Identifying the laws of arithmetic used in steps in simplification of 4 × 37 + (56 + 4 × 13)

[Ando839]

Been a little stuck on this question,
any help would be greatly appreciated!!

Consider the following calculation. State which laws of arithmetic are used and indicate at what stage they are used.

4 × 37 + (56 + 4 × 13) = 4 × 37 + (4 × 13 + 56)

= (4 × 37 + 4 × 13) + 56

= 4(37 + 13) + 56

= 4 × 50 + 56

= 256

 

[topsquark]

a + (b + c) = (a + b) + c ... The associative law of addition
ab + ac = a(b + c) ... The distributive law of multiplication over addition

Otherwise you are using PEDMAS (or BODMAS or whatever) to do multiplication before addition.

These are the rules you followed to simplify your expression. Can you fill in the blanks?

-Dan

 

[Otis]

… a little stuck on this question, any help would be greatly appreciated …

… Identifying the laws of arithmetic …

… 4 × 37 + (56 + 4 × 13) = 4 × 37 + (4 × 13 + 56) …

Sure, but next time please explain what you've thought about and where you got stuck.

4 × 37 + (56 + 4×13) = 4 × 37 + (4×13 + 56)

Start by examining the steps, to see what changed from one step to the next. In their first step above, we see two quantities added in a different order than they were to begin with (those quantities are highlighted in red and green).

Which law of arithmetic deals with changing the order in which two numbers are added?

?

 

[Ando839]

Awesome thanks guys!

Both posts helped and i ended up getting through it, just had to break down the equation with the definitions more. I'll be sure to include more information next time!

Again most appreciated!

 

[ksdhart2]

I got a serious sense of deja vu on this problem, and I knew I'd seen it before. In fact, this exact same problem was posted last week, right here on this forum.

 

[Ando839]

This was a question from a take home assessment from my current course at my University, perhaps it may of been a fellow student seeking assistants as well ?