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03 Jul 2016, 07:48
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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.
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.
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Updated on: 04 Jul 2016, 10:38
Originally posted by Abhishek009 on 03 Jul 2016, 12:27.
Last edited by Abhishek009 on 04 Jul 2016, 10:38, edited 1 time in total.
Last edited by Abhishek009 on 04 Jul 2016, 10:38, edited 1 time in total.
Edited TYPO
Kudos
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Lets try with the definition first -
RATIO : The quantitative relation between two amounts showing the number of times one value contains or is contained within the other.
FRACTION : A fraction represents a part of a whole or any number of equal parts.
So, there exists a difference in the usage...
Consider a simple example there are two boys and one girl...
Untitled.png [ 5.68 KiB | Viewed 3313 times ]
So, Total no of children = 2 + 1 => 3
As per the definition of Fraction ( a part of a whole or any number ) the fraction representing Boys is 2/3 and the part of fraction representing Girls is 1/3
Again as per definition of Ratio ( The relation between two amounts ) the ratio of Boys to Girls is 2 : 1
Hope this helps you...
In case of any doubt feel free to revert...
RATIO : The quantitative relation between two amounts showing the number of times one value contains or is contained within the other.
FRACTION : A fraction represents a part of a whole or any number of equal parts.
So, there exists a difference in the usage...
Consider a simple example there are two boys and one girl...
Attachment:
Untitled.png [ 5.68 KiB | Viewed 3313 times ]
So, Total no of children = 2 + 1 => 3
As per the definition of Fraction ( a part of a whole or any number ) the fraction representing Boys is 2/3 and the part of fraction representing Girls is 1/3
Again as per definition of Ratio ( The relation between two amounts ) the ratio of Boys to Girls is 2 : 1
Hope this helps you...
In case of any doubt feel free to revert...
04 Jul 2016, 01:55
Kudos
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Thank you for your reply!
In the last sentence you say that the ratio boys to girls is 2:3 Isn't it 2:1 ?
Also, when you see in a word problem that the ratio of X to Y is A to B. Should I read it as a fraction or as a ratio definition? because the way I read it will change the way I use the data.
It seems that these terms are used interchangeably and it's confusing!
Thank you!
In the last sentence you say that the ratio boys to girls is 2:3 Isn't it 2:1 ?
Also, when you see in a word problem that the ratio of X to Y is A to B. Should I read it as a fraction or as a ratio definition? because the way I read it will change the way I use the data.
It seems that these terms are used interchangeably and it's confusing!
Thank you!
