How to work out ratios - calculating ratios made simple
94Ratio: a tricky topic in mathematics
If you ever did ratio and proportion in maths classes at school, you may have found it one of the harder topics to grasp. This hub will try and demystify the subject, with the help of easy-to-understand examples. And if you want to ask any questions or make suggestions on how to improve/add to the information I've given, you're more than welcome to do so via the comments section at the bottom of the page!
Equivalent ratio or splitting ratio?
Sometimes it’s hard to work out what you need to do when confronted with a problem involving ratio. Hopefully the following two examples will help clarify.
Example 1
To make Elephant Grey paint, you need
to mix Snow White and Ebony Black together in a ratio of 3:2. How much
Snow White will you need if you’re using 4 litres of Ebony Black?
Example 2
To make Elephant Grey paint, you need to mix Snow White and Ebony Black together in a ratio of 3:2. How much Snow White will you need if you want to make 10 litres of Elephant Grey?
Example 1 is an “equivalent ratio” question, where each quantity is multiplied by the same number to “bulk out” the quantities. The 2 (the number of parts Ebony Black) is multiplied by 2 to make 4 litres, which means that the 3 (the number of parts Snow White) also has to be multiplied by 2 to make 6 litres. You can draw it like the picture to the right, in a sort of flow chart:
In Example 2, you have a different sort of problem. You only know how much of the mixed finished product you are going to end up with, not how much of either colour. You therefore need to “split” the finished product into 3 parts of Snow White and 2 parts of Ebony Black (hence the term “splitting ratio” to describe this sort of problem).
You have 3 parts of Snow White and 2 parts of Ebony Black, which gives a total of 5 parts (3 + 2 = 5).
Ten litres of Elephant Grey divided by 5 gives 2. Therefore each part of paint is 2 litres.
For US readers
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Three parts of Snow White = 3 x 2 = 6 litres
Two parts of Ebony Black = 2 x 2 = 4 litres.
For when you have to work back the other way
Sometimes you're just given some raw numbers and have to work out the ratio from that. For example, suppose you work in a company with a total of 450 employees. The number of men is 270. What is the ratio of women to men?
Firstly you find the number of women, which is a straightforward question of subtraction, i.e. 450 - 270 = 180
The ratio of women to men can be written as 180:270. (Side note: if you were talking about the ratio of men to women, you'd write it the other way round, i.e. 270:180.)
The ratio 180:270 can be cancelled down to a simpler form. This is EXACTLY like cancelling fractions. So in this instance it's possible to cancel, by dividing by ten and then by 9, i.e.
180:270 = 18:27 = 2:3
Thus the ratio of women to men in the company is 2:3 in its simplest form.
© Empress Felicity December 2009
PS: Following on from this, I've now done a second hub entitled How to calculate ratio part II, with some worked examples and problems to solve.
PPS: Do you want a platform to write whatever you want, whenever you want and even (with a bit of time and work) earn some money doing it? Then why not join Hub Pages yourself? Sign up here. You need to be over 18.
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Thank you! And, er, Merry Christmas.
Oh yeah. You too. xD.
Hey can you help, please?
there are sweets in a bag.
-12 are toffees
-18 are mints
write down the ratio of mints to toffee in its simplest.
what that be #
18-12 for the frist section then 18/6 then 12/6 which is 3:2? im confused is this right?
Hi Matt, you are right about the first stage - the ratio of mints to toffee would be 18:12. But it went a bit wrong after that - there's no way that cancelling (aka reducing) 18:12 would give 12:6. If you divide both the 18 and the 12 by 3, you would get 6:4, which then cancels down to 3:2. Or you could just go via a more direct route and divide both the 18 and the 12 by 6 - this would get you straight to 3:2. Hope that helps.
Ok, i had a ratio at work to figure out. can you help?
i need to blend 8kg of bread crumbs and 1.6kg of pasley total weight 9.6kg. what is the ratio of that. (how do u work that out)
The ratio for pasley is to high to blend with breadcrumbs. so i need to make the ratio of 8:1 so how much more bread crumbs do i need to bring it to that ratio. how to work that out on the calculator?
Hello Ian. To find the ratio of parsley to breadcrumbs on a calculator, just divide 8 by 1.6. (It should come to 5, which means you have a ratio of 5:1.) If you don't have a calculator, you can still do it, by playing around with the numbers until it's possible to cancel them.
