Ellen S. answered • 09/05/13
Tutor
4.8
(88)
Math and Writing Geek
Just elaborating a bit on the thought process behind ratios for you:
A ratio is the relationship of one quantity to another. So in the example you gave, a ratio of 7:12 means that for every 7 of the first item, there are 12 of the second. The order becomes very important, as changing the ratio to 12:7 would mean that for every 12 of the first item, there are 7 of the second, which is not the same thing at all.
Here's an example: suppose you have two bags of candy; one bag of M&M's and one bag of Skittles. Say you count the candy in each bag, and find out that there are 35 M&M's and 60 Skittles. You notice that both numbers are multiples of five, so you decide to split each bag into five piles. You wind up with 7 M&M's in each pile from the first bag, but 12 Skittles in each pile from the second. This means that for every 7 M&M's, there are 12 Skittles. So the ratio of M&M's to Skittles would be 7:12.
If you regroup them, there'll still be the same number of candies of each type, so the ratio won't change. It'll always be 7 M&M's to 12 Skittles. In order for the ratio of M&M's to Skittles to be 12:7, you'd have to add M&M's to the pile (or remove Skittles) until you had 12 M&M's for every 7 Skittles (which would probably involve some regrouping).
As the previous tutor said, ratios are often written as fractions since there is so much manipulation that can be achieved simply when the ratio is structured as a fraction. When doing this, the first item is always the numerator (top), and the second item is the denominator (bottom). Here's our example again using fractions:
So we have 35 M&M's and 60 Skittles. If we were asked to find the ratio of M&M's to Skittles, the quickest way to achieve that would be to write the totals as a fraction and work from there. So let's write the ratio as:
35/60
Now, remember we noticed that both numbers are divisible by 5? Well, that's the next step here as well. Simply factor out common elements until you've arrived at the fraction's simplest form, which will be your final ratio:
35/60 = (5*7)/(5*12)
So we factor out the 5 because 5/5 is just a fancy way of writing 1, so we can divide the fraction by our fancy 1 and know that the result will be equivalent (the same value, just written differently):
(5*7) / 5 = 7/12
(5*12) 5
And there you have it. Hope this helps you - just remember to double-check what order the items are asked about, and keep that order the same the whole way through the problem.
