Maths for Healthcare Professionals
Mathematics Skills Guide
All the information that you require to enable you to pass the mathematics
tests within your course is contained within.
Contents
Fractions
Page 2
Decimals
Page 11
Ratio
Page 17
Percentages
Page 21
BMI
Page 29
Averages
Page 30
Unit
Conversion
Page 31
Dosage
Calculations
Page 36
Web: www.hull.ac.uk/skills
Email: skills@hull.ac.uk
Fractions
A fraction is the ratio of two integers (whole numbers)
Example
,
The number at the top is called the numerator, the number at the bottom is called
the denominator.
has a numerator 2 and denominator 5. It is spoken ‘two fifths’.
has a numerator 3 and denominator 7. It is spoken ‘three sevenths’.
Equivalent Fractions
Here
is shaded
Here
is shaded
Here
is shaded
In all three diagrams the shaded regions represent the same quantity so that
=
=
The fractions are said to be equivalent.
Fractions are equivalent if you can convert one into the other by multiplying (or
dividing) the numerator and the denominator by the same number.
Examples
is equivalent to
since
→
is equivalent to
2
→
since
is equivalent to
→
since
Equivalent fractions are needed when we come to addition and subtraction of
fractions.
The preferred form for a fraction is the simplest i.e. when numerator and
denominator have no common factors so that we cannot divide any further.
For example
can be made simpler by dividing numerator and denominator by 7
to get
and we cannot make any simpler.
This simplification is called cancelling.
Cancelling fractions makes them easier to work with particularly when multiplying
and dividing them.
The four operations we need to look at are , +, - and ÷ and in that order:Multiplication
We can get a simple rule for this operation as follows:
↑
The shaded area in the diagram
Represents 3 x 4 = 12
4
↓
←
→
3
and if we use the same idea but the sides of the diagram now represent 1 unit we
can illustrate
The shaded area in the diagram
represents x =
↑
(= after cancelling)
↓
←
→
3
The rule is:- multiply numerators, multiply denominators
Examples
i)
ii)
iii)
Algebraically
=
(=
after cancelling)
=
Addition +
Type I
If two (or more) fractions have the same denominator, then we just add the
numerators
Examples
It is easy to see this is the correct method by looking at the following diagram
←
→+←
2/8
→
The shaded region is
Similarly
Type II
If the fractions have different denominators then it is not possible to use the above
method. We do, however, have a technique for changing fractions to equivalent
fractions and we use this to convert two fractions with different denominators into two
fractions with the same denominator and then just use the Type I method.
Examples
i)
If we multiply the numerator and denominator of
4
by 4 i.e.
→
and if we multiply the numerator and denominator of
by 5 i.e.
→
we have produced two equivalent fractions whose denominators are the same.
We can now simply add:ii)
=
+
Multiply numerator and denominator of
by 4 and
multiply numerator and denominator of
by 3 to produce two equivalent fractions:-
→
,
and
+
=
Choosing what we multiply by is not difficult. It is (usually) the denominator of the
other fraction.
Example
+
Multiply numerator and denominator of
by 5 (the denominator of
) to get
Multiply numerator and denominator of
by 7 (the denominator of
to get
=
Then
Do not forget to cancel your fractions, if possible, to produce the simplest form of
your answer.
Example
=
and
So,
,
which equals
, which equals
(simplest form)
Subtraction This is done in exactly the same way except instead of adding we subtract!
Example
(same denominators, so Type I subtraction)
5
-
(different denominators so produce equivalent fractions)
→
and
→
so
Algebraically,
so
+
- =
=
and
-
=
=
This looks a little awkward, but if we look at the answer we can, very quickly,
produce it as follows
+
2nd term
A
C
+
B
D
3rd term
1st term
3
1
1
4
+ 3
7
=
+
3
4
12
3
4
4
12
12
5
2
+ 1
5
2
=
10
4
+
5
=
9
10
10
4
Division ÷
To find a method for this operation we proceed as follows:
6
(just rewriting the sum)
=
(multiply numerator and denominator by the same number to produce an
equivalent fraction)
x 12
= 2 x 124
31
3 x 123
41
=
=
(simplifying)
Before working this out (using the method from multiplying fractions) look at the
expression we have obtained.
has become
i.e. the first fraction has remained the same, the divide sign ÷ has become times x,
and the second fraction has turned upside down.
This happens in general and gives us a simple method for dividing fractions.
