+0  
 
-3
1696
5
avatar+73 

1. What is the additive inverse of 2/3 ?

 

2. What is the multiplicative inverse of 2/3 ?

 

3. Justify the statement, "Division is not commutative."

 

4. Is the set of whole numbers closed under subtraction? Justify your answer.

 

5. To find the product of x and 5 , which property allows us to perform the following step? x • 5 = 5x

 

6. When adding 2 to the sum, 3 + x , which porperty allows us to perform the first step below?

 

7. What is the additive inverse of the expression -ab ?

 

8. What is the multiplicative inverse of the expression -1/ab ?

 

9. Is the set of non-zero integers closed under division? Justify your answer.

 

10. Show the set of non-zero rational numbers is closed under division.

 Sep 3, 2016

Best Answer 

 #4
avatar+249 
+5

5. communitive property of multiplication (yx = xy)

 

6. associtative property of addition ((a + b) + c = a + (b + c))

 Sep 3, 2016
 #1
avatar+249 
+5

1. Additive inverse is the number you add to the given number in order to get 0. So -2/3.

 

2. Muiltiplicatice inverse of a/b is b/a. So 3/2.

 

3. x-y ≠ y-x. Just plug in numbers - 1-2≠2-1, 3-4≠4-3, etc...

 

4. Set of closed number is closed under addition and multiplication. Not subtraction because x-y can be negative, and negative numbers are not whole numbers (example: 3-5 = -2).

 

7. ab

 

8. ab/-1

 

9. No. Integers are closed under addition, subtraction, and multiplication. (Example: 8/6 is 4/3, which is not an integer.)

 Sep 3, 2016
edited by higgsb  Sep 3, 2016
 #2
avatar+128053 
+5

Here's a few....

 

1. What is the additive inverse of 2/3 ?   →    -2/3

2. What is the multiplicative inverse of 2/3 ?    → 3/2

3. Justify the statement, "Division is not commutative." → for example,   15/3  = 5  but  5/15  = 1/3

4. Is the set of whole numbers closed under subtraction? Justify your answer.

Whole numbers are 0,1,2,3,4.........

"Closed" in this case means that when we perform a certain operation with two set members, we get a third set member returned. The set of whole numbers is not closed under subtraction because, for example.....   0 - 4  = -4     and -4 is not a member of the set of whole numbers

 

7. What is the additive inverse of the expression -ab ?  →  ab  ....   because -ab + ab = 0

 

9. Is the set of non-zero integers closed under division? Justify your answer.
Definitely not.....example  .......22/7  = 3 +1/7    and this is not a non-zero integer

 

10. Show the set of non-zero rational numbers is closed under division.

Let m = a/b   and n = c/d    such that a/b and c/d ≠ 0. Them m/n  =  a/b ÷ c/d  =   [ad] / [ bc]   which is also a non-zero rational

 

 

 

cool cool cool

 Sep 3, 2016
 #3
avatar+73 
-1

Um guys thanks for the help but what about number 5 and 6?

 

5. To find the product of x and 5 , which property allows us to perform the following step? 

 

x • 5 = 5x

 

6. When adding 2 to the sum, 3 + x , which porperty allows us to perform the first step below?

 

2 + (3 + x) =

(2 + 3) + x =

5 + x

 

Please Help!!!!!!!!!!!

 Sep 3, 2016
 #4
avatar+249 
+5
Best Answer

5. communitive property of multiplication (yx = xy)

 

6. associtative property of addition ((a + b) + c = a + (b + c))

higgsb  Sep 3, 2016
 #5
avatar+9466 
+4

1) 

Additive inverse of 2/3?

2/3 + x = 0

x = -2/3

Same answer as everyone

2)

Multiplicative inverse of 2/3?

(2/3)(x) = 1

x = 1/ (2/3) = 3/2 = 1 1/2

Same answer as everyone

3)

Justify the statement 'Division is not commutative'?

a/b does not equal b/a.

Same answer as higgsb.(I think his/her '-' means 'vinculum' or 'fraction')

4)

I doesn't agree with CPhill in this one as I usually do.

0 - 4 = -4

Whole number does not depend on it's positivity or negativity, -4 is still a whole number: Therefore it is closed under subtraction! (Whole number means no fractions, no decimals, and no percentages unless it's 100k% for any integer k.)

5) commutative property of multiplication

6) associative property of addition

7) -ab + x = 0

             x = ab

ab is the additive inverse of -ab

8) -x/ab = 1

     x = -ab

-ab is the multiplicative inverse of -1/ab

9) It is not closed under division.......

Example: 22/7 = 3 1/7

Idk how to do 10). Thanks CPhill!! :D

 Sep 4, 2016

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