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

- ijarritos

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

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- katieb

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- ijarritos

Should I upload an image of the homework?

- ijarritos

http://i.imgur.com/A2bEoQO.jpg

- ijarritos

I know how to do a lot of it, I just don't know how to explain it.....

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## More answers

- ijarritos

Someone please explain how I would start doing this

- 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

Here is the page that is supposed to explain it but it doesn't make any sense http://i.imgur.com/bcRmUTL.jpg

- Nnesha

http://prntscr.com/87q3vq thats the explanation :=)

- ijarritos

@Nnesha In step B of 17, I know they just multiplied the parentheses, would I just say that?

- ijarritos

@Nnesha Also for 17 A I put "distribute the parentheses with the distributive property", would that be correct?

- 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

for 17 a just write *distributive property |dw:1440277416871:dw|

- ijarritos

@Nnesha What about 17B

- 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

is**

- ijarritos

@Nnesha this is so confusing I don't know how to tell which property is which

- Nnesha

just look at the 2nd sheet they gave you. :=)

- Nnesha

http://i.imgur.com/bcRmUTL.jpg this one

- ijarritos

@Nnesha Thats the confusing part

- ijarritos

@Nnesha Like I dont know how to tell which one from which ughh

- ijarritos

@Nnesha Also is 17 b the associative property of addition or multiplication

- Nnesha

would you multiply 1/2 times 2 or add ??

- ijarritos

multiply

- ijarritos

I have a question

- Nnesha

i'm here please don't tag me on every comment
it creates lag:(

- 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

And I would look at it like that in comparison to the other sheet?

- ijarritos

Or would you find it in a different way?

- 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

these*

- Nnesha

for C i would say simplify
bec they just divided 2 by 2 :=)

- ijarritos

i forgot how to simplifyy

- ijarritos

thats the problem

- ijarritos

im 100% going to fail algebra II

- Nnesha

nah you will not!!
think about good stuff
algebra is not just abt these properties :=)

- 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

this last one is called "inverse property of multiplication"

- Nnesha

last one ??

- ijarritos

is cancelling out 2's the associative property?

- phi

notice
\[ \frac{ 1 }{\cancel{ 2} } \times \cancel{2} \]
matches your "cheat sheet"
\[ \frac{ 1 }{\cancel{ a} } \times \cancel{a} =1\]

- ijarritos

where on the sheet?

- phi

4th from the bottom

- ijarritos

omg how do you even get that out of it

- ijarritos

all i know about simplification is to combine like terms

- ijarritos

and i dont even see that going on like what ????

- phi

do you see the line that says Inverse property of multiplication?

- ijarritos

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
\[ 2 \cdot \frac{1}{2} \\ 3 \cdot \frac{1}{3} \\ \frac{2}{3}\cdot \frac{3}{2}\]

- ijarritos

the teacher said this was "review work" and I don't even know how do do this

- ijarritos

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

- ijarritos

Yes

- ijarritos

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?

- ijarritos

Yes

- ijarritos

And I don't know what I'd multiply by 4/5

- ijarritos

4/5 x 1/5?

- phi

you "flip it"

- ijarritos

4/5 x 5/4?

- ijarritos

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

- ijarritos

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?

- ijarritos

to 17b and I didn't really understand it

- ijarritos

@phi are you going to be here in 30 minutes or less? I might need a break for a sec

- ijarritos

Ok I'll tag you when I get back

- ijarritos

@phi Im back

- phi

what is the difference between line 17a and 17b?

- ijarritos

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.

- ijarritos

1/2 x 2

- phi

the difference is this part
\[ \frac{1}{2}(2t) \text{ vs } \left( \frac{1}{2}\cdot 2 \right) t \]

- ijarritos

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?

- ijarritos

Yes

- ijarritos

Associative property

- phi

yes, specifically associative property of multiplication

- ijarritos

what about b to c?

- ijarritos

on 17

- ijarritos

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 ?

- ijarritos

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

- ijarritos

Yes it does change

- phi

what changes?

- ijarritos

nvm

- ijarritos

what about c to d?

- ijarritos

1/2 x 1 is 1 and 1 x t is 1

- phi

1/2*1 is not 1

- ijarritos

i meant 1 x 1/2 is 1/2

- phi

yes, and that is an important property

- ijarritos

I know how it works im just trying to find which property

- phi

look for 1 times "something" equals "something"

- ijarritos

identify property of multiplication?

- phi

yes. thought it is spelled identity

- ijarritos

omg im getting it

- phi

ready for Q 18?

- ijarritos

Yes

- phi

what is the exact difference between the left and right sides of 18a?

- ijarritos

switched around

- ijarritos

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"

- ijarritos

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

- ijarritos

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?

- ijarritos

Brackets are switched around

- ijarritos

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?

