ijarritos one year ago Can you help me with properties of real numbers and listing the steps?

1. ijarritos

Should I upload an image of the homework?

2. ijarritos
3. ijarritos

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

4. ijarritos

Someone please explain how I would start doing this

5. Nnesha

start with distributive property $\huge\rm \color{Red}{a}(b+c)$ distribute the parentheses by outside number $\large\rm \color{Red}{a} \times b + \color{Red}{a} \times c = \color{Red}{a}b+\color{Red}{a}c$

6. ijarritos

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

7. Nnesha

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

8. ijarritos

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

9. ijarritos

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

10. Nnesha

|dw:1440277087992:dw| look at the last one distributive property that's what they used for first question (a) $\large\rm \frac{ 1 }{ 2 }(1+2t)=\frac{ 1 }{ 2} \times 1 + \frac{ 1 }{ 2 } \times (2t)$

11. Nnesha

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

12. ijarritos

@Nnesha What about 17B

13. 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*

14. Nnesha

is**

15. ijarritos

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

16. Nnesha

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

17. Nnesha

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

18. ijarritos

@Nnesha Thats the confusing part

19. ijarritos

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

20. ijarritos

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

21. Nnesha

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

22. ijarritos

multiply

23. ijarritos

I have a question

24. Nnesha

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

25. 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

26. ijarritos

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

27. ijarritos

Or would you find it in a different way?

28. 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 :=)

29. Nnesha

these*

30. Nnesha

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

31. ijarritos

i forgot how to simplifyy

32. ijarritos

thats the problem

33. ijarritos

im 100% going to fail algebra II

34. Nnesha

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

35. 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 $\frac{ 1 }{ 2 } \times 2t = (\frac{ 1 }{\cancel{ 2} } \times \cancel{2})t$

36. phi

this last one is called "inverse property of multiplication"

37. Nnesha

last one ??

38. ijarritos

is cancelling out 2's the associative property?

39. phi

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

40. ijarritos

where on the sheet?

41. phi

4th from the bottom

42. ijarritos

omg how do you even get that out of it

43. ijarritos

all i know about simplification is to combine like terms

44. ijarritos

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

45. phi

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

46. ijarritos

yes

47. 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 $2 \cdot \frac{1}{2} \\ 3 \cdot \frac{1}{3} \\ \frac{2}{3}\cdot \frac{3}{2}$

48. ijarritos

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

49. ijarritos

like before she starts teaching us things and I don't even know the basics

50. 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

51. ijarritos

Yes

52. ijarritos

Are they using PEMDAS in 17a to get to 17b?

53. phi

what is the multiplicative inverse of 4/5 ? (what do you multiply it by so you get 1)?

54. phi

we'll get to 17a in just a minute.

55. phi

Do you have time to learn this now?

56. ijarritos

Yes

57. ijarritos

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

58. ijarritos

4/5 x 1/5?

59. phi

you "flip it"

60. ijarritos

4/5 x 5/4?

61. ijarritos

20/20 = 1 ohh

62. 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

63. ijarritos

but where did you get the 5/4 from

64. 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 $$\frac{5}{4}$$

65. 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

66. phi

that is enough about the multiplicative inverse. how far did you get answering your questions?

67. ijarritos

to 17b and I didn't really understand it

68. ijarritos

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

69. ijarritos

Ok I'll tag you when I get back

70. ijarritos

@phi Im back

71. phi

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

72. ijarritos

1/2 was multiplied into 2 and t so distributive property

73. 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.

74. ijarritos

1/2 x 2

75. phi

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

76. ijarritos

Right I knew that but just didn't know how to explain it

77. 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.

78. phi

do you see the property on your cheat sheet that shows "moving the parens" when multiplying?

79. ijarritos

Yes

80. ijarritos

Associative property

81. phi

yes, specifically associative property of multiplication

82. ijarritos

what about b to c?

83. ijarritos

on 17

84. ijarritos

inverse property of multiplication?

85. 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 ?

86. ijarritos

no

87. 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

88. ijarritos

Yes it does change

89. phi

what changes?

90. ijarritos

nvm

91. ijarritos

what about c to d?

92. ijarritos

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

93. phi

1/2*1 is not 1

94. ijarritos

i meant 1 x 1/2 is 1/2

95. phi

yes, and that is an important property

96. ijarritos

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

97. phi

look for 1 times "something" equals "something"

98. ijarritos

identify property of multiplication?

99. phi

yes. thought it is spelled identity

100. ijarritos

omg im getting it

101. phi

ready for Q 18?

102. ijarritos

Yes

103. phi

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

104. ijarritos

switched around

105. ijarritos

are there alot of trolls like that? xD

106. phi

yes, specifically when adding

107. phi

so look for a property related to addition that shows "switching"

108. ijarritos

Is it associative property of addition?

109. phi

associative is "where to put the parens"

110. 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

111. ijarritos

commutative property of addition?

112. phi

yes. they show a+b= b+a and that shows the "switching around" that you noticed with 2+a and a+2

113. phi

now for 18a to 18b what is different?

114. ijarritos

Brackets are switched around

115. ijarritos

distributive property?

