Question

Determine whether the ratios in each pear are proportioanal. 5/8, 12/20

Answer 1

No

Answer 2

ha ha funny

Answer 3

Two ratios a/b and c/d are proportional if ad = bc.

Here you have a/b = 5/8 and c/d = 12/20.
i.e.,
a = 5
b = 8
c = 12
d = 20

That being the case, does ad = bc?

Answer 4

no

Answer 5

And btw, this relation ad = bc is true because if
\[ \frac{a}{b} = \frac{c}{d} \]
then there exists some number, k say, such that
\[ \frac{a}{b} = \frac{ka}{kb} \]
For example, 1/2 = 2/4 and here k = 2.

That being the case
c = ka
d = kb

Thus ad = a(kb) = abk
and bc = b(ka) = abk

Hence a/b = c/d if and only ad = bc.

Answer 6

Right, in this case, they are not proportional.

Answer 7

I like your answers becuase you explain them alot beter than any one else /THANKS!

Answer 8

thanks

Answer 9

4/10,2/5 yes or no

Answer 10

James what grade are you in?

Answer 11

yes, 4/10 = 2/5. I've finished my studies.

Answer 12

kewl !

Answer 13

24/15 ,4/3

Answer 14

Well, if those two are proportional, you can see that k must be 5 because 15 = 5 x 3
But ...

Answer 15

what on earth???

Answer 16

I dont understand

Answer 17

if 24/15 = 4/3 then there exists some number k such that
\[ \frac{24}{15} = \frac{4k}{3k} \]

Well, comparing denominators, that means 15 = 3k. Hence k = 5.

But if that's right, then 4k = 20. But then the numerators aren't the same. So they are not proportional.

Answer 18

Another example, is it true that 24/15 = 8/5 ?

Answer 19

Well, if that is true, there is a number k so that
\[ \frac{24}{15} = \frac{8k}{5k} \]
that is, 8k = 24 and 5k = 15.
Well, k = 3 fits the bill because 8 x 3 = 24 and 5 x 3 = 15.

Hence they are proportional, or equal.

Answer 20

yes