Examples
i)
ii)
=
iii)
Algebraically
Summarising
i)
=
7
ii)
iii)
It is best NOT to remember these as formulas but as methods.
Mixed Numbers
If we have a, so called, mixed number to deal with, i.e. a fraction and a whole
number Examples 2 , 4 , it is best to convert the whole number to a top heavy
fraction or improper fraction, perform the operation using the above rules, and then
convert back to a mixed number if necessary.
Examples
i)
2
3
2 →
So
2
ii)
3
3
So
3
and 3 →
(cancelling)
and 2
→
=
To convert a mixed number to a fraction we multiply the whole number by the
denominator of the fraction and then add on the numerator.
Schematically
A
Again do NOT remember this as a formula but as a method.
8
Fractions Exercise
1. For each group of fractions, state which fractions are equivalent:
a)
1,1,2,3
2 4 4 4
6 4
b) 83 , 72 , 21
, 15
9 2 12
c) 54 , 10
, 3 , 15
2. Cancel the following fractions down to their simplest form:
a)
5
25
36
108
b)
20
c) 64
3. For each of the following pairs of fractions, state which one is the larger:
a)
3 7
,
4 8
b)
5,6
8 7
c)
12 , 3
15 5
4. Convert the following mixed fractions into improper fractions:
a) 5 78
5
c) 2 16
b) 6 81
5. Convert the following improper fractions into mixed fractions:
a)
18
5
c) 19
3
b) 26
7
6. Work out the following (simplify your answer if possible):
a) 4× 15
3
c) 6× 12
b) 5× 89
Note: Any whole number can be written as a fraction with denominator 1, ie. 3 = ,
7 = , and we just use the usual rules so 3 x
= x
=
7. Work out the following (simplify your answer if possible):
a)
1
4
× 15
b)
3
8
× 12
c) 54 × 23
8. Work out the following divisions (simplify your answer if possible):
a)
8
9
÷ 23
b)
3
7
÷
1
2
c)
4
5
÷ 15
9. Work out the following divisions (simplify your answer if possible):
a)
2
3
÷4
b)
1
2
÷8
c)
9
5
8
÷6
Fractions Exercise - Answers
1. a) 1 , 2
2 4
6
b) 72 , 21
c) 4 , 12
6.
a) 54
b) 40
9
c) 32
2. a) 1
5
b) 13
5
c) 16
7.
1
a) 20
3
b) 16
8
c) 15
3. a) 7
8
b)
8.
a) 43
b) 76
c) 4
4. a) 47
8
b) 49
8
37
c) 16
9.
a) 16
1
b) 16
5
c) 48
5. a) 3 3
5
b) 3 75
c) 6 13
6
7
5 15
c)
12
15
10
Decimals
1.5, 2.7, 1.333, 12.6 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
123.456. Here we have 123 and a bit. The bit is 0.456.
Place Value
The value of a number is dependent upon its position.
This is called its place value.
Thousands Tens Units • Tenths Hundredths Thousandths
1
1
•
0
2
•
5
5
7
•
9
6
0
•
0
1
0
4
The table above shows how place value works for decimals.
1.01
means one unit and one hundredth.
2.5
means two units and 5 tenths.
57.9
means five tens, seven units and 9 tenths
160.004 means one hundred, 6 tens, and 4 thousandths
Decimal-Speak
It is usual to say the numbers after the decimal point as individual numbers. For
example 4.93 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 numbers following. In this way 0.2 is different from
0.02 in the same way that 20 is different from 2.
As with numbers in front of the decimal point, noughts not contained within a number
are not usually written
i.e. 5.1 is really 5.1000000000000000000000000… but we can just assume that the
following noughts are there.
11
Multiplying and dividing by 10/100/1000 etc.
When we multiply a number by ten its digits remain the same but the decimal point
moves one place to the right.
Examples
12.4 x 10 = 124
231.47 x 10 = 2314.7
14 x 10 = 140
0.03 x 10 = 0.3
When we multiply a number by one hundred its digits remain the same but the
decimal point moves two places to the right.
Examples
1.24 x 100 = 124
433.62 x 100 = 43362
8.4124 x 100 = 841.24
When we multiply a number by one thousand its digits remain the same but the
decimal point moves three places to the right.
Examples
2.316 x 1000 = 2316
81.42 x 1000 = 81420
0.0031 x 1000 = 3.1
When multiplying we just move the decimal point as many places as there are
noughts to the right.
Division is the inverse process to multiplication so that when dividing by 10/100/1000
we simply reverse the above process.
Examples
12 ÷ 10 = 1.2
21 ÷ 100 = 0.21
274 ÷ 1000 = 0.274
ie. we move the decimal one, two or three places but this time to the left.
12
Multiplying Decimals
We get a method for this by noting that 32.4 =
and 2.42 =
using
the ideas from the previous section.
So 32.4 x 2.42 =
x
We perform the usual long multiplication
324
242
64800
And now divide by 10 and 100, ie. move the decimal point
three places,1 place from 32.4 and 2 places from 2.42 to get
78.408
12960
648
78408
This is why the method works. We can abbreviate it to:


