List of Notes - Category: Number Expressions

Commutative Property of Addition

Commutative property of addition:

` huge color(purple)(a+b=b+a) `

What does it mean?

It means, that order of numbers doesn't matter.

Indeed, suppose your first friend (let's call it Tom) gave you 3 apples, then your another friend (let's call it Jim) gave your 4 apples. You got total of 7 apples.

Associative Property of Addition

Associative property of addition:

`huge color(purple)(a+(b+c)=(a+b)+c)`

Intuitively, we understand, that it is correct.

Indeed, suppose your friend Ann has 3 apples, Bob has 5 apples and Cliff has 4 apples.

Identity Property of Addition

Identity property of addition:

` huge color(purple)(a+0=a) `

What does it mean?

It means, that addition of zero to the number will not change the number.

Indeed, suppose your first friend (let's call it Tom) gave you 3 apples, but your second friend (let's call it Jim) gave you nothing. So, you are left with 3 apples.

Inverse Property of Addition

Inverse property of addition:

`huge color(purple)(a+(-a)=(-a)+a=0) `

`-a` is called the additive inverse of `a`.

Inverse property is true for any real number `a`.

Notice, that we wrote, that `a+(-a)=(-a)+a`. This is true, according to the commutative property of addition.

Commutative Property of Multiplication

Commutative property of multiplication:

` huge color(purple)(a times b=b times a) `

What does it mean?

It means, that order of numbers doesn't matter.

Indeed, as can be seen from illustration, we can count there are 3 circles in a row, and there are 2 rows, so total number of squares is `3times2=6`.

Associative Property of Multiplication

Associative property of multiplication:

`huge color(purple)(a times (b times c)=(a times b) times c)`

As with commutative property order is not important.

Indeed, you can make sure on a couple of examples, that it is correct.

Distributive Property of Multiplication

Distributive property of multiplication:

`huge color(purple)(a times (b+c)=a times b+a times c)`

Intuitively, we understand, that it is correct.

Indeed, multiplication is just a shorthand for addition.

Identity Property of Multiplication

Identity property of multiplication:

` huge color(purple)(a times 1=a) `

What does it mean?

It means, that multiplication of the number with one will result in original number.

Recall, that multiplication is shorthand for addition.

Inverse Property of Multiplication

Inverse property of multiplication:

`huge color(purple)(a times 1/a=1/a times a=1) `

`1/a` is called the multiplicative inverse of `a`.

Inverse property is true for any real number `a`.

Notice, that we wrote, that `a times 1/a=1/a times a`. This is true, according to the commutative property of multiplication.

Order of Operations (PEMDAS)

Order of Operations (PEMDAS):

  1. Parentheses
  2. Exponent
  3. Multiplication
  4. Division
  5. Addition
  6. Subtraction

Note, that multiplication and division rank equally. Also addition and subtraction rank equally.