How do equivalent ratios work in practical terms?

[SHASHWAT PRATAP SING]

my doubt is that let's say we have a ratio 5:10 now the equivalent ratio for this would be 1:2 but what I am not able to understand is - let's say we have a situation in which it is given that the ratio of girls to boys is 5:10 which means for every 5 girls we have 10 boys but if we see the equivalent ratio for this which would be 1:2 now this means for every 1 girl we have 2 boys. 5:10=1:2 While this is mathematically equivalent to the original ratio, but how does 5 girls for 10 boys equals to 1 girl for 2 boy. so, in this situation how are both the ratios same, as the concept of equivalent ratios says? While 1:2 is mathematically equivalent to the original ratio 5:10, but how does 5 girls for 10 boys equals to 1 girl for 2 boy. I mean, if we see mathematically 5:10 is same as 1:2 but in practical terms(when we visualize them) they are different but the concept of equivalent ratios says they are equal, so how ?

 

[phinds]

I mean, if we see mathematically 5:10 is same as 1:2 but in practical terms(when we visualize them) they are different but the concept of equivalent ratios says they are equal, so how ?

No, they are not. I am puzzled as to why you think they are. Just because the numerator and denominator are different, that is irrelevant to the ratio.

Suppose the statement had been "there are 50% few girls than boys". That implies BOTH of the ratios you listed. Would you complain that 50% of 10 boys is different than 50% of 2 boys? They absolute numbers are different but so what? It's 50%.

 

[SHASHWAT PRATAP SING]

No, they are not. I am puzzled as to why you think they are. Just because the numerator and denominator are different, that is irrelevant to the ratio.

please, help me I am not able to understand this concept .

 

[phinds]

please, help me I am not able to understand this concept .

I still don't understand what your problem is. A ratio is a ratio.

 

[PeroK]

my doubt is that let's say we have a ratio 5:10 now the equivalent ratio for this would be 1:2 but what I am not able to understand is - let's say we have a situation in which it is given that the ratio of girls to boys is 5:10 which means for every 5 girls we have 10 boys but if we see the equivalent ratio for this which would be 1:2 now this means for every 1 girl we have 2 boys. 5:10=1:2 While this is mathematically equivalent to the original ratio, but how does 5 girls for 10 boys equals to 1 girl for 2 boy. so, in this situation how are both the ratios same, as the concept of equivalent ratios says? While 1:2 is mathematically equivalent to the original ratio 5:10, but how does 5 girls for 10 boys equals to 1 girl for 2 boy. I mean, if we see mathematically 5:10 is same as 1:2 but in practical terms(when we visualize them) they are different but the concept of equivalent ratios says they are equal, so how ?

If there are 200 girls and 400 boys at a school and someone argues that the ratio of girls to boys is 1:2 and someone else argues that the ratio is 5:10, who is correct? Or, are they both wrong?

 

[SHASHWAT PRATAP SING]

In a situation suppose the ratio comes to be 5:10 which can be simplified to 1:2. so,5:10=1:2 I know that mathematically they are equal but when we visualize them they are (according to me) kinda different. Like suppose our situation was that we have to find the ratio of girls to boys which comes out to be 5:10, now this ratio tells us that for every 5 girls we have 10 boys, which I understand but when we see the simplified form of this ratio which is 1:2 this ratio tells us that for every 1 girl we have 2 boys, so how 5 girls for 10 boys can be considered the same as 1 girl for 2 boys, despite the mathematical equivalence. Please help me .
So, despite the differences in practical interpretation why are the ratios equal.

 

[PeroK]

So, despite the differences in practical interpretation why are the ratios equal.

Which one is right, practically, in a given situation? When is 1:2 correct and when is 5:10 correct? Not mathematically, but practically.

 

[SHASHWAT PRATAP SING]

Which one is right, practically, in a given situation? When is 1:2 correct and when is 5:10 correct? Not mathematically, but practically.

well both are mathematically same so both are right but both have different practical interpretation.

 

[PeroK]

well both are mathematically same so both are right but both have different practical interpretation.

When would you use one and when would you use the other? Give a practical example.

 

[SHASHWAT PRATAP SING]

When would you use one and when would you use the other? Give a practical example.

