ijarritos
  • ijarritos
Can you help me with properties of real numbers and listing the steps?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
ijarritos
  • ijarritos
Should I upload an image of the homework?
ijarritos
  • ijarritos
http://i.imgur.com/A2bEoQO.jpg
ijarritos
  • ijarritos
I know how to do a lot of it, I just don't know how to explain it.....

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ijarritos
  • ijarritos
Someone please explain how I would start doing this
Nnesha
  • Nnesha
start with distributive property \[\huge\rm \color{Red}{a}(b+c)\] distribute the parentheses by outside number \[\large\rm \color{Red}{a} \times b + \color{Red}{a} \times c = \color{Red}{a}b+\color{Red}{a}c\]
ijarritos
  • ijarritos
Here is the page that is supposed to explain it but it doesn't make any sense http://i.imgur.com/bcRmUTL.jpg
Nnesha
  • Nnesha
http://prntscr.com/87q3vq thats the explanation :=)
ijarritos
  • ijarritos
@Nnesha In step B of 17, I know they just multiplied the parentheses, would I just say that?
ijarritos
  • ijarritos
@Nnesha Also for 17 A I put "distribute the parentheses with the distributive property", would that be correct?
Nnesha
  • Nnesha
|dw:1440277087992:dw| look at the last one distributive property that's what they used for first question (a) \[\large\rm \frac{ 1 }{ 2 }(1+2t)=\frac{ 1 }{ 2} \times 1 + \frac{ 1 }{ 2 } \times (2t)\]
Nnesha
  • Nnesha
for 17 a just write *distributive property |dw:1440277416871:dw|
ijarritos
  • ijarritos
@Nnesha What about 17B
Nnesha
  • Nnesha
that's same as first step they just rearrange 2nd term \[\frac{ 1 }{ 2 } \times 2t = (\frac{ 1 }{ 2 } \times 2)t\] which *associate property*
Nnesha
  • Nnesha
is**
ijarritos
  • ijarritos
@Nnesha this is so confusing I don't know how to tell which property is which
Nnesha
  • Nnesha
just look at the 2nd sheet they gave you. :=)
Nnesha
  • Nnesha
http://i.imgur.com/bcRmUTL.jpg this one
ijarritos
  • ijarritos
@Nnesha Thats the confusing part
ijarritos
  • ijarritos
@Nnesha Like I dont know how to tell which one from which ughh
ijarritos
  • ijarritos
@Nnesha Also is 17 b the associative property of addition or multiplication
Nnesha
  • Nnesha
would you multiply 1/2 times 2 or add ??
ijarritos
  • ijarritos
multiply
ijarritos
  • ijarritos
I have a question
Nnesha
  • Nnesha
i'm here please don't tag me on every comment it creates lag:(
ijarritos
  • ijarritos
Ok so for C, would the problem in question be 1/2 x 1 + (1/2 x 2)t = 1/2 x 1 + 1 x t
ijarritos
  • ijarritos
And I would look at it like that in comparison to the other sheet?
ijarritos
  • ijarritos
Or would you find it in a different way?
Nnesha
  • Nnesha
we shouldn't depends on one sheet i understand there isn't enough information to understand theses all properties :=) here is a better link http://www.purplemath.com/modules/numbprop.htm :=) with examples :=)
Nnesha
  • Nnesha
these*
Nnesha
  • Nnesha
for C i would say simplify bec they just divided 2 by 2 :=)
ijarritos
  • ijarritos
i forgot how to simplifyy
ijarritos
  • ijarritos
thats the problem
ijarritos
  • ijarritos
im 100% going to fail algebra II
Nnesha
  • Nnesha
nah you will not!! think about good stuff algebra is not just abt these properties :=)
Nnesha
  • Nnesha
simplify means make something easier to understand u know i HATE fraction pretty sure you don't like it either so that's why i cancel out 2's to make it simple \[\frac{ 1 }{ 2 } \times 2t = (\frac{ 1 }{\cancel{ 2} } \times \cancel{2})t\]
phi
  • phi
this last one is called "inverse property of multiplication"
Nnesha
  • Nnesha
last one ??
