Question

ALGEBRAIC FRACTIONS
1. Simplify https://media.glynlyon.com/g_alg02_2012/5/2019.gif
a) 1/2
b)3m / 3m + 2
c) m - 1 / 3m + 2

2. Simplify the expression. https://media.glynlyon.com/g_alg02_2012/5/269.gif
a) -y / x
b) y / y - x
c) y - x / y

3. Change the mixed expressions to fractions. https://media.glynlyon.com/g_alg02_2012/5/2016.gif
a) y^2 - y + 1 / y + 3
b) y^2 + 2y - 8 / y + 3
c) y^2 + 2y - 2 / y + 3

4. Change the mixed expressions to fractions. https://media.glynlyon.com/g_alg02_2012/5/2017.gif
a) 11 - 15a / 7a - 5
b) 11a + 9 / 5 - 7a
c) 6a - 7 / 7a - 5

5. https://media.glynlyon.com/g_alg02_2012/5/2012.gif
a) 2y^2 + 2xy + x - y / x^2 - y^2
b) 3x / x^2 - y^2
c)2xy + x - y / x^2 - y^2

Answer 1

Okay, so yesterday, I showed you a really simple technique for determining which solution was correct. However, this only works under circumstances where you have the potential solution.

So, if I asked you to find the answer through simplification for #1, could you do that?

Answer 2

1 / 2

Answer 3

Nope. Lets start at the beginning.
\[\frac{\frac{m-2}{m+1}+2}{1+\frac{1+2m}{m+1}}\]
Remember when I said that it was easier to deal with everything as a fraction? This is one of those times.

How can we get:
\[ \frac{m-2}{m+1}+2 \]
to add together?

Answer 4

They need to have the same denominator, correct?

Answer 5

yes

Answer 6

so, how do we get 2 to have a denominator of m+1?

Answer 7

do you know that it's okay to multiply any term by 1, and it won't change its value, right?

Answer 8

yes

Answer 9

well, does:
\[1=\frac{m+1}{m+1}\]
?

Answer 10

yes

Answer 11

so what happens if you multiply:

\[2*\frac{m+1}{m+1}\]
?

Answer 12

3m+2??

Answer 13

hmm... would it be possible to show me your work?

Answer 14

2m+ 1

Answer 15

\[\frac{m-2}{m+1}+2*\frac{m+1}{m+1}\] = ?

Answer 16

m-1 / 3m+2

Answer 17

\[\frac{m-2}{m+1}+\frac{2m+2}{m+1}\]
see how I got that?

Answer 18

for the numerator?

Answer 19

yes im am so sorry for confusing you as you can see i am not the best in math lol

Answer 20

That's okay, lol. So you see, it's possible to put the whole numerator into a single fraction without changing its value simply by multiplying one of it's terms by 1 (which is the same as (m+1)/(m+1)). This is a very powerful and simply way to get things to have the same denominator so you can add them.

Can the same thing be done with the denominator:
\[1+\frac{1+2m}{m+1}\]

Can you add the 1 to (1+2m)/(m+1) like I showed you?

Answer 21

3m+ 2 / m+ 1

Answer 22

correct; so on the top, you have:

3m/m+1 and on the bottom you have 3m+2/m+1

What can you do to remove the m+1 from both the numerator and the denominator?

Answer 23

eliminate

Answer 24

lol, yep. To do so:

\[\frac{\frac{3m}{m+1}}{\frac{3m+2}{m+1}}*\frac{m+1}{m+1}\]

See, it's the same thing as multiplying by 1 again!

Answer 25

so, what's our answer?

Answer 26

m - 1 /3m+2

Answer 27

look at the last equation I gave you. Look at the numerator in the numerator, and the numerator in the denominator.

Answer 28

yea yea 3m / 3m+2

Answer 29

lol, yeah.

Answer 30

so, that's the answer.

Answer 31

whew!! lol

Answer 32

lol, yeah. Algebra II is not for the faint of heart. The second one can be approached in almost the same manner.

Answer 33

OK

Answer 34

So, first add the terms in the numerator together. Multiply the terms by 1 to get the same denominator if necessary.
Then do the same with the terms in the denominator of our question.

