Mathematics Practice For Nursing and Midwifery

Transcription

1 Study Advice Service Student Support Services Mathematics Practice For Nursing and Midwifery This leaflet contains theory, examples and exercises on the topics: Fractions Decimals Ratio Percentage Using Formulae Unit Conversion Dosage Calculation There are often different ways of doing things in Mathematics and the methods suggested in the worksheets may not be the ones you were taught. If you are successful and happy with the methods you use it may not be necessary for you to change them. If you have problems or need help in any part of the work then there are a number of ways you can get help. For students at the University of Hull Ask your lecturers You can contact a Mathematics Tutor from the Study Advice Service on the ground floor of the Brynmor Jones Library if you are in Hull or in the Keith Donaldson Library if you are in Scarborough; you can also contact us by Come to a Drop-In session organised for your department Look at one of the many textbooks in the library. For others Ask your lecturers Access your Study Advice or Maths Help Service Use any other facilities that may be available. If you do find anything you may think is incorrect (in the text or answers) or want further help please contact us by . Tel: Web: studyadvice@hull.ac.uk

2 Where can you find help for your mathematics? There are many sources of mathematics help available to you. The Study Advice Services desk is located in the Brynmor Jones Library on the Hull campus. Turn left after entering via the turnstiles and you will find our desk. In Scarborough we are based in room C7b, and appointments are made via the Keith Donaldson Library. Help is available from the Study Advice Services in two main ways: A large number of leaflets containing theory, examples and exercises (with answers) on different mathematical topics. These can be collected from the desk or downloaded from the internet via the Study Advice Services website. Individual appointments with the Mathematics Tutor. These last 0 minutes, and provide help with your specific difficulty. If your colleagues also have the same problem as you, it may be possible to book a room in order to hold a workshop on that topic. For Scarborough students, mathematics support is available by or by a pre-arranged telephone link with the Hull tutor. Mathematics leaflets are available in the corridor opposite the library entrance, in the Library Quiet Room and on the Study Advice Services website. The Internet There are many useful sites out there to explain and help you practise mathematics. Some of the best are: S-cool This site offers revision on all school subjects up to and including A level. BBC AS-Guru This links to GCSE bite-size and AS-Guru. Nursing Standard This site contains help for drugs calculations as part of its Resources section. The School of Nursing Dr Bunnell provides support for students with their mathematics. To contact Dr Bunnell, on 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. Version of this leaflet produced Sept-Nov 00, by L.Towse. If you find any errors in this document, please tell me via . A version adapted from Version, Jan 0. Updated June 00 by L. Ireland

3 . Fractions is a fraction of a whole. The bottom number, the denominator tells us how many equal parts the whole has been split into. The top number, the numerator, tells us how many of these parts we have. In this diagram, the whole is split into equal parts. of these parts are shaded. This represents. In this diagram, the whole has been split into equal parts. of these are shaded. This represents. The greater the number of pieces a whole is cut into, the smaller each piece is. e.g. 9 is smaller than, but is larger than 0 Fraction-speak - is one half, is three halves, is one third, is one quarter, is one fifth Equivalent Fractions When two fractions represent the same quantity, they are said to be equivalent fractions. In the diagram above, you can see that, is the same as. This is because a quarter, ( ) twice as big as an eighth ( ). So is equivalent to., is Two fractions are equivalent if you can produce one from the other by multiplying the top and bottom by the same number. Example 6 9 In general, the preferred form for a fraction is the simplest, where the numerator and denominator have no common factor other than. Dividing the top and bottom of a fraction by the same number is called cancelling down.

4 Example. Cancel down Notice that both the top and bottom numbers are divisible by. Dividing top and bottom by we get. Note we could have divided through by instead of, this would have given us. This is valid, but and 6 have a common factor of. So we need to repeat the process, dividing through by this time. So, 6 as before. Cancelling down fractions makes them easier to work with-for example it is simpler to work out of a quantity than. Adding Fractions The key to adding fractions is to notice that is a different type of creature to. You cannot add fractions with different denominators together as they stand. However, if you convert them into fractions with the same denominator, you can. Examples.What is +? We need to get both fractions over the same denominator. We do this by finding the smallest common multiple of the two denominators, ie the smallest nubmer that they both divide into exactly. In this case, we have and and their smallest common multiple is. We need these fractions to be put into the form A, where A is a value we have to find. To make into we multiply by. To ensure that the fraction stays the same size, any multiplication of it must happen to both the numerator and the denominator. Hence we must multiply both top and bottom by. (We are performing the opposite operation to cancelling down.) To make into we multiply by. Again, we must also multiply the numerator by the same amount. So we now have as our question What is +? Our answer is. What is +? + The lowest common multiple of and is. So we calculate and 7 6

