I was told there would be no additional math
June 7, 2018 4:50 PM Subscribe
I don't understand how to calculate a proportion as a ratio and nothing online is helping me. Can you explain it?
I have to calculate proportions expressed as a ratio for a biology class. For example, someone has a 65" wingspan and a 65" height-- that's 1:1. After that, I'm totally lost.
How do I calculate a ratio from something like a 73.5" wingspan and a 75" height? Is it just 73.5:75 or is there a better way to do it? It's embarrassing that I don't know how to Google this.
Please explain it like I'm someone who only has a grasp of basic arithmetic, because that's what I am! I don't need to be able to understand it, I just need a checklist of steps to follow that generate a right answer.
I have to calculate proportions expressed as a ratio for a biology class. For example, someone has a 65" wingspan and a 65" height-- that's 1:1. After that, I'm totally lost.
How do I calculate a ratio from something like a 73.5" wingspan and a 75" height? Is it just 73.5:75 or is there a better way to do it? It's embarrassing that I don't know how to Google this.
Please explain it like I'm someone who only has a grasp of basic arithmetic, because that's what I am! I don't need to be able to understand it, I just need a checklist of steps to follow that generate a right answer.
Is it just 73.5:75
Yes! Only, to simplify, if this was 100:50 then the ratio is 2:1. You simplify the ratio.
So for your example you'd divide both sides by five and get 14.7:15
Sometimes (and I do not know this especially well when you do this and when you do not) places want one side to be one. So in your example you'd have 1:1.02 (basically what you'd get if you divided both sides by 14.7).
The only trick is just making sure you have the same values on both sides in the same order as Mid says..
So you have a rectangle that is four units tall and two units wide.
The height to width ratio is 4:2 (which is the same as 2:1)
The width to height ratio is 2:4 or 1:2.
posted by jessamyn at 5:07 PM on June 7, 2018 [5 favorites]
Yes! Only, to simplify, if this was 100:50 then the ratio is 2:1. You simplify the ratio.
So for your example you'd divide both sides by five and get 14.7:15
Sometimes (and I do not know this especially well when you do this and when you do not) places want one side to be one. So in your example you'd have 1:1.02 (basically what you'd get if you divided both sides by 14.7).
The only trick is just making sure you have the same values on both sides in the same order as Mid says..
So you have a rectangle that is four units tall and two units wide.
The height to width ratio is 4:2 (which is the same as 2:1)
The width to height ratio is 2:4 or 1:2.
posted by jessamyn at 5:07 PM on June 7, 2018 [5 favorites]
A proportion and a ratio are really the same thing. It's a comparison of one quantity with another, expressed as one divided by the other. You can write it as a fraction [a/b], or as the quotient of doing the division expressed by the fraction [a รท b]. I.e., if "a" is 73.5 and "b" is 75, you can write it either as 73.5/75 or as the quotient, .98. So in your example, the wingspan is .98 (or 98%) of the height. Or 73.5/75 of the height. Same. exact. thing.
What gets confusing is, which quantity is supposed to be the divisor and which the dividend? That's where your story problem skills come in. In this case, you want to focus on the words "of" and "to." Are we looking for the proportion of a to b, or of b to a? If you want to know the proportion of the height (75) to the wingspan (73.5), you divide the height by the wingspan and get (roughly) 1.02. If it's the other way around--the proportion of the wingspan to the height--you divide the wingspan by the height. So, shorthand: in a phrase like "proportion of x to y", divide x by y.
If you have to return a fraction for an answer on a multiple-choice quiz, you'll need to take the further step (possibly) of reducing the fraction to its lowest terms.
posted by bricoleur at 7:23 PM on June 7, 2018 [5 favorites]
What gets confusing is, which quantity is supposed to be the divisor and which the dividend? That's where your story problem skills come in. In this case, you want to focus on the words "of" and "to." Are we looking for the proportion of a to b, or of b to a? If you want to know the proportion of the height (75) to the wingspan (73.5), you divide the height by the wingspan and get (roughly) 1.02. If it's the other way around--the proportion of the wingspan to the height--you divide the wingspan by the height. So, shorthand: in a phrase like "proportion of x to y", divide x by y.