So, starting with 8:1.6
Multiplying both sides by ten gives 80:16
Then you can start cancelling. For example, you can divide both sides by 8, which gives
10:2
And then by 2, giving 5:1
There are other ways to cancel down to get this answer - for example, you can just keep dividing the 80 and the 16 by 2, which will get you there eventually!
For the last bit, just multiply the weight of parsley (1.6 kg, which is the "1" in the 8:1 ratio) by 8.
Cheers.
Oh i get it know. some playing around with the calculator. Thanks.
simple maths Really. just can be confusing get muddled up with numbers
Dani and Kylie have a 5:2 ration in a business worth $1,500,000. find the value of danis share in the business?
help
Hi Bonnie, this is a classic "splitting ratio" type of question. Dani has five parts of the business and Kylie has two, making seven parts in all. Divide the $1.5M by 7 to find out what each part is worth, and go from there.
in a office the ratio of staff who supported footy to those who supported soccer was 5:2 If 21 staff gave there opinions who many supported soccer? i know the answer but dont know how to work it out
Hello, "??" (sure that's not your real name LOL). I won't tell you the answer, but I'll give you a clue: it's a "splitting ratio" type of problem, i.e. the 21 staff covers both the 5 parts who supported football and the 2 parts who supported soccer. In other words, there are 7 parts altogether, covering 21 people.
Very useful information!
A 720 ml container holds a mixture of red, yellow, and white paint in a 5 : 3 : 12 ratio. How much more red paint than yellow is present in the mixture?
Hi Rea, thanks for your question. You add the 5, the 3 and the 12 to find out how many "parts" of paint there are overall (20 parts), and then work out what amount of paint each part corresponds to (hint: 20 parts - 720 ml). From there on, you work out the volume of red paint and the volume of yellow paint. Then subtract one from the other to get your answer. Hope that helps.
Hi im abit stuck on a paper and have been going over and over ratio's and still cant work them out can you please help me
your the responsibilitie as a school caretaker include keeping the school free of graffiti. You have a special paint that you can put on buildings of fences that stops other paint sticking to it. This formula is 9 litres of repellent to 150 litres of paint.
What is the ratio of repellent to paint?
i keep coming up with 3:50 cause you cant take 9 into 150 or can you?
how they can best achieve a high rate lambing rate from their ewes (female sheep). you have advised your client that a ratio of 1:40 rams (male sheep) to ewes is necessary. your client has 3360 ewes.
how much rams are needed for this number of sheep?
Hi Christine and Ellen, thanks for reading this hub!
Christine, you're absolutely right - if you want to use whole numbers in your answer, then 3:50 is as far as you can go, because you can't divide the numbers any further (3 doesn't go into 50 without leaving a remainder). Although having said that, it's also possible to use decimals in a ratio - you can also express this particular ratio as 1:16.67 (to two decimal places).
As this hub has generated so many questions, what I think I'll do is write a second hub with some more worked examples and a few problems that people can solve! (Followed shortly by a third hub with answers to the problems in the second.) Watch this space - give it 24 hours.
Vreni walked along the road 3km/h and along the footpath at 2.5km/h. How long in hours and minutes did Vreni take to walk the 2o kilometres??
-Help please.
Hi there, Silentsss. Your question isn't about ratio but I'll have a go at answering it anyway - however, you'll need to tell me the length of the bit of road she walked on and the length of the footpath. (I know the two together add up to 20 km, but that alone isn't enough information for me.)
im completly confused can u help me?????
Hi Jock, tell me what you're confused about and I'll do my best LOL.
glad to find this. These ratio problems are hell.
i still don't get ratio, my maths teacher isn't very good at explaining things so i get really confused!!
Josie makes fruit punch by mixing fruit juice and lemonade in the ratio 3:4. She needs to make 56 litres of punch.
How much of each ingredient does she need?
and
During the party Josie decides to make some more. She has 9 litres of fruit juice left and plenty of lemonade. How much extra punch can she make?
help!
In 2009 the wimbledon ladies singles champion won £850,000. The ratio for 2008 to 2009 is 15:17. Work out the champion's prize money in 2008.......
three boys shared £48 in the ratio 5:4:3
Daniel received the smallest amount
how much did Daniel recieve?
@Amrita
"Josie makes fruit punch by mixing fruit juice and lemonade in the ratio 3:4. She needs to make 56 litres of punch. How much of each ingredient does she need?"