5 . What is 0 +? Here we have denominators of 0 and. As is a factor of 0, we can leave the first fraction as it stands and only alter the second one, converting it into tenths. 0. So we have Note: Subtracting fractions works in exactly the same way, except that the last step is a subtraction, not an addition. Relative Size of Fractions We have seen that the larger the denominator the smaller the pieces are that the whole has been cut into. So we know that a quarter is smaller than a third. But if the numerator is not equal to, it is harder to tell the difference in size. To get around this problem, we put the fractions we are comparing over the same denominator, like we do for adding fractions. Then the difference should be clear. Examples. Which is larger or? It is not immediately obvious. In example above, we found that 0 and. Since the second fraction has more fifteenths than the first, it is the larger.. Which is larger or 9? The smallest common multiple of and 9 is 97. So 9 7 and, and we can see that is larger than Mixed Fractions Mixed fractions are a combination of a whole number and a fraction, such as This represents wholes and quarters of a whole.. In other words: + + As each whole can be split into equal pieces, we have a total of quarters. (Equivalently the process is as follows: multiply the whole number by the denominator and then add this result to the numerator) is called an improper or top-heavy fraction, because the numerator is greater in value than the denominator.

6 We can also convert improper fractions into mixed fractions by the following method: We want to convert 6. As 6++ we can split the fraction up: We know that, so we have As and have a common factor of, we can cancel this fraction down to 6, leaving us with 6 (You could also work this out by dividing the numerator by the denominator- the whole number result becomes the number of wholes and the remainder becomes the fractional part) Multiplying fractions To multiply a fraction by a whole number, you just multiply the numerator by the whole number and leave the denominator alone. Example What is? We multiply the numerator 6 and leave the denominator alone. Our result is 6. (If we multiplied both numerator and denominator by we would get 6 which is equivalent to and so is not times the size of ) To multiply a fraction by another fraction, we multiply the numerators together and the denominators together. Example Multiply by 7 We perform two calculations. 6 and 7 Our result is 6 Dividing fractions How would we work out 7? To work this out we use a trick. Using the fact that dividing by a number (such as ) is the same as multiplying by over that number (such as ), we can turn our division into a multiplication: is the same as 7 7 We can then continue as before: 7, So 7 6

7 In general the procedure is change the division sign to a multiplication sign, turn the second fraction upside down and then multiply. This method does not work immediately for mixed fractions, which need to be converted back into improper fractions first. Note that this procedure works every time you want to divide by a fraction, whether or not the first value is in the form of a fraction, a decimal or a whole number. To divide a fraction by a whole number, we can follow the same procedure as above, only this time our second fraction will consist of our whole number over one. For example to divide by is the same as to divide by. Example Exercise. For each group of fractions, state which fractions are equivalent. a),,, b), 6, 7, c), 9, 0,. Cancel the following fractions down to their simplest form: a) b) 6 c) For each of the following pairs of fractions, state which one is the larger: a) 7, b), 6 c), 7. Convert the following mixed fractions into improper fractions: a) 7 b) 6 c). Convert the following improper fractions into mixed fractions: a) b) 6 c) Work out the following (simplify your answer if possible): a) b) 9 c) 6 7. Work out the following (simplify your answer if possible): a) b) c). Work out the following divisions (simplify your answer if possible): a) b) c) Work out the following divisions (simplify your answer if possible): a) b) c) 6 7

