraction Action: Number Line Mines: Level R: Rounding Decimals
SET E: Mega Math: The Number Games: Tiny's Think Tank: Level L: +/- Decimals
SET D: Mega Math: The Number Games: Tiny's Think Tank: Level R: Multiply Decimals
Mega Math: Fraction Action: Number Line Mine: Level T
Mega Math: Fraction Action: Number Line: Level C
Mega Math: The Number Games: Up, Up, and Array: Level K: Multiply by 2-digit Number