Answer 35

so what do you get in the numerator when you add the terms together?

Answer 36

is the awnser B?

Answer 37

... yes, it's B.

Answer 38

yayy on to #3

Answer 39

is the awnser A?

Answer 40

You might want to re-check your math on that.

Answer 41

C

Answer 42

How did you get C?

Answer 43

i see my mistake

Answer 44

i multiplied instead of dividing

Answer 45

can we go to #4 now

Answer 46

sure... fortunately, 4 isn't too hard by relative standards.

Answer 47

ok lets go :)

Answer 48

so, what is necessary to be able to add (6a-4)/(7a-5) to 3?

Answer 49

hmmmm....

Answer 50

they need to have the same denominator. So how do we get 3 to have a denominator of (7a-5)?

Answer 51

divide

Answer 52

\[3*\frac{(7a-5)}{(7a-5)}\]

See? Multiply by 1? That will convert the 3 to an expresion that has the same denominator as the first term, (6a-4)/(7a-5)

Answer 53

the final awnser is (6a-4)/(7a-5)

Answer 54

So then it becomes:
\[\frac{6a-4}{7a-5} - \frac{21a-15}{7a-5}\]

Answer 55

\[\frac{6a-4-21a-15}{7a-5}\]

Answer 56

sorry, plus 15 (+15).

Answer 57

which simplifies to:
\[\frac{-15a+11}{7a-5}\]

Answer 58

switch the order of the 2 terms in the numerator, and that's the answer.

Answer 59

yayy thanks can we go on to #5

Answer 60

i got c am i correct?

Answer 61

C

Answer 62

you are correct, lol

Answer 63

Yayyy!!

Answer 64

CAN we do the other 5

Answer 65

The last one was a tricky one, but you managed... do you really need my help?

Answer 66

YESSS

Answer 67

lol

Answer 68

Let's see the problems.

Answer 69

1. Simplify https://media.glynlyon.com/g_alg02_2012/5/276.gif
a) a - b
b) a - b / a
c) -ab / a + b

2. https://media.glynlyon.com/g_alg02_2012/5/209.gif
a) 3a+2b+c / abc
b) 6 / abc
c) 8

3. https://media.glynlyon.com/g_alg02_2012/5/2013.gif
a) 2a^2 - 6a + 15 / 8a^2 - 22a + 15
b) -3 / 7
c) 1 / 2a - 3

4. Find the lowest common denominator for the fractions shown. https://media.glynlyon.com/g_alg02_2012/5/205b.gif
a) a³ - 1
b) (a³ - 1)(a²+a+1)
c) (a + 1)²(a - 1)

5. Simplify the expression. https://media.glynlyon.com/g_alg02_2012/5/303.gif
a) -5x^2 - 2x / x^3 - 1
b) x / x^3 - 1
c) -x^2 + 2x / x^3 - 1

Answer 70

#1 looks almost identical to the first one we did the other day.

Answer 71

it does

Answer 72

In fact, I think the answer is the same.

Answer 73

what was the awnser for that one

Answer 74

what did you get?

Answer 75

a -b / a

Answer 76

am i correct?

Answer 77

nope.

Answer 78

-ab / a+b

Answer 79

C

Answer 80

...

Answer 81

im wrong

Answer 82

is it a-b?

Answer 83

well, it is the only remaining answer... listen, I can't really help you if you don't show me your work or your thinking... and if I just kinda give you the answer after you guess the 2 wrong ones, I'm not really helping...

Answer 84

ok

Answer 85

ok for this quiz can i get the answers to them

Answer 86

and for the lessons can you tutor me with them

Answer 87

because the quizzes & tests have time limits with them and with the lessons i can take all the time i want (its so silly for the website to do that)

Answer 88

please

Answer 89

what do you think the answer for #2 is?

Answer 90

B

Answer 91

well, I can tell you your off.

Answer 92

B is not right.

Answer 93

ok hold on

Answer 94

3a+2b+c/

Answer 95

abc

Answer 96

yep, that's more like it.

Answer 97

Sweet :) is #3 C

Answer 98

sorry, this one is a little harder lol, so, I'm not quite sure yet... but almost