8 For extra help with Fractions please consult Mathematics leaflet Fractions. Decimals.,.7,.,.6 are all decimals. The decimal point (.) is used to distinguish the parts of the number. Numbers to the left of the decimal point are the normal counting numbers. Numbers to the right of the decimal point are parts of numbers. Example.6. Here we have and a bit. The bit is 0.6. Place Value The value of a number is dependent upon its position. This is called place value. Thousands Tens Units Tenths Hundredths Thousandths The table above shows how place value works for decimals..0 has one unit and one hundredth.. has two units and tenths. 7.9 has five tens, seven units and 9 tenths has one hundred, 6 tens, and thousandths Decimal-Speak It is usual to say the numbers after the decimal point as individual numbers. For example.9 would be said as four point nine three not four point ninety-three Notice that where a number does not have a value for a column, a nought is used. This preserves the value of the following numbers. In this way 0. is different from 0.0 in the same way that 0 is different from. As with numbers in front of the decimal point, noughts not contained within a number are not usually written. i.e.. is really but we can just assume that the following noughts are there. Multiplying by 0, 00, 000 If you multiply a number by ten, its digits will remain the same, but they will move in relation to the decimal point. Example 0 0 As is the same as.0, all we have done is to move the decimal point one place to the right, so.0 becomes 0. Alternatively you can think of this as the number moving one place to the left. Whichever you prefer, the end result is the same. This system works for numbers with decimal places too. Examples

9 Notice that in the last example, the nought is treated in the same way as all other digits. When you are on a ward or in a clinic, you may be asked to measure doses of medication. For these calculations, a sound grasp of place value is essential, as 0. grams is 00 times the amount of a medicine that 0.00 grams would be. Multiplying by 00, 000 etc is performed in a similar way to multiplying by 0. Example We have seen that. 0. Multiplying by 0 again gives. 0 As , multiplying by 00 is exactly the same as multiplying by 0, then multiplying the result by 0. Each time we multiply by 0 we move the decimal point one place to the right. Multiplying by 00 moves the decimal point one place to the right twice, so the overall effect is to move the decimal point two places to the right. So, looking at the example again: More examples The most common multiplication of this type you will have to do will be multiplication by 000. As , we can look at multiplying by 000 as multiplying by 0 three times in succession. Looking at our example: The overall effect of multiplying by 000 is to move the decimal point three places to the right. Division by 0, 00, 000 As division by 0 is the inverse process to multiplication by 0, we simply apply the same processes but in reverse. To multiply by 0, we move the decimal point one place to the right. To divide by 0 we move the decimal point one place to the left. Examples In the same way we can divide by 00 and 000. Examples Note- when dividing by 0, 00, 000 etc, it may be useful to write some noughts in front of your number so that you don t lose track. 9

10 i.e , so Dividing by numbers smaller than Sometimes you may be asked to divide by numbers smaller than one. Example Evaluate 0.. Essentially this is asking us how many 0.s are in. The first thing that we do is note that 0. is one tenth. We know from our work on fractions that there are ten tenths in a unit. We have of these units. Hence our question can be changed to: Evaluate 00 When you divide by a number less than, your answer will be larger than the value we started with. Exercise. Express the following in terms of hundreds, tens, units, tenths etc a).9 b) 7.0 c) Write these numbers in figures a) One unit, six tenths and one thousandth b) Five tens and five tenths c) Three hundreds, six units, nine hundredths and one thousandth. Evaluate the following: a) 0 b). 0 c) d) e) f).9 00 g). 000 h) i) Evaluate the following: a) 0 b). 0 c) d) e) f).9 00 g). 000 h) i) Copy the procedure below to answer the following questions: The question asks for I am dividing by is one hundredth, so there are 00 of them in unit. I have 6. units, so I must have hundredths. The question is equivalent to , so a).9 0. b) 0.00 c) For extra help with this section please consult Mathematics leaflet Powers of 0 0

11 . 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 white squares. The ratio of grey squares to white squares is 6:. However, as can be seen from the diagram, in each row we have grey squares for every white squares. This means that a ratio of 6: is the same as a ratio of :. We have cancelled down the ratio by dividing both sides by a common factor (in this case ). Looking at the ratio :, we can see that and have a common factor of. This means that the ratio can be cancelled down further (as we did with fractions earlier). So for every 6 grey we have white becomes: The ratio of grey to white is 6: This is the same as : 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 we have that 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 00ml.

