Can you help me with properties of real numbers and listing the steps?

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Can you help me with properties of real numbers and listing the steps?

Mathematics
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Should I upload an image of the homework?
http://i.imgur.com/A2bEoQO.jpg
I know how to do a lot of it, I just don't know how to explain it.....

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Other answers:

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

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