- Assignment 1: 04-Properties of Operations
- Assignment 2: 05-Distributive Property
The mathematical properties tell us things that are true under any situation. There are four of them we will be dealing with this year, but we will certainly be putting the most focus on the distributive property, which I will get to later in this blog.
Commutative Property
The base word commute means to travel. The commutative property means the numbers can switch places and will still wield the same results. The commutative property works only with addition and multiplication.
Examples:
- 4 + 3 = 3 + 4 (They both equal 7)
- 7 x 5 = 5 x 7 (They both equal 35)
Non-examples:
- 4 – 3≠ 3 – 4 (1 ≠ -1)
- 8 ÷ 2 ≠ 2 ÷ 8 (4 ≠ 0.25)
Associative Property
When we associate things, we connect them together. We may think of the people we associate with as our friends. This is the same with numbers. The associate property allows us to connect certain numbers together, without there being any change to the value of the expression. Again, this only works with addition and multiplication. Notice in the examples, we represent these “associations” by separating them with parenthesis.
Examples:
- 3 + (4 + 5) = (3 + 4) + 5 (They both equal 12)
- 2 x (5 x 6) = (2 x 5) x 6 (They both equal 60)
Identity Property -
The identity property takes a number and has it act as a mirror. There are two numbers. With addition and subtraction, the identity number is 0 because any number add or subtract 0 is still the same number.
3 + 0 = 3
7 – 0 = 7
The other identity number is for multiplication and division. It is 1 because any number multiplied or divided by 1 is still the same.
5 x 1 = 5
9 ÷ 1 = 9
Distributive Property
The distributive property get it’s own lesson because it is our main focus in 6th grade with the mathematical properties. The basic idea behind it is a number sharing itself through multiplication. Example:
3(7 + 4) =
3(7) + 3(4) =
21 + 12 =
33
where 3(7+4) = 3(11) = 33.
This property really comes of value when trying to multiply larger numbers, let’s say 3 x 112. The larger math is tougher to do, especially in your head, but if you break it apart, 112 = 100 + 12, these two numbers are a lot easier to multiply by 3.
3 x 112 =
3(100 + 12) =
3(100) + 3(12) =
300 + 36 =
336
You could also split apart other numbers. Maybe you’re not so good with your 8 times tables and there is a problem that requires you to do 6 x 8. You could split that apart just as easily:
6 x 8 =
6(5 + 3) =
6(5) + 6(3) =
30 + 18 =
48
These concepts can take some harder problems and really simplify the math you might have to do.