12 Ratios can also be linked to fractions. Examples. The ratio of drug A to water in a solution is :. 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 are water. So, of the solution is A.. The ratio of A to B in a solution is :. This means that for every parts of A there are parts of B. It also means that out of every 7 parts, are A and are B. So, 7 of the solution is A and 7 is B. 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 shaded to unshaded; ii) the ratio of unshaded to shaded: 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) : b) : c) :7. 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 0 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 00mg of Q how many mls of A, B and C would you need? c) There are 0mls 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) : c): d) :

13 . 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: 00% of something means the whole amount. (Literally 00 per 00) 0% of something means that you are looking at half of it, as 0 is half of 00. 0% of something means that you are looking at a tenth of it as 0 is a tenth of 00. 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 0% means 0 out of a hundred, so we can write this as 0 in the same way as 00 we know that out of can be written as. The following table shows the fraction form of some common percentages: Percentage Fraction Simplified Fraction 00% 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: 00 Write the percentage as a fraction of 00 i.e. 00 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 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.

14 Example Find 0% of 0. 0% is the same as 0 (from the table). So 0% of as we first multiply by the numerator. 0 0 as 0 and 0 have a common factor of 0 0 Example Find 0% of. 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 Method - Use Decimals As the number is used to represent a whole, we can also use it to represent 00%. We know that 0% is half of 00%, so 0% of must be half of, which as a decimal is 0.. The following table shows the decimal form of some common percentages: Percentage Decimal 00% 0% 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 00. So % 0.. That s all there is to it. Example Find 0% of so 0% of 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.

15 More Examples John weighs 0lbs and is 6ft. 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 00 0 % by cancelling 00 so % of 0 is 0 His total weight will be lbs Method - Decimals % His total weight will be lbs An alternative method is to notice that his total weight will be 00% 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: 00 0 % by cancelling 00 His total weight will be 0 lbs % His total weight will be 0 lbs Decreasing by a percentage Extra care needs to be taken when decreasing by a percentage. 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% The final cost is Method We notice that if we take away 0% of an item, we have 0% left. So we can work out what 0% is in one calculation. 0% The final cost is

16 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 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) % d) 9% e) 9% f) % g) % h) 9%. Using the method of your choice, evaluate the following: a) 0% of b) 0% of 0 c) % of 00 d) 9% of 00 e) 9% of 00 f) % of 0 g) % 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?. An item costs 0. 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 please consult Mathematics leaflets Linking Fractions, Decimals and Percentages and Percentages.. Using Formulae Algebra is widely used in mathematics and is often used as a form of shorthand. In algebra, letters are used to denote numbers. We do this if the number the letter represents is still to be worked out, or if this number could change. You may use formulae in order to work out medicine doses which are dependent on the patients weight. Example We could use p as the price in pounds of an item. Then p (written p) would represent the total cost of items at p each. In order to make our work look neater/save time, we often omit the multiplication sign when using algebra. To do this we simply write the items being multiplied next to each other: x x g g f g fg Formulae Formulae is the plural of formula. A formula is an algebraic expression or rule. Examples Volume of a box: Length Width Height 9 + l w h lwh Converting Temperatures: F ( C) where F is Fahrenheit and C is Celsius Substitution Putting a known value into a formula in order to work out an unknown value. 6

17 Example The relationship between quantities X and Z is such that XZ+ What is the value of X when Z? Solution The meaning of this formula in words is multiply Z by, then add and you get the value of X. We have been given the value of Z so the only unknown value is X We substitute Z into the equation XZ+ X( )+ (as Z means Z) X+ Exercise. For the following formulae i) explain in words what the formula means ii) substitute in the given value of Z iii) work out the value of X a)xz, Z b)xz+, Z c)xz-6, z. Find the value of X in the following formulae when Z Z + 6 Z Z + a) X b) X Z c) XZ+ ( ) Z (You are unlikely to meet anything more complicated than the previous formulae) For extra help with Algebra please consult Mathematics leaflet Basic Algebra 6. Unit Conversion In your chosen field you are likely to need to convert weights and volumes from one unit to another. Metric Measurements of Weight Name Abbreviation Notes Kilogram kg Approximate weight of a litre of water Gram g One thousand grams to a kilogram Milligram mg One thousand mg to the gram Microgram mcg One million mcg to the gram Nanogram ng One thousand ng to the mcg 7

18 Conversion Chart Number of Kilograms Number of Grams Number of Milligrams Number of Micrograms Number of Nanograms To move up one stage we divide by 000 and to go down one stage we multiply by 000. If we want to move up two stages we divide by 000 two times (i.e. divide by million) Example Convert kilograms into grams. As we can see from the table, there are 000 grams in a kilogram. We have kilograms, so kg000g. From the conversion chart, the arrow from kilograms to grams carries the instruction 000. So We have 000g. Note There is a greater chance of serious error when using abbreviations of measures. For example mg, ng, and mcg may be hard to distinguish if written by hand. To avoid this, it is always best to write out the whole name of the measure.

