Hi everyone!
A question on ratios.
Theory says that ratios and fractions are the same. I don't get how is that.
Case 1:
We have: the ratio of boys to girls is 1 to 3. That is the same as 1:3 or \(\frac{1}{3}\) It happens that in this case we have the total of four parts, so the total number of boys to girls would have to be a multiple of 4. Important for my question:
boys represent 25% of the total! Imagine a pie with four parts and 1 is highlighted.
Case 2: Now imagine a fraction \(\frac{1}{3}\) How does it refer to a ratio?.. How can it be the same as a ratio?
Here we say that we have 3 total parts, not four.
And 1 represents 33% of the total not 25% like in the previous case!
Imagine a pie with 3 parts and one of them is highlighted, this is what a fraction represents to me! If we want to get a multiple of that fraction it would be a multiple of 3, not a multiple of 4 as in case one.
So, do you get my doubt here? Where is the similarity between fractions and ratios? I always thought that ratios and fractions are different things and my examples seem to demonstrate what I mean by that.
Can you please give me some help on this?
Thank you!
PS: I have read the
Magoosh article on fractions, Manhattan and Veritas materials and still have this doubt.