How Do Properties of Real Numbers Simplify Basic Arithmetic Operations?

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SUMMARY

The discussion focuses on simplifying basic arithmetic operations using properties of real numbers, specifically through examples provided by users. The computations include addition and multiplication problems: 5+37, 6*17, 12*16, and 64+55. Key properties utilized in the breakdown include the commutative and associative properties of addition, as well as the distributive property of multiplication over addition. The breakdown of these operations illustrates how these properties can simplify calculations effectively.

PREREQUISITES
  • Understanding of the commutative property of addition
  • Familiarity with the associative property of addition
  • Knowledge of the distributive property of multiplication over addition
  • Basic arithmetic skills for addition and multiplication
NEXT STEPS
  • Study the commutative property of addition in detail
  • Learn about the associative property of addition and its applications
  • Explore the distributive property of multiplication over addition
  • Practice breaking down complex arithmetic operations using these properties
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Students, educators, and anyone looking to enhance their understanding of arithmetic operations and the properties of real numbers for simplified calculations.

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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