Distributive property
The distributive property comes into play when an expression involving addition is then multiplied by something. It tells us that we can add first and then multiply, or multiply first and then add. Either way, the multiplication is "distributed" over all the terms inside the parentheses.
In the example, we can either add the numbers inside the parentheses first -- 4+3 -- and then multiply the result by -2; or, we can multiply the -2 and each term separately and then add the two products together. The answer is the same in both cases.
-2(4 + 3) = (-2 x 4) + (-2 x 3)
Watch out!
Subtraction is neither commutative nor associative.
Division is neither commutative nor associative.
Examples
1. We can add numbers in any order. (Commutative property of addition.)
-2 + 4 = 4 + -2
2. We can multiply numbers in any order. (Commutative property of multiplication)
-2 x 4 = 4 x-2
3. We can group numbers in a sum any way we want. (Associative property of addition.)
(-2 + 4) + 3 = -2 + (4 + 3)
4. We can group numbers in a product any way we want. (Associative property of multiplication)
(-2 x 4) x 3 = -2 x (4 x3)
5. With this type of expression, we can add first, then multiply,OR
multiply first, then add. (Distributive property of multiplication over addition.)
-2 x (4 + 3) = (-2 x 4) + (-2 x 3)
The distributive property comes into play when an expression involving addition is then multiplied by something. It tells us that we can add first and then multiply, or multiply first and then add. Either way, the multiplication is "distributed" over all the terms inside the parentheses.
In the example, we can either add the numbers inside the parentheses first -- 4+3 -- and then multiply the result by -2; or, we can multiply the -2 and each term separately and then add the two products together. The answer is the same in both cases.
-2(4 + 3) = (-2 x 4) + (-2 x 3)
Watch out!
Subtraction is neither commutative nor associative.
Division is neither commutative nor associative.
Examples
1. We can add numbers in any order. (Commutative property of addition.)
-2 + 4 = 4 + -2
2. We can multiply numbers in any order. (Commutative property of multiplication)
-2 x 4 = 4 x-2
3. We can group numbers in a sum any way we want. (Associative property of addition.)
(-2 + 4) + 3 = -2 + (4 + 3)
4. We can group numbers in a product any way we want. (Associative property of multiplication)
(-2 x 4) x 3 = -2 x (4 x3)
5. With this type of expression, we can add first, then multiply,OR
multiply first, then add. (Distributive property of multiplication over addition.)
-2 x (4 + 3) = (-2 x 4) + (-2 x 3)