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How would proportions be used to "scale up" or "scale down" something?

(Not really sure if I even understand what this means. I even read my text and I can't figure this out.)

  • Math -

    Let's say that you have a concentrated disinfectant that says that you should mix one cup of disinfectant to one quart of water - but you need one gallon (sixteen cups) of water plus the added disinfectant to make enough of the mixture. Your proportion would be 1 cup of disinfectant to 4 cups of water, since a quart is four cups. Using this ratio, or proportion, you can scale the amount up to what you need: 1/4 = x/16, where x is the amount of disinfectant (which would be 4 cups).
    If you need to use less water than the quart, you can use the same ratio to scale down your amount. Let's say that, instead of a quart, you want to use only two cups of water. You would now need: 1/4 = x/2, where x is again the amount of disinfectant (which would now be only 1/2 of a cup). This is how proportions can be used to scale something up or down.

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