How Do Properties of Real Numbers Simplify Basic Arithmetic Operations?

[bergausstein]

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.

 

[caffeinemachine]

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?

 

[bergausstein]

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.

 

[caffeinemachine]

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.

 

[CellCoree]

Sure, let's break down these computations using properties of real numbers:

a. 5+37
Step 1: Use the commutative property of addition to rearrange the numbers in any order:
5+37 = 37+5
Step 2: Use the associative property of addition to group the numbers in a different way:
37+5 = (37+2)+3
Step 3: Use the identity property of addition to show that adding 0 does not change the value:
(37+2)+3 = (37+2)+3+0
Step 4: Use the associative property again to group the numbers in a different way:
(37+2)+3+0 = 37+(2+3)+0
Step 5: Use the distributive property to simplify the expression inside the parentheses:
37+(2+3)+0 = 37+5+0
Step 6: Use the identity property again to show that adding 0 does not change the value:
37+5+0 = 37+5
Step 7: Use the commutative property again to rearrange the numbers in the original order:
37+5 = 5+37
Step 8: Use the identity property one last time to show that adding 0 does not change the value:
5+37 = 5+37+0
Step 9: Simplify the expression by using the identity property again:
5+37+0 = 5+37
Step 10: Use the commutative property one last time to rearrange the numbers in the original order:
5+37 = 37+5
Therefore, 5+37 = 37+5 = 42.

b. 6*17
Step 1: Use the commutative property of multiplication to rearrange the numbers in any order:
6*17 = 17*6
Step 2: Use the associative property of multiplication to group the numbers in a different way:
17*6 = (10+7)*6
Step 3: Use the distributive property to simplify the expression inside the parentheses:
(10+7)*6 = (10*6)+(7*6)
Step 4: Use the identity property of multiplication to show that multiplying by 1 does not change the value:
(10*6)+(7*6) = (10*6)+(7*6)*1