Mathematics Practice for Nursing and Midwifery Ratio Percentage. 3:2 means that for every 3 items of the first type we have 2 items of the second.

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1 Study Advice Service Student Support Services Author: Lynn Ireland, revised by Dave Longstaff Mathematics Practice for Nursing and Midwifery Ratio Percentage Ratio Ratio describes the relationship between two quantities. Here we have grey squares and white squares. We can say that the ratio of grey squares to white squares is to. This is usually written : where the colon replaces the to. : means that for every items of the first type we have items of the second. Similarly the ratio of white squares to grey squares is :. In this diagram, we have 6 grey squares and 8 white squares. The ratio of grey squares to white squares is 6:8. However, as can be seen from the diagram, in each row we have 4 grey squares for each white squares. This means that a ratio of 6:8 is the same as a ratio of 4:. We have cancelled down the ratio by dividing both sides by a common factor (in this case 4). Looking at the ratio 4:, we can see that 4 and have a common factor of. This means that the ratio can be cancelled down further (as we did with fractions in a separate leaflet). Tel: Web: studyadvice@hull.ac.uk

2 So for every 6 grey we have 8 white becomes: The ratio of grey to white is 6:8 This is the same as 4: Which is the same as :. So the ratio of grey to white, is :. Using Ratios Examples. A chocolate cake recipe requires the ratio of cocoa to flour to be :. You have measured out ounces of cocoa. How much flour do you need? Here part of cocoa is ounces. We need parts of flour. So we need to measure out = 6 6 ounces of flour.. Solution X is made from the contents of bottles A and B at a ratio of :. We have already measured out 600ml of A. How many mls of B are required to make up X? : means that for every parts of A we need parts of B. We have 600ml of A. This is the same as parts of 00ml each. To make up the solution we need parts of B. So we need x 00ml = 400ml. Ratios can also be linked to fractions. Examples. The ratio of drug A to water in a solution is :4. This means that for every part of A we need four parts of water. Alternatively, it means that for every parts of the solution, is A and 4 are water. So, of the solution is A.. The ratio of A to B in a solution is :4. This means that for every parts of A there are 4 parts of B. It also means that out of every 7 parts, are A and 4 are B. So, 7 of the solution is A and 74 is B.

3 Note Some drugs may be labelled by ratios of milligrams to millilitres; in these situations the units are not the same on both sides. Always check labels carefully. Also 0mg per ml may be written 0mg/ml. Exercise. For the following diagrams, state i) the ratio of grey to white; ii) the ratio of white to grey: a) b) c) d) If possible cancel the ratios down to their simplest form.. Draw diagrams to represent the following ratios: a) : b) : c) 6:7. Write the following ratios in their simplest forms a) :8 b) : c) 8:7 4. The ratio on ward X of male patients to female patients is :. a) If there are 6 male patients, how many female patients are there? b) If there are 0 female patients, how many male patients are there?. Medication Q is made up of solutions A, B and C. To make mg of the medication you need 0mls of A 0mls of B mls of C a) What is the ratio of: i) A to B? ii) B to C? iii) C to A? b) If you needed to produce mg of Q how many mls of A, B and C would you need? c) There are 40mls of A left. i) What is the maximum dosage of Q that you can produce? ii) What quantities of B and C are needed to produce this dose? 6. For the following ratios of A:B, state what fraction of the solution is A and what fraction of the solution is B. Cancel down where possible. a) :6 b) :8 c): d) :

4 Percentage Per cent literally means per hundred, so percentage is concerned with parts of a hundred. The symbol % is used to denote percentages. Some commonly used percentages are: % of something means the whole amount. (Literally per ) % of something means that you are looking at half of it, as is half of. 0% of something means that you are looking at a tenth of it as 0 is a tenth of. We can work out percentages in many different ways. The best method to use is the one that you find easiest. Two of the methods are detailed below. Method - Use Fractions As percentages are closely linked to fractions, we can use this fact to help with our calculations. We know that % means out of a hundred, so we can write this as in the same way as we know that out of can be written as. The following table shows the fraction form of some common percentages: Percentage Fraction Simplified Fraction % % % 0% 0 % % You may wish to perform the cancelling down yourself to check the final column. The general procedure for converting a percentage (say %) into a fraction is: Write the percentage as a fraction of i.e. Cancel the fraction down to its lowest terms. In this case we can divide top and bottom by the common factor,. When the fraction is in its lowest terms, the job is done. %= 0 4