Imagine you have a group of 5 girls and 10 boys. When you express this group as a ratio, you write it as 5:10. This ratio tells you that for every 5 girls, there are 10 boys.

Now, let's simplify this ratio. We can divide both sides by 5, which gives us 1 girl for every 2 boys. So, the simplified ratio is 1:2.
So,

• The ratio 5:10 tells us that there are 5 girls for every 10 boys.
• The ratio 1:2 tells us that there is 1 girl for every 2 boys.

I know 5:10=1:2. but I mean, if we see mathematically 5:10 is same as 1:2 but in practical terms(when we visualize them) they are different as how does 5 girls for 10 boys can be considered the same as 1 girl for 2 boys, despite the mathematical equivalence.

 

[PeroK]

Imagine you have a group of 5 girls and 10 boys. When you express this group as a ratio, you write it as 5:10. This ratio tells you that for every 5 girls, there are 10 boys.

You are saying there are precisely 5 girls and precisely 10 boys. That's not what a ratio is telling you. A ratio isn't telling you how many people there are.

In that way a ratio is like a percentage. You can say something like 10% of people are smokers. That tells you something, but it doesn't tell you how many people there are or how many smokers there are.

A percentage, like a ratio, is sometimes a good way to express a measurement about data, by not specifying all the details. You could even call a ratio a statistic.

https://en.wikipedia.org/wiki/Statistics

 

[DrClaude]

I know 5:10=1:2. but I mean, if we see mathematically 5:10 is same as 1:2 but in practical terms(when we visualize them) they are different as how does 5 girls for 10 boys can be considered the same as 1 girl for 2 boys, despite the mathematical equivalence.

Put all 15 people in a room, spread out the girls in the room, then take two boys, group them with a girl and repeat. You will have 5 groups with 1 girl and 2 boys. So a 5:10 girl-to-boy ratio is the same as a 1:2 girl-to-boy ratio.

 

[SHASHWAT PRATAP SING]

Put all 15 people in a room, spread out the girls in the room, then take two boys, group them with a girl and repeat. You will have 5 groups with 1 girl and 2 boys. So a 5:10 girl-to-boy ratio is the same as a 1:2 girl-to-boy ratio.

what I have understood is that- in this situation 5:10 ratio represents the number of girls to the number of boys in the original scale( without any simplification) and when we take this ratio in simplified form which is 1:2 we can understand this as this ratio 1:2 represents this situation in simplified form, this ratio is representing the situation that would be if it was in simplified form. So by this understanding we can now say that the ratio 5:10 is same as 1:2 but just one has to keep in mind that 1:2 represents the situation in simplified form.

Thus, this expression 5:10=1:2 says that in the original scale If we compare the two quantities then our ratio would be 5:10 and if we compare the two quantities in the simplified scale then the same comparison which was in the original scale 5:10 would now be 1:2 in the simplified scale.

Am I correct ?Have I understood this concept correctly ?

 

[Steve4Physics]

what I have understood is that- in this situation 5:10 ratio represents the number of girls to the number of boys in the original scale( without any simplification) and when we take this ratio in simplified form which is 1:2 we can understand this as this ratio 1:2 represents this situation in simplified form, this ratio is representing the situation that would be if it was in simplified form. So by this understanding we can now say that the ratio 5:10 is same as 1:2 but just one has to keep in mind that 1:2 represents the situation in simplified form.
Thus, this expression 5:10=1:2 says that in the original scale If we compare the two quantities then our ratio would be 5:10 and if we compare the two quantities in the simplified scale then the same comparison which was in the original scale 5:10 would now be 1:2 in the simplified scale. Am I correct ?Have I understood this concept correctly ?

That's one way to look at it but doesn't give the full picture. I'd say this...

A ratio is not meant to express all the information. It is only for comparison.

For example, you are asked to mix cordial and water in the ratio 2:10. That means 2 parts of cordial to 10 parts of water. This is no dfferent to mixing 1 part of cordial to 5 parts of water.

You can use this to help you mix a batch of 5 litres or 700 litres - the ratio (cordial:water) is the same in all cases.

G:B = 5:10 does not necessarily mean there are 5 girls and 10 boys (though there might be). It only tells you that for every 5 girls there are 10 boys.