116. 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?

117. ijarritos

associative

118. ijarritos

119. 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))

120. ijarritos

are c and d identity property of addition?

121. phi

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

122. ijarritos

the addition in the brackets is added

123. phi

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

124. ijarritos

is 18c inverse of addition?

125. 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 !

126. ijarritos

ok!

127. phi

now 18c to 18d a+0 becomes a

128. ijarritos

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

129. ijarritos

same as the cheat sheet

130. phi

yes. adding 0 to anything does not change it.

131. phi

Q19 looks almost the same as Q18

132. ijarritos

19a associative property of multiplication?

133. phi

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

134. ijarritos

5 and n are switched

135. phi

and be able to switch order is what property?

136. ijarritos

commutative?

137. phi

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

138. ijarritos

then i have no idea for 19b

139. phi

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

140. ijarritos

associative

141. 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))

142. ijarritos

143. phi

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

144. ijarritos

associative property of addition?

145. phi

19 b is associative prop of add 19 c is ?

146. ijarritos

omg i was looking at the wrong one

147. ijarritos

identity for 19c

148. ijarritos

149. phi

what is different between 19b and 19c ?

150. phi

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

151. ijarritos

152. phi

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

153. ijarritos

5+0 = 5

154. ijarritos

identity property of addition

155. phi

yes

156. phi

now the difference between 19D and 19E ?

157. ijarritos

then 19e is inverse of miltiplication

158. phi

yes. Is this making sense?

159. ijarritos

yes

160. ijarritos

Theres another side I did before I knew all this

161. ijarritos

Could you check it?

162. phi

can you do Q20?

163. ijarritos

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

164. ijarritos

and I think so

165. ijarritos

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

166. ijarritos

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

167. phi

check 2,8,10,11

168. ijarritos

ok

169. phi

20C and 20D are not correct.

170. ijarritos

Oh

171. phi

what is the difference between 20B and 20C ?

172. ijarritos

3 is switched to the other side

173. phi

and "switching" is what property?

174. ijarritos

itentity

175. ijarritos

176. phi

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

177. ijarritos

oh yeah

178. ijarritos

179. phi

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

180. ijarritos

associative property of addition

181. phi

yes. the parens were changed

182. ijarritos

is 21a commutative property of addition?

183. phi

what is different between 21 left and right ?

184. ijarritos

no its associative property of addition

185. phi

yes

186. phi

from 21A to 21B, they are using the property "backwards" but you should be able to figure out which property they are using.

187. ijarritos

umm

188. phi

write down the difference

189. ijarritos

multiplication of negative 1?

190. phi

21A to 21B ? k becomes 1*k

191. ijarritos

identity of multiplication

192. phi

yes. notice we went "backwards" from k to k*1 but that is ok. these rules work both ways

193. phi

what is different between 21B and 21C ?

194. ijarritos

then identify again?

195. phi

write down the "before" and "after"

196. ijarritos

wait what

197. ijarritos

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

198. ijarritos

then after for 21c

199. phi

yes, but just the part that is different

200. ijarritos

both of them are identity of multiplication?

201. phi

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

202. ijarritos

tell me how to write it XD I think I have the right answer

203. phi

which property shows something on the outside of the parens "going inside" (or in this case vice versa)

204. ijarritos

for 21b and 21c

205. 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?

206. ijarritos

Yes

207. phi

what property is that?

208. ijarritos

identity of multiplication?

209. phi

distributive

210. ijarritos

for 21c?

211. phi

yes. we are going from (1*k+1*k) to (1+1)*k which is like (ab+ac) to (b+c)*a

212. ijarritos

im confused about c.5 to d

213. ijarritos

substitution to d

214. 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.

215. ijarritos

For 21c how does 2*1 go to 2(k+1)

216. 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.

217. phi

finally 2*k +2*1 becomes 2(k+1) that is the distributive property (backwards)

218. 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)

219. ijarritos

ok!

220. ijarritos

is 22a identity property of multiplication?

221. phi

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

222. ijarritos

x is moved around

223. phi

switched around? what property?

224. ijarritos

commutative

225. phi

for mult.

226. ijarritos

Yes

227. phi

now what is different between 22a and 22b ?

228. ijarritos

x is removed and brackets are added

229. phi

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

230. ijarritos

Yes

231. phi

and what property?

232. ijarritos

Distributive backwards

233. phi

yes

234. phi

22b to 22c . what is different?

235. ijarritos

is 22c associative property of multiplication?

236. phi

(y+1) + (-1) becomes y+ (1 + (-1)) we are moving parens, so associative, but we are adding not multiplying

237. ijarritos

The parentheses are moved in 22d

238. phi

22c is associative property of addition 22c to 22d the change is (-1 + (-1) ) becomes 0

239. phi

**(1+(-1)) becomes 0

240. ijarritos

Inverse property of addition?

241. phi

yes

242. ijarritos

then 22d is identity property of addition

243. phi

yes

244. ijarritos

thank you so much for helping me learn this!!

245. 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.

246. ijarritos

what about the other side?

247. ijarritos

2 8 10 11

248. ijarritos