MHB How Do Properties of Real Numbers Simplify Basic Arithmetic Operations?

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The discussion focuses on simplifying basic arithmetic operations using properties of real numbers. Participants seek guidance on breaking down computations such as addition and multiplication into simpler steps. For example, the addition of 5 and 37 is simplified using the associative and commutative properties, leading to a final result of 42. Similarly, the multiplication of 6 and 17 is broken down using the distributive property, resulting in 102. The thread emphasizes the importance of understanding these properties to facilitate easier calculations.
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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.
 
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bergausstein said:
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?
 
caffeinemachine said:
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.
 
bergausstein said:
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.
 

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