ijarritos
  • ijarritos
is cancelling out 2's the associative property?
phi
  • phi
notice \[ \frac{ 1 }{\cancel{ 2} } \times \cancel{2} \] matches your "cheat sheet" \[ \frac{ 1 }{\cancel{ a} } \times \cancel{a} =1\]
ijarritos
  • ijarritos
where on the sheet?
phi
  • phi
4th from the bottom
ijarritos
  • ijarritos
omg how do you even get that out of it
ijarritos
  • ijarritos
all i know about simplification is to combine like terms
ijarritos
  • ijarritos
and i dont even see that going on like what ????
phi
  • phi
do you see the line that says Inverse property of multiplication?
ijarritos
  • ijarritos
yes
phi
  • phi
it is saying (in short hand) that if you have two numbers and one is the "flip" of the other when you multiply them you get 1 here are examples \[ 2 \cdot \frac{1}{2} \\ 3 \cdot \frac{1}{3} \\ \frac{2}{3}\cdot \frac{3}{2}\]
ijarritos
  • ijarritos
the teacher said this was "review work" and I don't even know how do do this
ijarritos
  • ijarritos
like before she starts teaching us things and I don't even know the basics
phi
  • phi
in that case, you are learning properties that are useful if you want to do algebra. Do you understand the multiply by the inverse idea? does it make sense 2*1/2 = 1
ijarritos
  • ijarritos
Yes
ijarritos
  • ijarritos
Are they using PEMDAS in 17a to get to 17b?
phi
  • phi
what is the multiplicative inverse of 4/5 ? (what do you multiply it by so you get 1)?
phi
  • phi
we'll get to 17a in just a minute.
phi
  • phi
Do you have time to learn this now?
ijarritos
  • ijarritos
Yes
ijarritos
  • ijarritos
And I don't know what I'd multiply by 4/5
ijarritos
  • ijarritos
4/5 x 1/5?
phi
  • phi
you "flip it"
ijarritos
  • ijarritos
4/5 x 5/4?
ijarritos
  • ijarritos
20/20 = 1 ohh
phi
  • phi
yes. that is the property you want to memorize notice when you multiply fractions you multiply top times top and bottom times bottom \[ \frac{4}{5}\cdot \frac{5}{4} = \frac{20}{20} =1 \] though it is better to notice that you have 5 up top and 5 down below and they "divide out" to 1 ditto for the 4's
ijarritos
  • ijarritos
but where did you get the 5/4 from
phi
  • phi
if you start with 4/5 (think of this as "a" ) then your cheat sheet says, multiply by 1/a \[ \frac{1}{\frac{4}{5}} \] and there is a way to simplify that so it looks like \(\frac{5}{4} \)
phi
  • phi
but it is easier (for me) to remember, "flip it" if you have a whole number like 2, then write it as 2/1, and now flip it to get 1/2
phi
  • phi
that is enough about the multiplicative inverse. how far did you get answering your questions?
ijarritos
  • ijarritos
to 17b and I didn't really understand it
ijarritos
  • ijarritos
@phi are you going to be here in 30 minutes or less? I might need a break for a sec
ijarritos
  • ijarritos
Ok I'll tag you when I get back
ijarritos
  • ijarritos
@phi Im back
phi
  • phi
what is the difference between line 17a and 17b?
ijarritos
  • ijarritos
1/2 was multiplied into 2 and t so distributive property
phi
  • phi
no , I mean the exactly what symbols are different? most of the line is identical but there is a difference in what is written down.
