Stanton D. answered • 04/28/14

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Tanya,

Here's another thought, to add to Jamal's:

It looks to me as if your teacher *may* be trying to get you to re-organize that "7k:3w" ratio, by pulling the 7 and 3 out front, so that you would get 7k:3w = (7/3) x (k:w) or (7/3) x (k/w). That's just my guess.

If you are furnished values for k and w, of course, you can just plug in and solve, so for example if k=20 and w=3, then 7k:3w = (7x20)/(3x3) = 140/9 = 15

^{5}/_{9}. But ratios also apply when the two things you are comparing aren't numbers; for example, they might be apples and oranges. Then you can better imagine doing what Jamal suggests. So if you have 7 apples and 3 oranges, how would you split up the apples *so as to have the same amount of apple for each orange*? You would cut the apples and put (7/3), or 2^{1}/_{3}, apples per orange. The term "ratio" would apply, and would be the same idea, whether you keep the fruit intact, slice and distribute, or make a combined juice drink out of them!Later on in life, when someone objects "that's like comparing apples to oranges" (when they're objecting to someone else making a comparison of unlike things), just remember, you already did that, it was a ratio!

By the way, there's a fancy name for the property of arithmetic operations you are using when you do that 7k:3w = (7/3)x(k/w) switch, it's "the commutative property of multiplication" and you are applying it to go from an expression of the form:

(a x b)

-------

(c x d)

to

(b x a)

--------

(c x d)

and then regrouping to:

(b/c) x (a/d)

(essentially!).

Hope this helps you.

P.S. If you want to keep some of the feeling of those variable letters k and w, there's always kiwifruit and watermelons!

-- S.