There are 3 parts of fruit juice and 4 parts lemonade, making 7 parts. You know that the 7 parts corresponds to 56 litres, so what does one part correspond to? Once you know that, you can multiply this out to find out the actual amount of each ingredient.
7 parts = 56 litres, therefore 1 part = 8 litres (56 divided by 7).
Amount of fruit juice = 3 x 8 = 24 litres
Amount of lemonade = 4 x 8 = 32 litres.
"During the party Josie decides to make some more. She has 9 litres of fruit juice left and plenty of lemonade. How much extra punch can she make?"
9 litres = 3 parts. Therefore 1 part = 3 litres.
Because there would be 4 parts of lemonade, the amount of lemonade she'd need would be 3 x 4 = 12 litres.
@ Kate
"In 2009 the wimbledon ladies singles champion won £850,000. The ratio for 2008 to 2009 is 15:17. Work out the champion's prize money in 2008."
Rephrase the question by saying "If £850,000 = 17 parts, then what does 15 parts correspond to?"
Then work out what one part is worth, and multiply by 15.
One part = £850,000 divided by 17, which is £50,000.
15 parts = £50,000 x 15 = £750,000. So that's what the champion won in 2008.
@ Susan
"three boys shared £48 in the ratio 5:4:3. Daniel received the smallest amount. how much did Daniel recieve?"
Again, this is another one where you add up all the parts and find out what one part is worth. 5+4+3 = 12 parts. One part is therefore 48 divided by 12, i.e. £4. Daniel gets three parts, so he gets £4 x 3 = £12.
Anyone else wants to ask a question, I STRONGLY recommend you try the problems in my follow-up hub (link at the bottom of this actual hub, above the comments section). Hopefully by then you'll be a lot more comfortable with this subject and won't need my help any more!
Hi,
I have some red balls and some blue balls in a bag with a ratio of 4:7.
I add 10 more red balls and end up with a ratio of 6:7.
How many blue balls do I have?
Many thanks.
Thank you so much for your shedding light on my knowledge in this arena. just going through it was truly an inspiration. God bless you. i wouldnt mimind you send me some of your info on other subject area OF MATHEMATICS.richard_preacher@yahoo.com
can u help
The ratio of men to women on a train was 5:8. there were 200 men, how many women on the train?
Hi, can you help,
I have my GCSE's (maths) coming up in about a week and a half and was wondering if you could put or put a link for a easy-hard set of questions to do with ratios please.
thanksss =]
@Andy: "I have some red balls and some blue balls in a bag with a ratio of 4:7. I add 10 more red balls and end up with a ratio of 6:7. How many blue balls do I have?"
You might be forgiven for thinking that this one involves algebra, but actually it doesn't.
The ten extra red balls that you add correspond to two "parts" (since 6 - 4 = 2). Therefore one part = 5.
If you have 4 parts red balls and 7 parts blue balls to begin with, then you have 20 red balls and 35 blue balls. (4 x 5 = 20, and 7 x 5 = 35).
@Louie: "The ratio of men to women on a train was 5:8. there were 200 men, how many women on the train?"
There are 5 parts men and 8 parts women. 5 parts = 200, therefore 1 part = 200/5 = 40. 8 parts = 40 x 8 = 320. so there are 320 women on the train.
@Vanita
"What is the approximate ratio to the number of telephones in india to the number of telephones in the uk? Telephones in the uk 29.20 million; Telephones in uk [you mean India?] 8.44 million.
There are 5 possible answers:
a) 1:5
b) 2:5
c) 2:7
d) 4:9
e) 1:2"
You need to round off the 29.2 and the 8.44 to something a bit more easy to work with. Say, 30 million and 8 million.
Approximate ratio of phones in India to phones in the UK is therefore
8 million : 30 million
or just 8 : 30, which cancels down to 4 : 15. Out of the above options, I'd say the nearest one is 2 : 7 (since if you double both the 2 and the 7 you get 4 : 14, which isn't too far off).
@Tom:
"Hi, can you help,
I have my GCSE's (maths) coming up in about a week and a half and was wondering if you could put or put a link for a easy-hard set of questions to do with ratios please. thanksss =]"
Go to my profile page (just click the name "Empress Felicity" anywhere it appears as a link), and you'll find links to all my maths hubs, including a few hubs that give you some ratio and scale problems to try. I've also given answers in separate hubs. I'd also recommend having a look at BBC Bitesize - here's the URL of its maths section below:
hi,thanks for the ratio info. I had an exam all about it
and guess what?