- ijarritos

associative

- ijarritos

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))

- ijarritos

are c and d identity property of addition?

- phi

what is the difference between line 18b and 18c ?

- ijarritos

the addition in the brackets is added

- phi

be more "literal"
(2 + (-2)) turns into 0
do you see a property that shows that?

- ijarritos

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 !

- ijarritos

ok!

- phi

now 18c to 18d
a+0 becomes a

- ijarritos

so would d be identity property of addition since its literally a+0

- ijarritos

same as the cheat sheet

- phi

yes. adding 0 to anything does not change it.

- phi

Q19 looks almost the same as Q18

- ijarritos

19a associative property of multiplication?

- phi

19a, what is different (the symbols) between the left side and the right side?

- ijarritos

5 and n are switched

- phi

and be able to switch order is what property?

- ijarritos

commutative?

- phi

yes, commute means switch
so here, commutative property of addition (same as in Q18a)

- ijarritos

then i have no idea for 19b

- phi

now 19a to 19b
we "move around" parens. what property is "move parens"?

- ijarritos

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))

- ijarritos

inverse of addition?

- phi

notice the pattern is
(a+b)+c becomes a+(b+c)

- ijarritos

associative property of addition?

- phi

19 b is associative prop of add
19 c is ?

- ijarritos

omg i was looking at the wrong one

- ijarritos

identity for 19c

- ijarritos

of addition

- phi

what is different between 19b and 19c ?

- phi

(n + (-n) ) becomes 0
what property is that ?

- ijarritos

inverse of addition

- phi

yes. 19C is inverse of addition
now what is different between 19C and 19D ?

- ijarritos

5+0 = 5

- ijarritos

identity property of addition

- phi

yes

- phi

now the difference between 19D and 19E ?

- ijarritos

then 19e is inverse of miltiplication

- phi

yes. Is this making sense?

- ijarritos

yes

- ijarritos

Theres another side I did before I knew all this

- ijarritos

Could you check it?

- phi

can you do Q20?

- ijarritos

sorry if im asking you for too much haha im still going to rate you best on qualified helper however that works

- ijarritos

and I think so

- ijarritos

http://i.imgur.com/bXgg5li.jpg Heres the other side

- ijarritos

Heres for 20-
A- distributive
B- identity of multiply
C- inverse of addition
D- distributive

- phi

check 2,8,10,11

- ijarritos

ok

- phi

20C and 20D are not correct.

- ijarritos

Oh

- phi

what is the difference between 20B and 20C ?

- ijarritos

3 is switched to the other side

- phi

and "switching" is what property?

- ijarritos

itentity

- ijarritos

identity of addition*

- phi

if you look on your cheat sheet identity of addition is a+0 becomes a

- ijarritos

oh yeah

- ijarritos

commutative of addition

- phi

yes, 20C is commutative of addition
what is different between 20C and 12D ?

- ijarritos

associative property of addition

- phi

yes. the parens were changed

- ijarritos

is 21a commutative property of addition?

- phi

what is different between 21 left and right ?

- ijarritos

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.

- ijarritos

umm

- phi

write down the difference

- ijarritos

multiplication of negative 1?

- phi

21A to 21B ?
k becomes 1*k

- ijarritos

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 ?

- ijarritos

then identify again?

- phi

write down the "before" and "after"

- ijarritos

wait what

- ijarritos

so for 21b i would put before identity of multiplication?

- ijarritos

then after for 21c

- phi

yes, but just the part that is different

- ijarritos

both of them are identity of multiplication?

- phi

(1*k + 1*k) becomes (1+1)*k

- ijarritos

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)

- ijarritos

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?

- ijarritos

Yes

- phi

what property is that?

- ijarritos

identity of multiplication?

- phi

distributive

- ijarritos

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

- ijarritos

im confused about c.5 to d

- ijarritos

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.

- ijarritos

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)

- ijarritos

ok!

- ijarritos

is 22a identity property of multiplication?

- phi

what is different between 22a left side and right side?

- ijarritos

x is moved around

- phi

switched around? what property?

- ijarritos

commutative

- phi

for mult.

- ijarritos

Yes

- phi

now what is different between 22a and 22b ?

- ijarritos

x is removed and brackets are added

- phi

notice the pattern
xA+xB becomes x(A+B)
?

- ijarritos

Yes

- phi

and what property?

- ijarritos

Distributive backwards

- phi

yes

- phi

22b to 22c . what is different?

- ijarritos

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

- ijarritos

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

- ijarritos

Inverse property of addition?

- phi

yes

- ijarritos

then 22d is identity property of addition

- phi

yes

- ijarritos

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.

- ijarritos

what about the other side?

- ijarritos

2 8 10 11

- ijarritos

http://i.imgur.com/bXgg5li.jpg

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