Arithmetic Laws

[jazz2112]

I have this question and I'm not sure if what I have is correct, I was wondering if someone could explain where the laws are and why and if I am correct or not? Thankyou.


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

4 x 37+ (56 + 4 x 13) = 4 x 37 + (4 x 13 + 56) ( I think this line shows Commutative law)
= (4 x 37 + 4 x 13) + 56 ( I think this line shows Associative law)
= 4 (37 + 13) + 56
= 4 x 50 + 56
= 256.

 

[pka]

I have this question and I'm not sure if what I have is correct, I was wondering if someone could explain where the laws are and why and if I am correct or not? Thankyou.


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

4 x 37+ (56 + 4 x 13) = 4 x 37 + (4 x 13 + 56) ( I think this line shows Commutative law)
= (4 x 37 + 4 x 13) + 56 ( I think this line shows Associative law)
= 4 (37 + 13) + 56
= 4 x 50 + 56
= 256.

You may find this page interesting.

 

[ksdhart2]

There's three basic laws of arithmetic: Associative Law, Commutative Law, and Distributive Law. You've correctly identified that the Commutative Law was used in the first line and the Associative Law was used to go from the first line to the second line. But which laws, if any, were used in the remaining lines?

When going from the second line to the third line, was the Commutative Law applied? That is, did any of the things you're adding or multiplying move around? Was the Associative Law applied? That is, did any of the parentheses move around? Or maybe the Distributive Law was used? Did any distributing (or factoring, since this is the law applied in "reverse") occur? Repeat this line of thinking for each of the other lines.

 

[Steven G]

I have this question and I'm not sure if what I have is correct, I was wondering if someone could explain where the laws are and why and if I am correct or not? Thankyou.


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

4 x 37+ (56 + 4 x 13) = 4 x 37 + (4 x 13 + 56) ( I think this line shows Commutative law)
= (4 x 37 + 4 x 13) + 56 ( I think this line shows Associative law)
= 4 (37 + 13) + 56 (factor----undoing the distributive law)
= 4 x 50 + 56 (addition)
= 200 + 56
= 256

See comments above

 

[Steven G]

There's three basic laws of arithmetic: Associative Law, Commutative Law, and Distributive Law. You've correctly identified that the Commutative Law was used in the first line and the Associative Law was used to go from the first line to the second line. But which laws, if any, were used in the remaining lines?

When going from the second line to the third line, was the Commutative Law applied? That is, did any of the things you're adding or multiplying move around? Was the Associative Law applied? That is, did any of the parentheses move around? Or maybe the Distributive Law was used? Did any distributing (or factoring, since this is the law applied in "reverse") occur? Repeat this line of thinking for each of the other lines.

I disagree with you here (sorry). I think that there are six basic laws of arithmetic. They are Associative Law of Addition, Commutative Law of Addition, Distributive Law over Addition, Associative Law of Multiplication, Commutative Law of Multiplication, Distributive Law over Subtraction

 

[ksdhart2]

I disagree with you here (sorry). I think that there are six basic laws of arithmetic. They are Associative Law of Addition, Commutative Law of Addition, Distributive Law over Addition, Associative Law of Multiplication, Commutative Law of Multiplication, Distributive Law over Subtraction

I think it all depends on how you think about things, really. I don't believe there's a "right" or a "wrong" way here. That said, my personal opinion is as follows: I see the distinction between the Associative/Commutative Law of Addition and Associative/Commutative Law of Multiplication as a difference of "flavors" rather than as distinct laws. In a similar manner, since subtraction is nothing more than adding a negative, I see no reason to say there's two Distributive Laws either.