Question

if to the numerator and denominator of the fraction 1/3 you add its
denominator, 3, the fraction will double [(1+3) / (3+3) = 4/6 = 2/3]. Find a fraction
which will triple when its denominator is added to its numerator and denominator; find
one that will quadruple.

Answer 1

kind of

Answer 2

what is it

Answer 3

don't be afraid to share

Answer 4

i'm still thinking as well

Answer 5

It is really hard for me to explain

Answer 6

So we have the equality \[\frac{a+b}{2b}=\frac{3a}{b}\]

Answer 7

maybe we can play with this somehow

Answer 8

\[\frac{\frac{a+b}{2}}{b}=\frac{3a}{b} \\ \frac{a+b}{2}=3a \\ a+b=6a \\ b=5a\]

Answer 9

So maybe if we choose a a and a b such that b=5a and it might work...

Answer 10

choose a random value a not equal to 0

Answer 11

3

Answer 12

ok so b=5a
so b has to be what if a=3?

Answer 13

b=5a
b=5(3) <---because you chose a to be 3

Answer 14

so b=?

Answer 15

ummmm 125?

Answer 16

3*5=15
\[\frac{a}{b}=\frac{3}{15}\]

Answer 17

oh

Answer 18

now see if that fraction works

Answer 19

i kinda get it

Answer 20

3/15 can actually be reduced before you begin

Answer 21

to 1/5

Answer 22

right now see what happens if you add 5 to top and bottom

Answer 23

we want triple of what we started with

Answer 24

15?

Answer 25

have you added 5 to the top
and added 5 to the bottom yet?

Answer 26

or 25?

Answer 27

\[\frac{1}{5} -> \frac{1+5}{5+5}=\frac{?}{?}\]

Answer 28

6/10

Answer 29

OR
2/3

Answer 30

I MEAN 3/5

Answer 31

guess what?

Answer 32

isn't that triple what we started with?

Answer 33

3*1/5=3/5

Answer 34

YA

Answer 35

THE ANSWER IS 3/5

Answer 36

now all i did was try to get a relationship between a and b I could work with
we had the equality \[\frac{a+b}{2b}=\frac{3a}{b} \\ \text{ then I played with the fraction on the left to get if over b } \\ \text{ so I could just set the tops equal } \\ \frac{\frac{a+b}{2}}{b}=\frac{3a}{b} \\ \\ \text{ so then we had } \frac{a+b}{2}=3a \\\text{ multiply } 3 \text{ on both sides } \\ a+b=6a \\ \text{ subtract } a \text{ on both sides } b=5a \]
the fraction you started with was the answer
we were checking to see if it was the answer by going through the steps your question had put forth
and in genernal where a and b do not equal 0 we have
\[\frac{a}{b}=\frac{a}{5a} \text{ will always work } \\ \frac{a}{5a} \text{ add 5a on top and bottom } \\ \frac{a+5a}{5a+5a}=\frac{6a}{10a}=3 \frac{2a}{10a}=3 \frac{a}{5a}\]

Answer 37

OK THANK YOU

Answer 38

you remember the fraction we started with was the one you made

Answer 39

ok

Answer 40

now see if you can come up with an answer for the next one

Answer 41

"find one that will quadruple"

Answer 42

also one more thing a/(5a)=1/5 for any value a not equal to zero
:)

Answer 43

you can use the same process i used above for the next question

Answer 44

except with a few tweaks

Answer 45

ok thank you