ijarritos
  • ijarritos
1/2 x 2
phi
  • phi
the difference is this part \[ \frac{1}{2}(2t) \text{ vs } \left( \frac{1}{2}\cdot 2 \right) t \]
ijarritos
  • ijarritos
Right I knew that but just didn't know how to explain it
phi
  • phi
in case it is not obvious both mean 1/2 times 2 times t the only difference is where the parens are. (in theory that could make a difference, because PEDMAS says you do the stuff in parens first) but when you multiply a bunch of numbers (or letters), you are allowed to change where you put the parens.
phi
  • phi
do you see the property on your cheat sheet that shows "moving the parens" when multiplying?
ijarritos
  • ijarritos
Yes
ijarritos
  • ijarritos
Associative property
phi
  • phi
yes, specifically associative property of multiplication
ijarritos
  • ijarritos
what about b to c?
ijarritos
  • ijarritos
on 17
ijarritos
  • ijarritos
inverse property of multiplication?
phi
  • phi
before moving on, let's make sure this make sense if you had 2*3*4*5*6 does it matter if we do 2*3 first or 5*6 ?
ijarritos
  • ijarritos
no
phi
  • phi
ok, so I hope that makes sense. if you have 2*3*4*5 you can associate them into pairs any way you like. for b to c, yes, that is the inverse property of multiplication
ijarritos
  • ijarritos
Yes it does change
phi
  • phi
what changes?
ijarritos
  • ijarritos
nvm
ijarritos
  • ijarritos
what about c to d?
ijarritos
  • ijarritos
1/2 x 1 is 1 and 1 x t is 1
phi
  • phi
1/2*1 is not 1
ijarritos
  • ijarritos
i meant 1 x 1/2 is 1/2
phi
  • phi
yes, and that is an important property
ijarritos
  • ijarritos
I know how it works im just trying to find which property
phi
  • phi
look for 1 times "something" equals "something"
ijarritos
  • ijarritos
identify property of multiplication?
phi
  • phi
yes. thought it is spelled identity
ijarritos
  • ijarritos
omg im getting it
phi
  • phi
ready for Q 18?
ijarritos
  • ijarritos
Yes
phi
  • phi
what is the exact difference between the left and right sides of 18a?
ijarritos
  • ijarritos
switched around
ijarritos
  • ijarritos
are there alot of trolls like that? xD
phi
  • phi
yes, specifically when adding
phi
  • phi
so look for a property related to addition that shows "switching"
ijarritos
  • ijarritos
Is it associative property of addition?
phi
  • phi
associative is "where to put the parens"
phi
  • phi
we have (2+a) vs (a+2) parens did not change what changed was 2+a became a+2 look for that rule on your list
ijarritos
  • ijarritos
commutative property of addition?
phi
  • phi
yes. they show a+b= b+a and that shows the "switching around" that you noticed with 2+a and a+2
phi
  • phi
now for 18a to 18b what is different?
ijarritos
  • ijarritos
Brackets are switched around
ijarritos
  • ijarritos
distributive property?
phi
  • phi
yes. we sometimes use brackets instead of parens if it makes the expression easier to read. what rule comes to mind when you change where you put parens?
ijarritos
  • ijarritos
associative
ijarritos
  • ijarritos
of addition
phi
  • phi
yes. associate property of addition they start with (a+2) + (-2) you can "move the parens" which is allowed by the associative property a+ (2 + (-2))
ijarritos
  • ijarritos
are c and d identity property of addition?
phi
  • phi
what is the difference between line 18b and 18c ?
ijarritos
  • ijarritos
the addition in the brackets is added
phi
  • phi
be more "literal" (2 + (-2)) turns into 0 do you see a property that shows that?
ijarritos
  • ijarritos
is 18c inverse of addition?
phi
  • phi
yes. this is an important property if you have x, and you want to add something to it to make zero what do you add? you add -x x + -x is 0 this always works no matter what "x" is !
ijarritos
  • ijarritos
ok!
phi
  • phi
now 18c to 18d a+0 becomes a
ijarritos
  • ijarritos
so would d be identity property of addition since its literally a+0
ijarritos
  • ijarritos
same as the cheat sheet
phi
  • phi
yes. adding 0 to anything does not change it.