19 Metric Measurements of Liquids Name Abbreviation Notes Litre l Abbreviation is a lower-case L Millilitre ml One thousand millilitres to a litre Conversion Chart Number of litres Number of Millilitres There is also the Centilitre (cl), so named as there are a hundred of them in a litre. A single Centilitre is equivalent to 0ml. Centilitres are normally used to measure wine. Examples. Convert 7 millilitres into litres. From the diagram, we see that to convert from millilitres to litres, we divide the number of millilitres by 000. So we have litres. Convert.67 litres into millilitres. To convert from litres to millilitres we multiply the number of litres by 000. So we have millilitres Estimation Always look at the answers you produce to check they are sensible. A good way to do this is to estimate. In Example above we can use our knowledge of litres and millilitres to estimate the result. We have 7 millilitres. If we had 000 millilitres we would have a litre. Half a litre would be 00 millilitres, so our result will be a little over half a litre. Exercise 6. Copy and complete the following, using the tables and diagrams a) kilogram grams b) gram milligrams c) gram micrograms d) microgram nanograms e) litre millilitres. Convert the following into milligrams a) 6 grams b) 6. grams c).9 grams d) 0 grams. Convert the following into grams a) 00mg b) 60mg c) 679mg d) mg. Convert the following into milligrams a) 0 micrograms b) 00 micrograms c) 67 micrograms d) 0 mcg 9

20 . Convert the following: (you may find it easier to work out the answers in two stages): a).67grams into micrograms b) 0.grams into micrograms c) micrograms into grams d) 67 micrograms into grams e).9 milligrams into nanograms f) 0 nanograms into milligrams 6. Convert the following into litres a) 0 millilitres b) millilitres c) 9 millilitres d). ml 7. Convert the following into millilitres a) litres b) 6. litres c) 0.9 litres d).7 litres. A patient needs a dose of 0. g of medicine A. They have already had 60mg. a) How many more mg do they need? b) What is this value in grams? c) A dose of 00 mcg has been prepared. Will this be enough? For extra help with Units please consult Mathematics leaflet Powers of 0 7. Dosage Calculations Dosage calculations vary depending on whether you are dealing with liquid or solid medications, or if the dose is to be given over a period of time. In this section I will go over each of these situations in turn. It is very important that you know how drug dosages are worked out, because it is good practise to always check calculations before giving medication, no matter who worked out the original amount. It is far better to point out a mistake on paper than overdose a patient. Tablets Working out dosage from tablets is simple. Formula for dosage: Total dosage required Number of tablets required Dosage per tablet Note-If your answer involves small fractions of tablets, it would be more sensible to try to find tablets of a different strength rather than try to make of a tablet for example. Examples. A patient needs 00mg of X per day. X comes in mg tablets. How many tablets per day does he need to take? Total dosage required is 00mg, Dosage per Tablet is mg 00 So our calculation is He needs tablets a day 0

21 Liquid Medicines Liquid medicines are a little trickier to deal with as they will contain a certain dose within a certain amount of liquid, such as 0mg in 0ml. To work out the dosage, we will use the formula: What you want What you ve got What it s in Note: In order to use this formula, the units of measurement must be the same for What you want and What you ve got ; i.e. both mg or both mcg etc. Examples. We need a dose of 00mg of Y. Y is available in a solution of 0mg per 0ml. In this case, What we ve got 0 What we want 00 What it s in 0 So our calculation is We need 00ml of solution.. We need a dose of 0mg of Z. Z is available in a solution of 00mg per 00ml. In this case, What we ve got 00 What we want 0 What it s in 00 So our calculation is We need ml of solution. Medicine over Time. Tablets/liquids This differs from the normal calculations in that we have to split our answer for the total dosage into or more smaller doses. Look at Example again. If the patient needed the 00mg dose to last the day, and tablets were taken four times a day, then our total of tablets would have to be split over doses. Total amount of liquid/tablets for day Amount to be given per dose Number of doses per day We would perform the calculation:. So he would need tablet times a day. Drugs delivered via infusion For calculations involving infusion, we need the following information: The total dosage required. The period of time over which medication is to be given. How much medication there is in the solution.