If you have to return a fraction for an answer on a multiple-choice quiz, you'll need to take the further step (possibly) of reducing the fraction to its lowest terms.
posted by bricoleur at 7:23 PM on June 7, 2018 [5 favorites]
A ratio is just a fraction. A relation of one number to another. The relation stays the same so long as both terms are divided or multiplied by the same amount. So 1:2 is 2:4 is 4:8 is 50:100 etc.
You can read more about it here: at Khan Academy
posted by dis_integration at 7:24 PM on June 7, 2018 [2 favorites]
You can read more about it here: at Khan Academy
posted by dis_integration at 7:24 PM on June 7, 2018 [2 favorites]
With a ratio, try to remember that the colon sign means "to":
Wingspan to height ratio =
Wingspan:Height =
Wingspan/Height
If you have 5" wingspan and a 10" height, then the wingspan to height ratio is:
Wingspan:Height =
5:10 =
5/10 =
In its simplest form, 1:2 =
1/2 =
1 to 2 =
1 unit of wingspan = 2 units of height
So a wingspan of 20" would mean height would be 20"x2, or 40"
posted by watrlily at 8:35 PM on June 7, 2018 [1 favorite]
Wingspan to height ratio =
Wingspan:Height =
Wingspan/Height
If you have 5" wingspan and a 10" height, then the wingspan to height ratio is:
Wingspan:Height =
5:10 =
5/10 =
In its simplest form, 1:2 =
1/2 =
1 to 2 =
1 unit of wingspan = 2 units of height
So a wingspan of 20" would mean height would be 20"x2, or 40"
posted by watrlily at 8:35 PM on June 7, 2018 [1 favorite]
There is a habit that helps keeo you from getting lost in the two methods above that's called "the factor label method" but just means "keep writing down what the numbers mean so you can tell what the final number means". Like, in all the examples above each number would be follwed by a "w" if it was width or "h" if it's height, and at the end you have w:h or h:w (or w/h or h/w, if writing it as a fraction).
And if you can find an example and add the factor labels to the example, you can check that your applications come out with the same labels in the same order.
posted by clew at 8:42 PM on June 7, 2018 [3 favorites]
And if you can find an example and add the factor labels to the example, you can check that your applications come out with the same labels in the same order.
posted by clew at 8:42 PM on June 7, 2018 [3 favorites]
Is it just 73.5:75
Yep! (assuming it asks "ratio of wingspan to height". Otherwise, switch the order.) If you need to "simplify" the ratio, that's a whole separate thing. My simplified answer would be 49:50, or 1:1.020... depending on how the question was worded.
If it doesn't specify the kind of format, I would accept any of those 3 (and others) as answers, 73.5:75, 49:50, or 1:1.020...
Pro tip: If it's multiple choice, you can quickly find the correct answer by dividing the first number by the second number and find which one is the same as 73.5 divided by 75, and you don't even have to understand simplifying or rounding.
posted by Pig Tail Orchestra at 5:17 AM on June 8, 2018 [1 favorite]
Yep! (assuming it asks "ratio of wingspan to height". Otherwise, switch the order.) If you need to "simplify" the ratio, that's a whole separate thing. My simplified answer would be 49:50, or 1:1.020... depending on how the question was worded.
If it doesn't specify the kind of format, I would accept any of those 3 (and others) as answers, 73.5:75, 49:50, or 1:1.020...
Pro tip: If it's multiple choice, you can quickly find the correct answer by dividing the first number by the second number and find which one is the same as 73.5 divided by 75, and you don't even have to understand simplifying or rounding.
posted by Pig Tail Orchestra at 5:17 AM on June 8, 2018 [1 favorite]
The ratio colon : is just a division sign ÷ with the central bar left out. It means exactly the same thing, except that it usually binds tighter.