phi
  • phi
Q19 looks almost the same as Q18
ijarritos
  • ijarritos
19a associative property of multiplication?
phi
  • phi
19a, what is different (the symbols) between the left side and the right side?
ijarritos
  • ijarritos
5 and n are switched
phi
  • phi
and be able to switch order is what property?
ijarritos
  • ijarritos
commutative?
phi
  • phi
yes, commute means switch so here, commutative property of addition (same as in Q18a)
ijarritos
  • ijarritos
then i have no idea for 19b
phi
  • phi
now 19a to 19b we "move around" parens. what property is "move parens"?
ijarritos
  • ijarritos
associative
phi
  • phi
I think of associative as allowing us to add or move parens (5+n) + (-n) drop the parens 5+n + (-n) put in new parens 5+ (n+(-n))
ijarritos
  • ijarritos
inverse of addition?
phi
  • phi
notice the pattern is (a+b)+c becomes a+(b+c)
ijarritos
  • ijarritos
associative property of addition?
phi
  • phi
19 b is associative prop of add 19 c is ?
ijarritos
  • ijarritos
omg i was looking at the wrong one
ijarritos
  • ijarritos
identity for 19c
ijarritos
  • ijarritos
of addition
phi
  • phi
what is different between 19b and 19c ?
phi
  • phi
(n + (-n) ) becomes 0 what property is that ?
ijarritos
  • ijarritos
inverse of addition
phi
  • phi
yes. 19C is inverse of addition now what is different between 19C and 19D ?
ijarritos
  • ijarritos
5+0 = 5
ijarritos
  • ijarritos
identity property of addition
phi
  • phi
yes
phi
  • phi
now the difference between 19D and 19E ?
ijarritos
  • ijarritos
then 19e is inverse of miltiplication
phi
  • phi
yes. Is this making sense?
ijarritos
  • ijarritos
yes
ijarritos
  • ijarritos
Theres another side I did before I knew all this
ijarritos
  • ijarritos
Could you check it?
phi
  • phi
can you do Q20?
ijarritos
  • ijarritos
sorry if im asking you for too much haha im still going to rate you best on qualified helper however that works
ijarritos
  • ijarritos
and I think so
ijarritos
  • ijarritos
http://i.imgur.com/bXgg5li.jpg Heres the other side
ijarritos
  • ijarritos
Heres for 20- A- distributive B- identity of multiply C- inverse of addition D- distributive
phi
  • phi
check 2,8,10,11
ijarritos
  • ijarritos
ok
phi
  • phi
20C and 20D are not correct.
ijarritos
  • ijarritos
Oh
phi
  • phi
what is the difference between 20B and 20C ?
ijarritos
  • ijarritos
3 is switched to the other side
phi
  • phi
and "switching" is what property?
ijarritos
  • ijarritos
itentity
ijarritos
  • ijarritos
identity of addition*
phi
  • phi
if you look on your cheat sheet identity of addition is a+0 becomes a
ijarritos
  • ijarritos
oh yeah
ijarritos
  • ijarritos
commutative of addition
phi
  • phi
yes, 20C is commutative of addition what is different between 20C and 12D ?
ijarritos
  • ijarritos
associative property of addition
phi
  • phi
yes. the parens were changed
ijarritos
  • ijarritos
is 21a commutative property of addition?
phi
  • phi
what is different between 21 left and right ?
ijarritos
  • ijarritos
no its associative property of addition
phi
  • phi
yes
phi
  • phi
from 21A to 21B, they are using the property "backwards" but you should be able to figure out which property they are using.
ijarritos
  • ijarritos
umm
phi
  • phi
write down the difference
ijarritos
  • ijarritos
multiplication of negative 1?
phi
  • phi
21A to 21B ? k becomes 1*k
ijarritos
  • ijarritos
identity of multiplication
phi
  • phi
yes. notice we went "backwards" from k to k*1 but that is ok. these rules work both ways
phi
  • phi
what is different between 21B and 21C ?
