Question

Which ratio is equal to 12:54

A. 3:13
B. 6:24
C. 24:104
D. 36:162

Answer 1

Hint: \(12:54 \implies \dfrac{12}{54} = \dfrac{6}{27} = \dfrac{2}{9}\)

Answer 2

A: 3:13 is already in it's lowest terms. So no good, there.

B: \(6:24 \implies \dfrac{6}{24} = \dfrac{3}{12} = \dfrac{1}{4} \ne \dfrac{2}{9}\)

Why did you think it might be 6:24? Seems a little like you were just guessing. Don't do that. Prove it!!

Answer 3

i never understood ratios :(

Answer 4

Now is the time.

Answer 5

well proportions ratios...

Answer 6

We're just hunting for common factors.

\(6:24 \implies \dfrac{6}{24}\) -- You just have to know that.

Both numerator and denominator are even. There must be a common factor of 2.

\(\dfrac{6}{24} = \dfrac{2\cdot 3}{2\cdot 12} = \dfrac{2}{2}\cdot\dfrac{3}{12} = 1\cdot \dfrac{3}{12} = \dfrac{3}{12}\)

Both numerator and denominator are divisible by 3. You show me how that works.

Answer 7

dividing by 3s?

Answer 8

Perfect. That gives 1/4 as I demonstrated above. Okay, let's move on to C:

\(24:104\implies \dfrac{24}{104}\) -- What to do first?

Answer 9

divide

Answer 10

by 24?

Answer 11

I don't think so. 104/24 = 4.333...

Think smaller. Generally shoot for prime numbers. The easiest is to notice that they are both even. There's a 2 in there.

Answer 12

so by 4rs?

Answer 13

4 is not a prime number, but after doing 2, we would have discovered that there is another 2. Thus, 4 is okay on this one. Go ahead and do it. Let's see what you get.

Answer 14

thanks but i have to move on to my next question.

Answer 15

Ah,well... Come back when you're ready.

Answer 16

its D

Answer 17

@mariruiz Please read the Code of Conduct and heed its wisdom.

Answer 18

i was about to explain why

Answer 19

After the OP already signed off? A little odd, but okay.

Answer 20

@Happie cross multiply (12*162) which gets you 1944. then multiply (36*54) which gets you 1944.

Answer 21

@tkhunny i hadn't realized they signed off

Answer 22

what? o.o

Answer 23

its a shortcut to finding equivalent ratios @Happie

Answer 24

the correct awnser was D. tkhunny u were way off.

Answer 25

?? That makes no sense. My purpose was to teach you how to find the answer on your own. If I was "way off", this can mean only that you only wanted the answer and didn't care to learn. I'm guessing that's not it, so I couldn't have been off at all.

I ruled out A
We ruled out B, together.
We were working on C, and this was not yet done when you signed off.
We hadn't yet gotten to D.

I never use the profanity "cross-multiply". Do you want to learn it, or not?

Answer 26

(sigh)