Two items with a division sign or ratio colon between them mean exactly the same thing when written as a fraction, with the item from the left of the division sign above the fraction bar, and the item from its right below.
So 3:4 means the same thing as (3 ÷ 4) means the same thing as 3/4 means the same thing as ¾ means the same thing as 0.75 means the same thing as 75/100 means the same thing as 75%.
Something with a 73.5" wingspan and a 75" height has a wingspan:height ratio of 73.5:75, which means the same thing as (73.5 ÷ 75), which means the same thing as 0.98, which means the same thing as 98%.
If you're given a wingspan and a wingspan:height ratio, and you want to calculate the height, and it's not immediately obvious to you what to do with those numbers, you can work it out with the following line of reasoning:
1. The wingspan to height ratio is defined as the result of dividing the wingspan by the height. That is:
(wingspan:height ratio) = wingspan ÷ height
2. If I multiply both sides of that equation by the (unknown) height, it will remain true (because I'm doing the same thing to both sides) and that would make the equation look like
(wingspan:height ratio) × height = (wingspan ÷ height) × height
3. After dividing the wingspan by a thing, multiplying immediately by the same thing undoes the division, so it's the same as not having done anything to the wingspan at all. So the right hand simplifies, and the equation becomes
(wingspan:height ratio) × height = wingspan
which is exactly what I'd need if I'd been given a height, and a ratio, and I needed to work out the wingspan.
4. But since what I have is the wingspan and the ratio, and what I need is the height, I need to do another transformation: divide both sides of equation (3) by the ratio.
(wingspan:height ratio) × height ÷ (wingspan:height ratio) = wingspan ÷ (wingspan:height ratio)
5. After multiplying the height and another thing together, dividing the result by the same thing undoes the multiplication, which is the same as not having done anything to the height at all. So the left hand side simplifies, and the equation becomes
height = wingspan ÷ (wingspan:height ratio)
Another result you might care to bear in mind is that if what you have is a wingspan:height ratio, and what you need is a height:wingspan ratio, and the ratios are expressed as decimals or percentages rather than as a pair of colon-separated numbers you could simply swap, then you can get the same effect as that swap if you divide 1 by the unswapped starting number.
For example, given a wingspan:height ratio of 80%:
height:wingspan = 1 ÷ wingspan:height ←(remember this relationship)
height:wingspan = 1 ÷ 80%
height:wingspan = 1 ÷ 0.80
height:wingspan = 1.25
height:wingspan = 125%
posted by flabdablet at 7:45 AM on June 8, 2018 [1 favorite]
Two items with a division sign or ratio colon between them mean exactly the same thing when written as a fraction, with the item from the left of the division sign above the fraction bar, and the item from its right below.
So 3:4 means the same thing as (3 ÷ 4) means the same thing as 3/4 means the same thing as ¾ means the same thing as 0.75 means the same thing as 75/100 means the same thing as 75%.
Something with a 73.5" wingspan and a 75" height has a wingspan:height ratio of 73.5:75, which means the same thing as (73.5 ÷ 75), which means the same thing as 0.98, which means the same thing as 98%.
If you're given a wingspan and a wingspan:height ratio, and you want to calculate the height, and it's not immediately obvious to you what to do with those numbers, you can work it out with the following line of reasoning:
1. The wingspan to height ratio is defined as the result of dividing the wingspan by the height. That is:
(wingspan:height ratio) = wingspan ÷ height
2. If I multiply both sides of that equation by the (unknown) height, it will remain true (because I'm doing the same thing to both sides) and that would make the equation look like
(wingspan:height ratio) × height = (wingspan ÷ height) × height
3. After dividing the wingspan by a thing, multiplying immediately by the same thing undoes the division, so it's the same as not having done anything to the wingspan at all. So the right hand simplifies, and the equation becomes
(wingspan:height ratio) × height = wingspan
which is exactly what I'd need if I'd been given a height, and a ratio, and I needed to work out the wingspan.
4. But since what I have is the wingspan and the ratio, and what I need is the height, I need to do another transformation: divide both sides of equation (3) by the ratio.