In term of fractions:
$\frac 5{5+10} = \frac 13$ are girls
$\frac {10}{5+10} = \frac 23$ are boys

It's no different from saying that for every girl there are 2 boys, G:B = 1:2.
$\frac 1{1+2} = \frac 13$ are girls
$\frac 2{1+2} = \frac 23$ are boys

 

[SHASHWAT PRATAP SING]

That's one way to look at it but doesn't give the full picture. I'd say this...

A ratio is not meant to express all the information. It is only for comparison.

For example, you are asked to mix cordial and water in the ratio 2:10. That means 2 parts of cordial to 10 parts of water. This is no dfferent to mixing 1 part of cordial to 5 parts of water.

You can use this to help you mix a batch of 5 litres or 700 litres - the ratio (cordial:water) is the same in all cases.

G:B = 5:10 does not necessarily mean there are 5 girls and 10 boys (though there might be). It only tells you that for every 5 girls there are 10 boys.

In term of fractions:
$\frac 5{5+10} = \frac 13$ are girls
$\frac {10}{5+10} = \frac 23$ are boys

It's no different from saying that for every girl there are 2 boys, G:B = 1:2.
$\frac 1{1+2} = \frac 13$ are girls
$\frac 2{1+2} = \frac 23$ are boys

I have understood what you are saying. But, you didn't answered - Am I correct ? Have I understood this concept correctly ?
Please reply.

 

[phinds]

I have understood what you are saying. But, you didn't answered - Am I correct ? Have I understood this concept correctly ?
Please reply.

I believe he DID answer your question. Your entire confusion seems to be because you are unable to accept the simple statement that:

G:B = 5:10 does not necessarily mean there are 5 girls and 10 boys (though there might be). It only tells you that for every 5 girls there are 10 boys.

or for every 15 girls there are 30 boys or for every 1,000 girls there are 2,000 boys. ETC ETC ETC

 

[Steve4Physics]

I have understood what you are saying. But, you didn't answered - Am I correct ? Have I understood this concept correctly ?
Please reply.

In my opinion, from what you said, you have at least partly understood the concept. But I can't tell if you have fully understood.

Let me ask some questions to help check your understanding!

1. You are told that the ratio of boys to girls at a school is 400:600. No other information is given. True or false:
a) There are definitely 1000 pupils at the school.
b) There might be 1000 pupils at the school.
c) There might be more than 1000 pupils at the school.
d) There might be less than 1000 pupils at the school.

2. You are asked to mix a drink with cordial and water in the ratio (cordial:water) 2:10.
a) How much water is needed if you use 3.2 litres of cordial?
b) How much cordial is needed if you use 35 litres of water?
c) If you need a make total volume of 72litres, how much cordial and how much water do you use?

 

[SHASHWAT PRATAP SING]

1. You are told that the ratio of boys to girls at a school is 400:600. No other information is given. True or false:
a) There are definitely 1000 pupils at the school.
b) There might be 1000 pupils at the school.
c) There might be more than 1000 pupils at the school.
d) There might be less than 1000 pupils at the school.

Q1,ans a) False
ans b) True
ans c) True
ans d) True

2. You are asked to mix a drink with cordial and water in the ratio (cordial:water) 2:10.
a) How much water is needed if you use 3.2 litres of cordial?
b) How much cordial is needed if you use 35 litres of water?
c) If you need a make total volume of 72litres, how much cordial and how much water do you use?

Q2, Ans a) 16 litres
Ans b) 7 litre
Ans c) cordial - 12 litre and water - 60 litre
So, what do you say have I understood the concept correctly ?

 

[Steve4Physics]

Q1,ans a) False
ans b) True
ans c) True
ans d) True

All correct!

Q2, Ans a) 16 litres
Ans b) 7 litre
Ans c) cordial - 12 litre and water - 60 litre

All correct.

So, what do you say have I understood the concept correctly ?

Yes (as far as a limited test can tell). Well done!

 

[SHASHWAT PRATAP SING]

All correct!


All correct.


Yes (as far as a limited test can tell). Well done!

Thanks Steve4Physics, My doubt is clear .

 

[WWGD]

It's possible such ratio assumes number of boys, girls assumes is a multiple of 5, 10 respectively. Do you have the definition of such ratio from your book, notes?