22 Example. A patient is receiving 00mg of medicine X over a 0 hour period. X is delivered in a solution of 0mg per 0ml. What rate should the infusion be set to? Here our total dosage required is 00mg Period of time is 0 hours There are 0mg of X per 0ml of solution Firstly we need to know the total volume of solution that the patient is to receive. Using the formula for liquid dosage we have: So the patient needs to receive 00mls. 0 We now divide the amount to be given by the time to be taken: The patient needs 00mls to be given at a rate of mls per hour 00 0 Note: Working out medicines over time can appear daunting, but all you have to do is to work out how much medicine is needed in total, and then divide it by the amount of hours/doses needed Drugs labelled as a percentage Some drugs may be labelled in different ways to those used earlier. V/V and W/V Some drugs may have V/V or W/V on the label. V/V means that the percentage on the bottle corresponds to volume of drug per volume of solution. i.e % V/V means for every 00ml of solution, ml is the drug. W/V means that the percentage on the bottle corresponds to the weight of drug per volume of solution. Normally this is of the form number of grams per number of millilitres. So in this case % W/V means that for every 00ml of solution there are grams of the drug. If we are converting between solution strengths, such as diluting a 0% solution to make it a 0% solution, we do not need to know whether the solution is V/V or W/V. Examples. We need to make up litre of a % solution of A. We have stock solution of 0%. How much of the stock solution do we need? How much water do we need? We can adapt the formula for liquid medicines here: What we want What we want it to be in What we ve got We want a % solution. This is the same as or We ve got a 0% solution. This is the same as 0 or We want our finished solution to have a volume of 000ml. Our formula becomes (using the rule for dividing fractions) We need 00mls of the A solution. Which means we need mls of water.

23 6. You have a 0% V/V solution of drug F. The patient requires 0ml of the drug. How much of the solution is required? 0% V/V means that for every 00ml of solution we have 0ml of drug F. Using our formula: What you want What you ve got What it s in This becomes We need 0mls of solution. 7. Drug G comes in a W/V solution of %. The patient requires grams of G. How many mls of solution are needed? % W/V means that for every 00mls of solution, there are grams of G. Using the formula gives us mls of solution are required. Note In very rare cases, a drug may be labelled with a ratio. If this is the case, refer to the Drug Information Sheet for the specific medication in order to be completely sure how the solution is made up. Exercise 7. How many 0mg tablets of drug B are required to produce a dosage of: a) 60mg b) 0mg c) mg d) 7mg. Medicine A is available in a solution of 0mg per 0ml. How many mls are needed to produce a dose of: a) 0mg b) mg c) 00mg d) mg. Medicine C is available in a solution of micrograms per 00ml. How many mls are needed to produce a dose of: a)0mcg b) mcg c)0mcg d) 7mcg. Medicine D comes in 0mg tablets. How many tablets are required in each dose for the following situations: a) total dosage 0mg, doses b) total dosage 60mg, doses c) total dosage 00mg, doses d) total dosage 0mg, doses. At what rate per hour should the following infusions be set? a) Total dosage 00mg, solution of mg per 00mls, over hours b) Total dosage 70mg, solution of 0mg per 0mls, over 0 hours c) Total dosage 0mg, solution of 90mg per 00mls, over 0 hours

24 6. Drug B comes in a 0% V/V stock solution. i) How much of the solution is needed to provide: a) 0ml of B b) 0ml of B c) 00ml of B ii) How would you make up the following solutions from the stock solution? a) Strength 0% volume litre b) Strength 0% volume 70ml iii) What strength are the following solutions? a) Volume litre, made up of 600ml stock solution, 00ml water b) Volume 600ml, made up of 00ml stock solution, 00ml water 7. Drug C comes in a % W/V stock solution. i) How much of the solution is needed to provide: a) 0g of C b) 7.gof C c) 90g of C ii) How would you make up the following solutions from the stock solution? a) Strength % volume 900ml b) Strength 0% volume 70ml iii) How many grams of C are in the following solutions? a) Volume litre, made up of 00ml stock solution, 600ml water b) Volume 00mls, made up of 0ml stock solution, 0ml water For further help on this topic there are several books available in the Brynmor Jones Library. Note, however, that books on the subject by non-british authors may use notation or measures not commonly used in the UK. Suggested Reading Drug Calculations for Nurses-A Step By Step Approach Robert Lapham and Heather Agar BJL nd Floor East RS7L ISBN Nursing Calculations Fifth Edition J.D. Gatford and R.E.Anderson BJL nd Floor East RT6G ISBN

