How Do Properties of Real Numbers Simplify Basic Arithmetic Operations?

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Discussion Overview

The discussion focuses on breaking down basic arithmetic computations using properties of real numbers. Participants seek to understand how these properties can simplify calculations involving addition and multiplication.

Discussion Character

  • Homework-related
  • Conceptual clarification

Main Points Raised

  • Several participants request assistance in simplifying computations such as 5+37, 6*17, 12*16, and 64+55 using properties of real numbers.
  • One participant provides an example from a book, showing how to express a number in terms of its digits and powers of ten, but expresses uncertainty about relating this to the properties of real numbers.
  • A response details a breakdown of the first two computations, illustrating the use of associativity and commutativity for addition, and distributivity for multiplication, but does not extend this to the remaining computations.

Areas of Agreement / Disagreement

Participants generally agree on the need for clarification on how to apply properties of real numbers to arithmetic operations, but there is no consensus on a complete method for all computations presented.

Contextual Notes

Some participants express uncertainty about the initial request and the specific application of properties of real numbers, indicating a potential lack of clarity in definitions or expectations.

bergausstein
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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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