Just perform a long multiplication, ignoring the decimal point
Now put the decimal point back in the answer – it will have just as many
decimal places as the two original numbers combined.
Example
214
231
42800
6420
214
49434
Example
11
3
33
21.4 x 2.31
We have 1 dp from 21.4
and 2 dp from 2.31
giving a total of 3 dp
Putting the decimal point in gives 49.434
0.03 x 1.1
We have 2 dp from 0.03
and 1 dp from 1.1
giving a total of 3 dp
Putting the decimal point in gives 0.033
13
You should always perform a rough check to make sure your answer is of the correct
order.
Example
20.42 x 3.12
2042
312
612600
We have 2 dp from 20.42
and 2 dp from 3.12
giving a total of 4 dp
20420
4084
637104
Putting the decimal point in gives 63.7104
As a rough check 20.42 is approximately 20 and 3.12 is approximately 3
So our answer should be about 60, which it is.
Dividing decimals
To get a method for this operation we use the idea of equivalent fractions.
(Remember we can produce a fraction equivalent to a given fraction by multiplying
(or dividing) the numerator and denominator by the same number)
5.39 ÷ 1.1 = 5.39
1.1
Now multiply numerator and denominator by 10 to produce 53.9 and we can now
perform the usual long division
11
Example
11
4.9
53.9
So that 5.39 = 4.9
1.1
As with multiplication, do a rough check to make sure your answer is of the correct
order.
Example
ie.
0.0325 ÷ 0.013
0.0325
0.013
14
Multiply numerator and denominator by 1000 to produce 32.5 and then perform the
long division.
13
2.5
32.5
13
Once again a rough check shows the answer is of the correct order.
As with multiplication of decimals we can abbreviate the method to:



Move the decimal point in the denominator to produce a whole number
Move the decimal point in the numerator the same number of places
Perform the long division
Example
Find
0.275
0.25
This becomes 27.5 (two places in the numerator and denominator)
25
25
1.1
27.5
A rough check shows the answer is of the correct order
Find
2.405
0.37
This becomes 240.5 (two places in the numerator and denominator)
37
37
6.5
240.5
Once again a rough check shows the answer is of the correct order
15
Decimals Exercise
1. Express the following in terms of hundreds, tens, units, tenths etc:
a) 125.9
b) 87.03
c) 102.065
2. 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
3. Evaluate the following:
a) 18 × 10
b) 1.4 × 10
c) 0.02 × 10
d) 26.8 × 100
e) 2.09 × 100
f) 3.94 × 100
g) 2.1 × 1000
h) 12.9 × 1000
i) 1.08 × 1000
4. Evaluate the following:
a) 18  10
b) 1.4  10
c) 0.02  10
d) 26.8  100
e) 2.09  100
f) 3.94  100
g) 2.1  1000
h) 12.9  1000
i) 1.08  1000
5. Find:
a) 2.54 ÷ 0.2
b) 34.56 ÷ 0.9
d) 30.72 ÷ 2.4
e) 0.085 ÷ 0.025
c) 18.48 ÷ 1.2
Decimals Exercise - Answers
1. 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
2.
3.
a) 1.601
a) 180
f) 394
b) 50.5
b) 14
g) 2100
c) 306.091
c) 0.2
h) 12900
16
d) 2680
i) 1080
e) 209
4.
5.
a) 1.8
f) 0.0394
a) 12.7
b) 0.14
g) 0.0021
b) 38.4
c) 0.002
h) 0.0129
c) 15.4
d) 0.268
i) 0.00108
d) 12.8
e) 0.0209
e) 3.4
Ratio
Ratio describes the relationship between two quantities.
Here we have 3 grey squares and 2 white squares. We can say
that the
ratio of grey squares to white squares is 3 to 2.
This is usually written 3:2 where the colon replaces the ‘to’.
3:2 means that for every 3 items of the first type we have 2 items of the second.
Similarly the ratio of white squares to grey squares is 2:3.
In the top part of this diagram, we have 16 grey squares and 8
white squares.
The ratio of grey squares to white squares is 16:8.
However, as can be seen from the bottom part of the diagram, in each row we have
4 grey squares for each 2 white squares. This means that a ratio of 16:8 is the same
as a ratio of 4:2.
We have cancelled down the ratio by dividing both sides by a common factor (in this
case 4).
Looking at the ratio 4:2, we can see that 4 and 2 have a common factor of 2. This
means that the ratio can be cancelled down further (as we did with fractions in the
fractions section).
So ‘for every 16 grey we have 8 white’ becomes:
The ratio of grey to white is 16:8
This is the same as 4:2
Which is the same as 2:1.
So the ratio of grey to white, is 2:1.
17
Using Ratios
Examples
1.
The small intestine is about 20 feet in
length. If the ratio of the small intestine to
the large intestine is 4:1 how long is the large intestine?
We have small:large ≡ 4:1 meaning to every 4 feet of small intestine we have
1 foot of large. So that for 20 feet of small intestine we must have 5 feet of
large. The large intestine is about 5 feet long.
2. Solution X is made from the contents of bottles A and B in the ratio of 3:2. We
have already measured out 600mL of A.
How many mL of B are required to make up X?
3:2 means that for every 3 parts of A we need 2 parts of B.
We have 600mL of A. This is the same as 3 parts of 200mL each.
To make up the solution we need 2 parts of B. So we need
2 x 200mL = 400mL.
Ratios can also be linked to fractions.
Examples
1.
The ratio of drug A to water in a
solution is 1:4.
This means that for every part of A we need four parts of water.
Alternatively, it means that for every 5 parts of the solution, 1 is A and 4 are
water. So, 15 of the solution is A.
2.
The ratio of A to B in a solution is 3:4.
This means that for every 3 parts of A there are 4 parts of B.
It also means that out of every 7 parts, 3 are A and 4 are B.
So, 73 of the solution is A and 74 is B.
18
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 10mg per mL may be written 10mg/mL.
Ratio Exercise
1. 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.
2. Draw diagrams to represent the following ratios:
a) 1:3
b) 3:5
c) 6:7
3. Write the following ratios in their simplest forms
a) 12:8
b) 5:15
c) 28:7
4. The ratio on ward X of male patients to female patients is 2:5.
a) If there are 6 male patients, how many female patients are there?
b) If there are 20 female patients, how many male patients are there?
5. Medication Q is made up of solutions A, B and C.
To make 50 mg of the medication you need
10mL of A
20mL of B
5mL 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 100mg of Q how many mL of A, B and C would you
need?
c) There are 40mL 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) 2:6
b) 1:8
c)12:3
d) 2:3
19
Ratio Exercise – Answers
a) i) 5:2
c) i) 3:3 = 1:1
2. a)
ii) 2:5
ii) 3:3 = 1:1
b)
3. a) 3:2
4. a) 15 women
5. a) i) 10:20 = 1:2
b) 20mL of A
c) i) 200mg
6. a) A. 82  14
c) A.
b) i) 1:4
d) i) 3:2
12
15