ijarritos
  • ijarritos
then identify again?
phi
  • phi
write down the "before" and "after"
ijarritos
  • ijarritos
wait what
ijarritos
  • ijarritos
so for 21b i would put before identity of multiplication?
ijarritos
  • ijarritos
then after for 21c
phi
  • phi
yes, but just the part that is different
ijarritos
  • ijarritos
both of them are identity of multiplication?
phi
  • phi
(1*k + 1*k) becomes (1+1)*k
ijarritos
  • ijarritos
tell me how to write it XD I think I have the right answer
phi
  • phi
which property shows something on the outside of the parens "going inside" (or in this case vice versa)
ijarritos
  • ijarritos
for 21b and 21c
phi
  • phi
the change is (1*k + 1*k) becomes (1+1)*k if we write it backwards (1+1)*k becomes (1*k + 1*k) does that look familiar?
ijarritos
  • ijarritos
Yes
phi
  • phi
what property is that?
ijarritos
  • ijarritos
identity of multiplication?
phi
  • phi
distributive
ijarritos
  • ijarritos
for 21c?
phi
  • phi
yes. we are going from (1*k+1*k) to (1+1)*k which is like (ab+ac) to (b+c)*a
ijarritos
  • ijarritos
im confused about c.5 to d
ijarritos
  • ijarritos
substitution to d
phi
  • phi
they are saying 1+1 is replaced with a 2 now from 2k+2 to 2k + 2*1 we change 2 to 2*1 that is the identity prop of mult.
ijarritos
  • ijarritos
For 21c how does 2*1 go to 2(k+1)
phi
  • phi
21c is (1+1)k+2 that changes to 2k+2 by substitution of 1+1 with 2 then we change that to 2k+2*1 by ident. prop of mult.
phi
  • phi
finally 2*k +2*1 becomes 2(k+1) that is the distributive property (backwards)
phi
  • phi
you should try to drill into your head the pattern A*(B+C) = A*B + A*C and vice versa: AB +AC = A(B+C)
ijarritos
  • ijarritos
ok!
ijarritos
  • ijarritos
is 22a identity property of multiplication?
phi
  • phi
what is different between 22a left side and right side?
ijarritos
  • ijarritos
x is moved around
phi
  • phi
switched around? what property?
ijarritos
  • ijarritos
commutative
phi
  • phi
for mult.
ijarritos
  • ijarritos
Yes
phi
  • phi
now what is different between 22a and 22b ?
ijarritos
  • ijarritos
x is removed and brackets are added
phi
  • phi
notice the pattern xA+xB becomes x(A+B) ?
ijarritos
  • ijarritos
Yes
phi
  • phi
and what property?
ijarritos
  • ijarritos
Distributive backwards
phi
  • phi
yes
phi
  • phi
22b to 22c . what is different?
ijarritos
  • ijarritos
is 22c associative property of multiplication?
phi
  • phi
(y+1) + (-1) becomes y+ (1 + (-1)) we are moving parens, so associative, but we are adding not multiplying
ijarritos
  • ijarritos
The parentheses are moved in 22d
phi
  • phi
22c is associative property of addition 22c to 22d the change is (-1 + (-1) ) becomes 0
phi
  • phi
**(1+(-1)) becomes 0
ijarritos
  • ijarritos
Inverse property of addition?
phi
  • phi
yes
ijarritos
  • ijarritos
then 22d is identity property of addition
phi
  • phi
yes
ijarritos
  • ijarritos
thank you so much for helping me learn this!!
phi
  • phi
OK, I hope it makes some sense. the names of the properties are not very interesting (but they will expect you to remember them), but the properties are important to know.
ijarritos
  • ijarritos
what about the other side?
ijarritos
  • ijarritos
2 8 10 11
ijarritos
  • ijarritos
http://i.imgur.com/bXgg5li.jpg

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