(wingspan:height ratio) × height ÷ (wingspan:height ratio) = wingspan ÷ (wingspan:height ratio)
5. After multiplying the height and another thing together, dividing the result by the same thing undoes the multiplication, which is the same as not having done anything to the height at all. So the left hand side simplifies, and the equation becomes
height = wingspan ÷ (wingspan:height ratio)
Another result you might care to bear in mind is that if what you have is a wingspan:height ratio, and what you need is a height:wingspan ratio, and the ratios are expressed as decimals or percentages rather than as a pair of colon-separated numbers you could simply swap, then you can get the same effect as that swap if you divide 1 by the unswapped starting number.
For example, given a wingspan:height ratio of 80%:
height:wingspan = 1 ÷ wingspan:height ←(remember this relationship)
height:wingspan = 1 ÷ 80%
height:wingspan = 1 ÷ 0.80
height:wingspan = 1.25
height:wingspan = 125%
posted by flabdablet at 7:45 AM on June 8, 2018 [1 favorite]
Ratios, proportions, and fractions are all essentially the same thing. (So are percentages, as flabdablet reminds us.)
Each comes at the same basic idea from a slightly different starting point and uses a slightly different notation. They're confusing precisely because they are so similar--yet, indeed slightly different from each other.
Video explanations like these at Khan Academy might be helpful if you're having trouble wading through the sort of "wall of text" explanations we're likely to have here at AskMeFi.
posted by flug at 8:28 PM on June 8, 2018 [1 favorite]
Each comes at the same basic idea from a slightly different starting point and uses a slightly different notation. They're confusing precisely because they are so similar--yet, indeed slightly different from each other.
Video explanations like these at Khan Academy might be helpful if you're having trouble wading through the sort of "wall of text" explanations we're likely to have here at AskMeFi.
posted by flug at 8:28 PM on June 8, 2018 [1 favorite]
So are percentages, as flabdablet reminds us.
If you're ever confused about how to deal with a percentage, it's worth knowing that the following two forms are always completely interchangeable:
anything%
(anything ÷ 100)
In other words, postfixing anything with a percentage sign % is just a shorthand way to express the idea of dividing that same thing by 100. That's all it ever is.
The reason the second form has the parentheses around it is to account for the fact that the percentage sign % binds tightly to the thing to its left; like the ratio sign : it has a higher precedence than the standard × and ÷ symbols.
posted by flabdablet at 12:58 AM on June 9, 2018 [1 favorite]
If you're ever confused about how to deal with a percentage, it's worth knowing that the following two forms are always completely interchangeable:
anything%
(anything ÷ 100)
In other words, postfixing anything with a percentage sign % is just a shorthand way to express the idea of dividing that same thing by 100. That's all it ever is.
The reason the second form has the parentheses around it is to account for the fact that the percentage sign % binds tightly to the thing to its left; like the ratio sign : it has a higher precedence than the standard × and ÷ symbols.
posted by flabdablet at 12:58 AM on June 9, 2018 [1 favorite]
Response by poster: All of these answers are helpful! I got 100% on the assignment, too.
Hypothesis: based on myself and my family, the majority of people will have a longer wingspan than height. Conclusion: welp! I was wrong, turns out my specific family is more bird than man.
posted by blnkfrnk at 6:21 PM on June 18, 2018 [2 favorites]
Hypothesis: based on myself and my family, the majority of people will have a longer wingspan than height. Conclusion: welp! I was wrong, turns out my specific family is more bird than man.
posted by blnkfrnk at 6:21 PM on June 18, 2018 [2 favorites]
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Then, divide the second number by the first. 75 divided by 73.5 = 1.020408163265306.
Then the ratio for wingspan to height is 1:1.02 (rounding). You can test this by then multiplying the wingspan (73.5) by the number to the right in the ratio (1.02), which should equal the height (75).
Caveat: I am bad at math.
posted by Mid at 5:07 PM on June 7, 2018 [2 favorites]