# Category: Number Expressions

 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.

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.

 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.

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