## anonymous one year ago Algebra Question

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1. anonymous

If $\frac{ a }{ 2 } + \frac{ b }{ 2 } = 3$ what is the value of 2a +2b?

2. anonymous

I haven't really been able to get anywhere on it, any form of help will help :D

3. anonymous

u still there

4. anonymous

what do u think

5. anonymous

yeah im back sorry

6. anonymous

@slade well I don't really have any idea on how to start

7. freckles

I dare you to multiply both sides by 4

8. anonymous

thats how u do it right there

9. freckles

double dog dare you

10. anonymous

what would that do? um okaay 3 x 4 = 12 on the right but i don't know how to multiply the fractions :/

11. freckles

do you know what 4/2=?

12. anonymous

yes 2

13. freckles

$4(\frac{a}{2}+\frac{b}{2}) \\ =\frac{4}{2}a+\frac{4}{2}b=?$

14. anonymous

a/2 and b/2 x 4?

15. anonymous

yes

16. anonymous

ah gotcha

17. anonymous

2a + 2b is what i get! and that means it eqauls 3 !!

18. freckles

no

19. freckles

3(4)

20. anonymous

but what would make me multiply each side by 4?

21. anonymous

oh yeah 12

22. freckles

to solve for 2a+2b

23. anonymous

24. anonymous

2 * 4 =?

25. anonymous

I dare you all to learn math :-D double dog dare at that :-D

26. anonymous

to solve yes but where did you think of 4 why not 3? like is there a specific reason or thats just how algebra works? common factor what was it?

27. freckles

well 4(a/2+b/2) would give me what I want which is 2a+2b

28. anonymous

i'm trying nixy lol

29. freckles

but if I multiply one side by 4 I have to multiply the other side by 4

30. anonymous

ah yes that is true that is how to get the end result

31. freckles

do you want to give you a problem that is similar ?

32. anonymous

sure

33. anonymous

@kevinhunterwood69 it is hard work but if you keep at it, it will get easier :-D

34. anonymous

yeah i am

35. freckles

solve for 6a+9b given $2a+3b=-1$

36. anonymous

im out

37. anonymous

no one is listening to me

38. anonymous

lol there

39. freckles

40. freckles

@kevinhunterwood69 do you notice how to find the value of 6a+9b yet?

41. anonymous

okay so I did: solve for 6a + 9b given: 2a + 3b = -1 work: 2a + 3b = -1 3 (2a + 3b) = -1(3) 6a + 9b = -3 answer: -3

42. anonymous

was that correct?

43. freckles

omg brilliant

44. anonymous

yay :D

45. anonymous

math is fun when i can finally understand algebra

46. freckles

good job I bet if that was the problem you had you would have had no problems do you think the fractions throw you off ?

47. anonymous

yes def fractions have always been a struggle to understand

48. anonymous

square roots too but mostly fractions

49. freckles

try this one: $\text{ If } a+\frac{b}{3}=4 \text{ then what is the value of } 21a+7b$ (this will has a fraction in it; let's see if it throws you off any this time )

50. anonymous

hmm

51. anonymous

if i move 3 to the other side will it be on top?

52. anonymous

actually wait i can't do that right ugh um if i move b let me see

53. freckles

so you want to multiply both sides 3 to remove the fraction you can do that 3a+b=12 but we still are not done

54. anonymous

all i know is im trying to get constants on one side and variables on the other right?

55. anonymous

sorry what

56. anonymous

how did you get 3a and b lost its 3? oh you moved the 3 from b next to a?

57. freckles

$a+\frac{b}{3}=4 \\ \text{ if you don't like the fraction there you can always multiply both sides by } \\ \text{ what is \in the denominator of that fraction } \\ 3(a+\frac{b}{3})=3(4) \\ 3(a)+3(\frac{b}{3})=3(4) \\ 3a+b=12$

58. anonymous

yes that explains it! thanks so much

59. anonymous

well 3a i understand actually haha 3(b/3) = b?

60. freckles

$3(\frac{b}{3})=3 \cdot \frac{b}{3}=\frac{3}{1} \cdot \frac{b}{3}= \frac{3}{3} \cdot \frac{b}{1}=1 \cdot b =b$

61. freckles

basically in summary 3/3=1 so you are left with 1*b which is just b

62. freckles

like in your problem we had above we had: $\frac{a}{2}+\frac{b}{2}=3 \\ \text{ we could have cleared the fractions before finding what we wanted } \\ \text{ by multiplying both sides by 2} \\ 2(\frac{a}{2}+\frac{b}{2})=2(3) \\ 2 \frac{a}{2}+2 \frac{b}{2}=2(3) \\ a+b=6$

63. anonymous

yes i follow up to the point 3/3 = b/1 why does b not become 3b? like 3/3 = 3b/1 ?

64. freckles

anything over itself is 1 (well except 0)

65. freckles

well 3/3 *b =b

66. freckles

first do you know that 3/3=1 ?

67. anonymous

yes i do

68. anonymous

no time for jokes lol

69. freckles

$\frac{3}{3}=1 \\ \text{ so if I multiply both sides by } b \text{ we have } \\ \frac{3}{3}b=1 b$

70. anonymous

yes

71. freckles

72. anonymous

no it did

73. anonymous

so we were at 3a + b = 12

74. anonymous

and m trying to figure out what is 21a + 7b so

75. freckles

right and we want 21a+7b 's value

76. anonymous

yes

77. freckles

any if you multiply both sides by s_v__ you will get?

78. freckles

I didn't put the full word there

79. anonymous

ah seven

80. anonymous

wait a second

81. anonymous

then we multiply 12 by 7 that means :O

82. freckles

yep! :)

83. freckles

just so you know we could have figured out 21a+7b in one step

84. freckles

85. anonymous

ya so 21a + 7b = 84

86. freckles

$a+\frac{b}{3}=4 \\ \text{ we wanted } 21a+7b \\ \text{ so we could have just multiplied 21 on both sides \to \begin with } \\ 21a+21(\frac{b}{3})=21(4) \\ 21a+7b=84$

87. anonymous

wow

88. freckles

anyways keep practicing and numbers will become easier to play with

89. anonymous

thanks for all the extra practice!

90. freckles

np :) these can get a lot funnier I promise $\text{ assume } a \text{ and } b \text{ are positive } \\\text{ if } a^2+2ab+b^2=4 \text{ then what is } (a+b)^4 \text{ or what is } a+b$ I think they can even get funnier than that

91. anonymous

uh lol

92. freckles

$a^2+2ab+b^2=(a+b)^2 \text{ is the trick there }$

93. anonymous

ah

94. anonymous

welp i'll go back to this sat book

95. freckles

k k have fun :)

96. anonymous

and ponder on about the funny stuff in math lol

97. anonymous

thx frecks

98. freckles

np :)

99. mathstudent55

@freckles Great explanations!