I passed! thanks, i couldn't have done it without u
Tania Tanisha
A model boat is made to a scale of 1:20 (1 to 20). This scale can be applied to any units, so 1mm measured on the model is 20mm on the actual boat, 1cm measured on the model is 20cm on the actual boat, and so on.
A)If the 1:20 model boat is 15cm wide, how wide is the actual boat?
plz can u help me wiv it thnks........!
Hey, lesha i think i knw the answer....
A)1cm on the model = 20cm on the boat, so:
15cm × 20 = 300cm.
15cm on the model = 300cm (3m) on the boat!
HOPE the answers right...Good luck wiv ur maths work...
"Thanks travie".......really usefull information u got their....lol! See u at school bye take care.....
Hi
Can you please help me with this problem..
Two ingots are melted together in a furnace - the first one weighing 12 kg and containing 64% iron while the second weighs 9 kg and contains 99% iron. What percentage of iron is present in the resultant large ingot?
Hi to everybody who's commented since I last came by here... it's getting quite busy LOL. Congratulations to anyone who's passed their exams. Varsha, you posted your iron ingot question to another one of my hubs so I've answered it there:
if a salad contains 320 grams and withing that salad is 4:3:1 how much amount of lettuce is there?
How do I do 1/4:1/3?
@ace: "if a salad contains 320 grams and within that salad is 4:3:1 how much amount of lettuce is there?"
I think there's a bit of information missing from this - what does the lettuce correspond to: the 4, the 3 or the 1?
@Daniel "How do I do 1/4:1/3?"
You're aiming to multiply the fractions out so that you end up with whole numbers. As long as you remember that you have to multiply each by the same number every time (to keep them balanced), then you should be OK. Multiply both sides by 3, which gives
3 x 1/4 : 3/3
= 3/4: 1
Then multiply both sides by 4, which gives
4 x 3/4 : (1 x 4)
= 3 : 4
Hi Felicity - keep up the good work..
Ratio of HDL/LDL cholesterol. I know I have to divide LDL(2.8) by HDL(1.3) = 2.15... but how do I turn this into a ratio?
Chelle: "Ratio of HDL/LDL cholesterol. I know I have to divide LDL(2.8) by HDL(1.3) = 2.15... but how do I turn this into a ratio?"
Hi Chelle, you could just say "the ratio of LDL to HDL is 2.8 : 1.3" and leave it at that.
But if you want to end up saying "the ratio of LDL to HDL is y : 1", then you have to divide both the 2.8 and the 1.3 by the smaller of the two numbers, i.e. 1.3.
2.8 divided by 1.3 gives you approx. 2.15
1.3 divided by 1.3 gives you (of course) 1
So you get a ratio of 2.15 : 1
If you ever did fractions at school you might remember about cancelling them - you had to cancel by the same amount top and bottom, to ensure that the fraction still represented the same quantity.
This type of problem is exactly the same thing, just written in a different way.
i need some help ...
how do i cancel down a ratio with a decimal eg. 1.26:14 ?
@Daisy: How do i cancel down a ratio with a decimal e.g. 1.26:14 ?
The way I did it was to get rid of the decimal point first (by multiplying both "sides" of the ratio by 100) and then cancel down. So
1.26 : 14 becomes
126 : 1400
Dividing both sides by 2 gives
63 : 700
Dividing by 7 gives
9 : 100
If you wanted to end up with a ratio 1 : x, you would need to divide both sides by 1.26, giving
1 : 11.1111111 recurring
Hi, hope you can help
3 men could repaint a house in 4 days.
How long would (a.) 1 man take (b.) 6 men take
Hi Danio
Your problem is an example of inverse (or indirect) proportion rather than ratios. I will write another hub specifically to talk about this kind of problem, and use your question as one of the examples. Watch this space!
In playing a particular card game, Sharon has won 37% of the total hands played. She has won a total of 222 games. How many total games did she play?
complete the ratio 1:13,4: idont get it
Hi EmpressFelicity,
My daughter had her 'functional skills' maths GCSE today, you have absolutely no idea of how your easy to follow guide as helped her to revise (and taught me a thing or two I might add) She has also been wandering around your other maths hubs which she has described as "cool and easy to follow" Next year she has another GCSE maths exam and she has said your hubs are the best revision guide. You have gained one new follower and two new fans!
