# Properties of Real nmbers

#### bergausstein

##### Active member
please help me break down this computations into the simplest possible steps using properties of real numbers.

a. 5+37
b. 6*17
c. 12*16
d. 64+55

i'm not quite sure where to start.

#### caffeinemachine

##### Well-known member
MHB Math Scholar
please help me break down this computations into the simplest possible steps using properties of real numbers.

a. 5+37
b. 6*17
c. 12*16
d. 64+55

i'm not quite sure where to start.
Hey Bergausstein.

I am not quite sure what you mean by 'breaking down the comoutation'. Can you give an example?

#### bergausstein

##### Active member
Hey Bergausstein.

I am not quite sure what you mean by 'breaking down the comoutation'. Can you give an example?
here's an example from my book.

243 = 2*10*10+4*10+3

i don't know how to relate the properties of real numbers to this.

#### caffeinemachine

##### Well-known member
MHB Math Scholar
please help me break down this computations into the simplest possible steps using properties of real numbers.

a. 5+37
b. 6*17
c. 12*16
d. 64+55

i'm not quite sure where to start.
For part a. I'd write:
5+37 = 5+30+7 = 30+5+7 = 30+12 = 30+10+2 = 40+2 = 42.
Here we used associativity and commutativity of addition.

For part b.
6*17 = 6*(10+7) = 6*10+6*7 = 60+42 = 60+40+2 = 100+2 = 102.
Here we used associtivity of addition and distributivity of multiplication over addition.

I think this is what you are looking for. The rest are similar.