5 Cancelling the fraction down means that any subsequent calculation we perform uses the smallest possible numbers and is thus easier to work out. When we have converted our percentage to a fraction it is quite simple to use. Example Find 0% of. 0% is the same as 0 (from the table). So 0% of = 0 as we first multiply by the numerator. 0 0 = as and 0 have a common factor of 0 Example Find 0% of. 0%= 0 0 0% of = As 7 and 0 have a common factor of, we can cancel the fraction down 7 0 This is an improper fraction, so we convert it into a mixed fraction. 4 =7 7 Method - Use Decimals As the number is used to represent a whole, we can also use it to represent %. We know that % is half of %, so % of must be half of, which as a decimal is 0.. The following table shows the decimal form of some common percentages: Percentage Decimal % % 0. % 0. 0% 0. % 0.0 % 0.0 The general procedure for converting a percentage (say %) into a decimal is: Take the numerical value of the percentage, in this case, and divide it by. So % = 0.. That s all there is to it.

6 Example Find 0% of 0 = 0. so 0% of = 0. = Notice that this result is the same as the one we found earlier, using fractions. Both methods will give the same answer for any percentage problem. Note In calculating medicines, it is vital that your calculations are accurate. A nought in the wrong place can make a large difference to a dose. For this reason it is always a good idea to check your results, preferably by performing the calculation again using a different method, or by performing it in reverse. More Examples John weighs 0lbs and is 6ft in He is in hospital and cannot leave until he has increased his weight by %. How much must he weigh when he is allowed to leave? The question asks for the total weight after the gain. To start off we need to know how much he needs to gain. He is currently 0lbs. We need to find % of 0 Method - Fractions % by cancelling 0 4 0=0 so % of 0 is 0 4 His total weight will be 0+0= lbs Method - Decimals 0. % 0. 0=0 His total weight will be 0+0= lbs An alternative method is to notice that his total weight will be % of his original weight + % of his original weight. So his eventual weight will be % of his original weight. This means that we can shorten the above calculations: % by 0 4 cancelling 0= 4 His total weight will be lbs %.. 0= His total weight will be lbs Decreasing by a percentage Extra care needs to be taken when decreasing by a percentage. 6

7 Example An item costing 0 is reduced by 0% in the sale. What is the new price? We can tackle this problem in two different ways. Method We find out what 0% of the item is and take that value away from the original cost. 0 0% =6 0-6=4 The final cost is 4 Method We notice that if we take away 0% of an item, we have 80% left. So we can work out what 80% is in one calculation % =4 The final cost is 4 As a rule, the fraction method is best if working on paper and the decimal method is best when using a calculator. Always check that your answer makes sense. A good check is to perform your calculation in reverse, so if you ve found % of something, multiply it by 4 and you should have your original quantity back. Exercise. Express as i) a fraction (simplify if possible), ii) a decimal a) 0% b) 0% c) 4% d) 9% e) 9% f) % g) 84% h) 9%. Using the method of your choice, evaluate the following: a) 0% of b) 0% of 0 c) 4% of 00 d) 9% of e) 9% of 00 f) % of g) 84% of h) 9% of 00. A baby s weight has increased since birth by 0%. When it was born it weighed kg. What is its new weight? 4. An item costs. There is a price increase of 0%, followed by a decrease of 0% in a sale. What is the sale price of this item? For extra help with Percentages consult Mathematics leaflets Fractions, Decimals and Percentages: how to link them and Percentages available on the web at 7

8 Answers to exercises Exercise a) i) : ii) : b) i) :4 ii) 4: c) i) : = : ii) : = : d) i) : ii) :. a) b) c). a) : b) : c) 4: 4. a) women b) 8 men. a) i) 0:0 : ii) 0: = 4: iii) = : b) 0mls of A 40mls of B 0mls of C c) i) 00mg ii) 80 80mls of B 0mls of C 6. 6 a) A. B b) A. 9 8 B. 9 4 c) A. B. d) A. B. Exercise a) 0. b) 0. c) 0. 4 d) e) f) 0. g) h) a) b) c) 90 d) 9 e) 7 f) 6 g) h) New weight is.kg=00g 4. After increase price is The sale price is 49. The Department of Nursing and Midwifery Dr Bunnell provides support for students with their mathematics. To contact Dr Bunnell, T.Bunnell@hull.ac.uk Disclaimer Please note that the author of this document has no nursing or medical experience. The topics in this leaflet are dealt with in a mathematical context rather than a medical one. The information in this leaflet can be made available in an alternative format on request. Telephone /008 8