@Chris: "In playing a particular card game, Sharon has won 37% of the total hands played. She has won a total of 222 games. How many total games did she play?"
You will be OK with this type of problem once you realise that if Sharon won 37% of the hands, then her opponent must have won 63% (37% + 63% = 100%).
Therefore
37 : 63
=
222 : ?
Hopefully this will look familiar - it's very similar to the "equivalent ratio" example I gave at the beginning of the hub, using the two shades of paint.
Finding out how many times 37 goes into 222 will tell you what you have to multiply the 37 and the 63 by to get the 222 and the "?"
As luck would have it, 37 goes into 222 exactly 6 times. Therefore the number of games won by Sharon's opponent is 63 x 6 = 378
@Hollie: thank you for your comment - v. glad to know my maths hubs are a help. I think I would like to find out more about GCSE functional maths, as I didn't know it existed!
Ok, he won't let me!! Right, What is an equivalent ratio to 18:3 I'm so confused, I hate MyMath.com !!!! Stupid online homework!!!... Help??
@Ella: "Ok, he won't let me!! Right, What is an equivalent ratio to 18:3 I'm so confused, I hate MyMath.com !!!! Stupid online homework!!!... Help??"
Hi Ella, you sound like someone who's at the end of their tether lol. I won't do your actual homework question, but I'll give you another example so you'll be able to apply the same technique.
Suppose you want to find an equivalent ratio to
24 : 8
Basically, you get equivalent ratios by dividing (or multiplying) both "sides" of the ratio by the same number.
So you could divide the 24 and the 8 by 8 to get
3 : 1
Or you could divide them both by 4 to get
6 : 2
Or you could multiply them by - say - 2, to get
48 : 16
So 3 : 1, 6 : 2 and 48 : 16 are all equivalent ratios to 24 : 8.
There are many more equivalent ratios you could generate, so this is a very open-ended question.
To everyone else who's asked questions over the last few months, sorry I haven't replied. I would suggest to anyone reading this hub for the first time who's tempted to ask me a question, that they try the questions in How To Work Out Ratio Part II (there's a link to it at the end of the hub, above the comments section). There are answers to those questions in third hub, which I've linked to from there (no cheating!).
Hi All,
I'm not sure if this is a % or Ratio question but i hope someone can help me work it out please,
I have 2 part bags of Animal Feed that i have mixed together and this has changed the amount of calcium in the feed and i need to work out how much i need to suplement the mix to bring it back to 4.5%.
one bag is 1/3 full and has a cacium content of 1.3%, I have mixed this with a bag of feed 3/4 full with a calcium content of 4.5%, my question is what will the total calcium content be of the end mix?
@Bigcityjps: your animal feed question is quite a hard one. I *think* I’ve got it right lol. I think it’s more of a fractions + ratio question than a percentages + ratio question.
You need to work out the ratio of the two fractions (1/3 and 3/4). To do this, find the lowest common denominator, which is 12.
1/3 becomes 4/12, and 3/4 becomes 9/12
Therefore the ratio of volumes in the two bags is 4/12 : 9/12. You can get rid of the 12s, to get 4 : 9.
Also, the total number of “parts” is 4 + 9 = 13
Four parts contain 1.3 % calcium and 9 parts contain 4.5 % calcium
The “average percentage” is [(1.3 x 4) + (4.5 x 9)]/13
Which comes to 3.5 %, to one decimal place.
Some of EmpressFelicity's other maths hubs
- How to work out ratios - calculating ratios made simple
A quick "how-to" guide on solving problems involving ratios. - 2 years ago
- How to calculate ratio part II: some worked examples and problems to solve
Some worked examples of problems involving ratio and proportion, followed by questions for you to try yourself - 21 months ago
- Million billion trillion - making sense of large numbers
Some hints and tricks on dealing with large numbers, including calculations involving them! - 2 years ago
- Working out percentages - a basic guide, including some simple shortcuts
A quick guide to working out percentages, including some handy shortcuts - 2 years ago
- How to calculate ratio part IV: scale drawings and maps
A guide to solving ratio and proportion problems involving scale. Includes some questions for you to try. - 21 months ago
- How to do long multiplication
A description of three methods used in long multiplication, with worked examples - 2 years ago
William R. Wilson 2 years ago
Nice useful information!