Question

what I like to do is make fractions out of our numbers:
1 44 ,1 10 ,1 31
and add them up to equal some arbitrary number.

1 44 +1 10 +1 31 =N
then I start clearing fractions and reducing as I go

Answer 1

right, does that make sense?

Answer 2

yes keep going

Answer 3

how do we clear a fraction then? we multiply the top by the bottom so that it becomes a rather useless form of "1"

Answer 4

1* anything doesnt change the value does it

Answer 5

dont you cross multiply

Answer 6

so lets start with multiplying it all by 44

\[44\left(\frac{1}{44}+\frac{1}{10}+\frac{1}{31}=N\right)\]
\[\frac{1(44)}{44}+\frac{1(44)}{10}+\frac{1(44)}{31}=(44)N\]
and reduce

\[\frac{1}{1}+\frac{22}{5}+\frac{44}{31}=44N\]

next we would clear off that "5" by doing the exact same process

Answer 7

\[5\left(\frac{1}{1}+\frac{22}{5}+\frac{44}{31}=44N\right)\]
\[\frac{1(5)}{1}+\frac{22(5)}{5}+\frac{44(5)}{31}=44(5)N\]

reduce

\[\frac{5}{1}+\frac{22}{1}+\frac{44(5)}{31}=220N\]

the left side is only there to help the process, so that 44(5) doesnt reduce so we can leave it there ... next is to clear that 31 off in the same process

Answer 8

\[31\left(\frac{5}{1}+\frac{22}{1}+\frac{44(5)}{31}=220N\right)\]
\[\frac{5(31)}{1}+\frac{22(31)}{1}+\frac{44(5)(31)}{31}=220(31)N\]
and reduce
\[\frac{5(31)}{1}+\frac{22(31)}{1}+\frac{44(5)}{1}=6820N\]
andwith all the fractions cleared we are left with our LCM; its the number stuck to our N

6820

Answer 9

so i would go 1(31)/31 + 1(31)/10 + 1(31)/31

Answer 10

no, you would go as I did above. I have no idea where you got that from

Answer 11

its similar yes, so i think your on the right track at least :)

Answer 12

44(1/31 +1/10 + 1/44)

Answer 13

You have to include an arbitrary number to collect it all on the left with

Answer 14

otherwise, your just throwing out the baby with the bathwater

Answer 15

ok show me what im leaving out please

Answer 16

44(1/31 +1/10 + 1/44 = N)

Answer 17

its that =N part; it subtle, but important. You dont have to name it N of course. name it LCM if you want, but stick it in there

Answer 18

44(1/31 +1/10 + 1/44)=N

Answer 19

almost, we need to include it in the process; so put it inside of the whole multiplication paranthesis

Answer 20

44(1/31 +1/10 + 1/44 = N )

Answer 21

OK i see i was trying to leave it out by accednt

Answer 22

now distribute the 44 thru all the terms inside the paranthesis and then simplify your results in order to go at it again

Answer 23

1 (44)/10 +1(44)/10 +1(44)/31

Answer 24

sorry 1(44)/44

Answer 25

soo close, but lets use what we created instead of making up something else.

44(1/31 +1/10 + 1/44 = N )

44/31 + 44/10 + 44/44 = 44 N

44/31 + 22/5 + 1/1 = 44 N

Answer 26

so i did it wrong

Answer 27

you did it almost right :)

Answer 28

you catched your 44/44, but you left off that = N part.

Answer 29

okay

Answer 30

now its important to know that this is just a method that I use. If there is an easier method for you, by all means use it

Answer 31

im going to tell you im having to reteach myself
it has been that long

Answer 32

i started college 20 years after high school :)

Answer 33

now that leads us with what

Answer 34

44 as the LCM

Answer 35

no, 44 is just the first round of 3 rounds to finish

44(1/31 +1/10 + 1/44 = N )

44/31 + 44/10 + 44/44 = 44 N

44/31 + 22/5 + 1/1 = 44 N

we have 2 more fractions to clear out

Answer 36

since 5 and 31 have nothing at all in common; we could shorten this to:

44(5)(31) and be done with it

Answer 37

mulitply it it together

Answer 38

yep

Answer 39

6820

Answer 40

thats it :)

Answer 41

now the last part GCF

Answer 42

gonna have to post that one up again on the left side; i have to run

Answer 43

good luck :)

Answer 44

OK