25 Answers to exercises Exercise. a), b), 6 c) 7. a) b) c) 6, a) a) 0 b) 9 0 b) 6 c) c). a) 7 b) 7 6 c). a) 6 b) c) 7. a) 7 b) 9 c) a) 6 b) 6 c). a) b) c) 6 7 Exercise. a) one hundred, two tens, five units and nine tenths b) eight tens, seven units, and three hundredths c) one hundred, two units, six hundredths and five thousandths.. a).60 b)0. c) a) 0 b) c) 0. d) 60 e) 09 f) 9 g) 00 h) 900 i) 00. a). b) 0. c) 0.00 d) 0.6 e) f) 0.09 g) 0.00 h) 0.09 i) a) x 0 9 b) 0.00 x c) x 00 Exercise. a) i) : ii) : b) i) : ii) : c) i) : : ii) : : d) i) : ii) :. a) b) c). a) : b) : c) :. a) women b) men. a) i) 0:0 : ii) 0: : iii) :0 : b) 0mls of A 0mls of B 0mls of C c) i) 00mg ii) 0mls of B 0mls of C 6. a) A. c) A. B. B. 6 b) A. 9, B. 9 d) A., B.

26 Exercise. a) 0 0. b) 0 0. c) 9 0. d) e) 09 f) g) h) 9. a) b) c) 90 d) 9 e) 7 f) 6 g) h) 7. New weight is.kg00g. After increase price is. The sale price is 9.0. Exercise. a) i) Multiply Z by to find the value of X ii)x iii) X b) i) Multiply Z by then add on to find the value of X ii) X( )+ iii) X c) i) Multiply Z by then subtract 6 to find the value of X ii) X( )-6 iii) X. a) X Z X b) X Z + 6 ( ) + 6 Z X ( ) c) X Z + ( Z ) ( ) ( X + ) + ( ) Z + Exercise 6. a) kg000g b) g000mg c) g mcg d) mcg000ng e) litre000ml. a) 6g6000mg b) 6g600mg c).9g9mg d) 0g0000mg. a) 00mg.g b) 60mg0.6g c) 679mg6.79g d) mg.g. a)0mcg0.mg b) 00mcg.00mg c)67 mcg.67mg d) 0mcg.0mg. a).67g670000mcg b) 0.g0000mcg c) mcg 0.000g d) 67mcg0.0067g e).9mg900000ng f) 0ng0.000mg 6. a) 0ml0.0litres b) ml0.litres c) 9ml.9litres d).ml0. litres 7. a) litres000ml b) 6.litres600ml c) 0.9litres90ml d).7litres70ml. a) 0 milligrams b) 0. grams c) no, the correct dose would be 0000mcg Exercise 7. a) tablets b) tablets c) tablet d) tablets. a) 0ml b) ml c) 000ml d) ml. a) 000ml b) 00ml c) 00ml d) 00ml. a) tablets b) tablets c) tablet d) tablet. a) 00ml per hour b). ml per hour c) 0ml per hour 6

27 6. i)a) 0ml b ) 0ml c) litre ii) a) litre stock, no water b) 7ml stock, 7ml water iii) a) 600ml stock contains 0ml B So 0ml in 000ml % 000 b) 00ml stock contains 60ml B So 60ml in 600ml 0% i) a) 00ml b) 0ml c) 600ml ii) a) 00ml stock, 600ml water b) 00ml stock, 0ml water iii) a) 60g b) 67.g We would appreciate your comments on this worksheet, especially if you ve found any errors, so that we can improve it for future use. Please contact the Maths tutor by at studyadvice@hull.ac.uk. updated 6 th June 00 The information in this leaflet can be made available in an alternative format on request. Telephone