Question

Please help explain this to me.
Rational Equations

The equation is 100/45 + 75/35 = 150/t
LCD: 20/9 + 15/7 =150/t

63t(20/9 +15/7) = 63t (150/t)
140t + 135t =9450<-----how do you get that?
275t= 9450
275/275 = 9450/275
t= 34 4/11 <--- how do you get that?

Answer 1

when you say "<----- how do you get that?" do you mean just the part to the right of the equals sign, or do you mean the entire line of math?

Answer 2

just that part of the equation

Answer 3

meaning just this part (140t + 135t =9450)

Answer 4

ok, that helps

Answer 5

sorry about that haha

Answer 6

So, we begin with 63t(20/9 +15/7) = 63t (150/t). On the left we distribute the 63t to get,

63t * (20/9) + 63t * (15/7) = 63t * (150/t)

Does that make sense so far?

Answer 7

yes

Answer 8

ok, so now just look at each piece:

for 63t * (20/9) we know that 63 is just 7*9 so the 9s cancel leaving us with 7t*20 = 140t

Answer 9

Do the same pattern for 63t * (15/7) to get 9t * 15 = 135t

Answer 10

And then, for the right we have 63t * (150/t) but the t's cancel out! leaving us with 63*150 = 9450. Any questions on that whole deal? :)

Answer 11

ohhhh okay I get it now

Answer 12

awesome! congrats! did you still want to go over the last line of the solution?

Answer 13

yes pleasee

Answer 14

ok, so we start with the "improper fraction" 9450/275 and for some reason we want to convert this to a mixed fraction, which will be 34 4/11, but let's see how we can do that.

Answer 15

okay

Answer 16

first let's try to simplify the 9450/275 by dividing top and bottom by 5. In other words how many times does 5 go into 9450 and how many times into 275?

Answer 17

1890 and 55

Answer 18

Ok, so we've reduced the fraction to 1890/55, looks like we can still "take out" more 5s! So how many times does 5 go into 1890 and 55?

Answer 19

by the way, we're almost there :)

Answer 20

I get 378/11, how about you?

Answer 21

I got the same

Answer 22

alright! so we can't reduce any farther, since 11 doesn't go into 378 evenly, so now for the grand finale

Answer 23

we will convert to a "mixed fraction" by figuring out how many 11s can fit into 378 and what remainder is left over.

Answer 24

34.36

Answer 25

OK, so we can get 11 in 34 times (ignore the .36 part)

Answer 26

notice that 11 times 34 is 374, which means that there are 4 pieces left over to reach 378 the target number.

Answer 27

What do you mean by that ?

Answer 28

so that means that as a "mixed number" 378/11 is the same as 34 4/11, literally 34 whole pieces and 4 small pieces left over

Answer 29

ah, you have a question? :)

Answer 30

i don't get how you get the 4

Answer 31

OK, good question.

Answer 32

Let me use an easier example to explain.

Answer 33

suppose we were trying to convert 15/11 into a mixed fraction.

Answer 34

Do you see that for this easier case that the answer should be 1 4/11? If not, no worries, I just want to see exactly where the confusion might be :)

Answer 35

no haha

Answer 36

I am really bad in math

Answer 37

Oh no, not at all, it's not obvious. :) Don't feel bad. No one is "good" or "bad" at math. We either see it one way or not that way. :)

Answer 38

haha that just made my day

Answer 39

lol, glad to help! :) Let's see if we can make sense of this weird symbol 15/11.

Answer 40

First, though, would you agree that 11/11 is the same as 1?

Answer 41

yes

Answer 42

OK, so then does it seem right that 15/11 = 11/11 + 4/11 ?

Answer 43

yes

Answer 44

Alright, so we just said that 11/11 is the same as 1, so I will write this as

15/11 = 1 + 4/11

Answer 45

Now, people are lazy, and so the shorthand was invented to write

15/11 = 1 4/11 and they just made the "plus" sign disappear for no good reason! But that's the way we've written it ever since! Crazy history!

Answer 46

And this is called "mixed fractions," which is really just adding fractions together! Any questions on this? :)

Answer 47

Nope I get it now. :D

Answer 48

Alright, so if you felt "bad" at math, it was really the inventors of math who did something "bad" by confusing people when they removed the plus sign!

Answer 49

So, going way back to our original 378/11...

Answer 50

We could write this as

378/11 = 11/11 + 11/11 + 11/11 + 11/11 + ... (34 times) and have 4/11 left over

Answer 51

ahhh okay

Answer 52

How do I know that? Well, I know that 378/11 = 34.36, and the whole number is 34, so that's a clue that 11 * 34 = 374

Answer 53

In other words, 378/11 = 374/11 + 4/11

Answer 54

but 374/11 = 34 a whole number! yay!

Answer 55

so 378/11 = 34 + 4/11 or 34 4/11 in shorthand

Answer 56

crazy math people! :D they like to be tricky! :)

Answer 57

Yes very tricky haha && yayy ! I finally get it now haha thankt you so much^-^ you just saved me 4 hours hahah

Answer 58

Glad to help, I've wasted many an hour on math problems myself, so I know the feeling, you did great! If you understood the explanation, you are actually very good at math! Maybe you just haven't read or heard the best explanations up to this point. Keep up the good work! :D

Answer 59

Thank you :)

Answer 60

Take care, it's lunch time here so I'm outta here!

Answer 61

Okay haha have a good lunch

Answer 62

thx