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Intern  B
Joined: 17 Sep 2015
Posts: 21
Ratio to fraction for 3 parts  [#permalink]

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Hi,

I know 1:2 can be written as 1 over 2 and 1:2:3 can be written as 1 over 6 but my question is why can't the first ratio cannot be written as 1 over 3 using the same logic of the multipart ratios?
Manhattan Prep Instructor G
Joined: 04 Dec 2015
Posts: 948
GMAT 1: 790 Q51 V49 GRE 1: Q170 V170
Re: Ratio to fraction for 3 parts  [#permalink]

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1
rajak01 wrote:
Hi,

I know 1:2 can be written as 1 over 2 and 1:2:3 can be written as 1 over 6 but my question is why can't the first ratio cannot be written as 1 over 3 using the same logic of the multipart ratios?

Just to make sure I understand the initial question, let me reword it:

So, you're saying that you have a three-part ratio, 1:2:3. For instance, the ratio of rabbits to cats to dogs at an animal shelter, is 1:2:3.

You can also talk about this same ratio in terms of fractions. 1+2+3 = a total of 6 "parts," so you can also say that 1/6 of the animals are rabbits, 2/6 are cats, and 3/6 are dogs.

Assuming that's what you're referring to, then let me answer your actual question!

How you translate a ratio into a fraction, depends on what you're actually trying to figure out. For example, suppose that the ratio of boys to girls in a classroom is 1:2.

If you want to know what fraction of the total is made up of boys, you'd do the exact same thing you did with the 3-part ratio. You'd add together 1 and 2 to get 3. Then, you'd say that 1/3 of the total students are boys, and 2/3 of the total students are girls.

But if you want to calculate the fraction b/g (boys/girls), then you do 1/2.

In summary: boys/total would equal 1/3, while boys/girls would equal 1/2.

And the reason you're confused is that you're thinking about a "part/part" fraction in the first half of your question (1:2 = 1/2), but a "part/whole" fraction in the second half (1:2:3 -> 1/6).
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Senior Manager  S
Joined: 18 Dec 2017
Posts: 308
Re: Ratio to fraction for 3 parts  [#permalink]

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rajak01 wrote:
Hi,

I know 1:2 can be written as 1 over 2 and 1:2:3 can be written as 1 over 6 but my question is why can't the first ratio cannot be written as 1 over 3 using the same logic of the multipart ratios?

How can 1:2:3 be written as 1:6?

Posted from my mobile device
Intern  B
Joined: 17 Sep 2015
Posts: 21
Re: Ratio to fraction for 3 parts  [#permalink]

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gurmukh wrote:
rajak01 wrote:
Hi,

I know 1:2 can be written as 1 over 2 and 1:2:3 can be written as 1 over 6 but my question is why can't the first ratio cannot be written as 1 over 3 using the same logic of the multipart ratios?

How can 1:2:3 be written as 1:6?

Posted from my mobile device

Because 1:2:3 total is 6, so the first part can be written as 1 over 6
Intern  B
Joined: 17 Sep 2015
Posts: 21
Re: Ratio to fraction for 3 parts  [#permalink]

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ccooley wrote:
rajak01 wrote:
Hi,

I know 1:2 can be written as 1 over 2 and 1:2:3 can be written as 1 over 6 but my question is why can't the first ratio cannot be written as 1 over 3 using the same logic of the multipart ratios?

Just to make sure I understand the initial question, let me reword it:

So, you're saying that you have a three-part ratio, 1:2:3. For instance, the ratio of rabbits to cats to dogs at an animal shelter, is 1:2:3.

You can also talk about this same ratio in terms of fractions. 1+2+3 = a total of 6 "parts," so you can also say that 1/6 of the animals are rabbits, 2/6 are cats, and 3/6 are dogs.

Assuming that's what you're referring to, then let me answer your actual question!

How you translate a ratio into a fraction, depends on what you're actually trying to figure out. For example, suppose that the ratio of boys to girls in a classroom is 1:2.

If you want to know what fraction of the total is made up of boys, you'd do the exact same thing you did with the 3-part ratio. You'd add together 1 and 2 to get 3. Then, you'd say that 1/3 of the total students are boys, and 2/3 of the total students are girls.

But if you want to calculate the fraction b/g (boys/girls), then you do 1/2.

In summary: boys/total would equal 1/3, while boys/girls would equal 1/2.

And the reason you're confused is that you're thinking about a "part/part" fraction in the first half of your question (1:2 = 1/2), but a "part/whole" fraction in the second half (1:2:3 -> 1/6).

That makes sense. Thank you. Following your example if the class has this ratio boys:girls:nosex as 1:2:3, does this mean the fraction of boys over girls will be 1/2 and boys over nosex 1/3? And the fraction of boys over total 1/6? Re: Ratio to fraction for 3 parts   [#permalink] 26 May 2020, 19:23

# Ratio to fraction for 3 parts  