4
5
ii) 4:1
ii) 2:3
c)
b) 1:3
b) 8 men
ii) 20:5 = 4:1
40mL of B
ii) 80mL of B
B. 86  34
B.
3
15

c) 4:1
iii) 5:10 = 1:2
10mL of C
20mL of C
b) A. 19
B. 89
1
5
d) A.
20
2
5
B.
3
5
Percentages
‘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:
100% of something means the whole amount. (Literally 100 per 100)
50% of something means that you are looking at half of it, as 50 is half of 100.
10% of something means that you are looking at a tenth of it as 10 is a tenth of 100.
We can work out percentages in many different ways. Two of the methods are
detailed below.
Method 1- Using Fractions
As percentages are closely linked to fractions, we can use this fact to help with our
calculations. We know that 50% means ‘50 out of a hundred’, so we can write this as
50
1
100 in the same way as we know that 1out of 2 can be written as 2 .
The following table shows the fraction form of some common percentages:
Percentage Fraction
100%
50%
25%
10%
5%
1%
Simplified
Fraction
100
100
50
100
25
100
10
100
5
100
1
100
1
1
2
1
4
1
10
1
20
1
100
You may wish to perform the cancelling down yourself to check the final column.
21
The general procedure for converting a percentage (say 15%) into a fraction is:

Write the percentage as a fraction of 100 i.e.

Cancel the fraction down to its simplest form. In this case we can divide top
and bottom by the common factor, 5.
3
When the fraction is in its simplest form, we are done. 15%= 20

15
100
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 10% of 50.
10% is the same as
So 10% of 50 =

501
10
1
10
1
10
(from the table).
×50
as we first multiply by the numerator.
50  5 as 50 and 10 have a common factor of 10
 10
1
=5
Example
Find 30% of 25.
30
3
30%= 100
 10
3
30% of 25 =25× 10

253
10
75
 10
As 75 and 10 have a common factor of 5, we can cancel the fraction down
75
10
 15
2
This is an improper fraction or top heavy fraction, so we convert it into a mixed
number.
=7
Method 2 - Using Decimals
As the number 1 is used to represent a whole, we can also use it to represent 100%.
We know that 50% is half of 100%, so 50% of 1 must be half of 1, which as a
decimal is 0.5.
The following table shows the decimal form of some common percentages:
Percentage
100%
50%
25%
Decimal
1
0.5
0.25
22
10%
5%
1%
0.1
0.05
0.01
The general procedure for converting a percentage (say 15%) into a decimal is:
 Take the numerical value of the percentage, in this case 15, and divide it by
100.
 So 15% = 0.15, 17% = 0.17, 37% = 0.37
Example
Find 10% of 50.
10÷100 = 0.1
so 10% of 50 = 0.1×50 = 5
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 decimal point 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 120lbs and is 6ft 1in
He is in hospital and cannot leave until he has increased his weight by 25%. How
much must he weigh before 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 currently weighs 120lbs.
We need to find 25% of 120
Method 1 - Fractions
25
 205  14 by cancelling
25%  100
1
4
× 120=30 so 25% of 120 is 30
His total weight will be
120+30=150
150 lbs
Method 2 - Decimals
25
 0.25
25%  100
0.25×120=30
His total weight will be
120+30=150
150 lbs
An alternative method is to notice that his total weight will be 100% of his original
weight + 25% of his original weight. So his eventual weight will be 125% of his
original weight.
This means that we can shorten the above calculations:
125

125%  100
25
20
 54 by
125
 1.25
125%  100
23
cancelling
5
4 × 120=150
His total weight will be 150 lbs
1.25×120=150
His total weight will be 150 lbs
Increasing by a percentage
Example
A patient weights 150 kg. They have a 12% weight gain. What is his new weight?
Method 1
Find out what 12% of 150 is and add that to the original weight.
12% =
= 0.12
And 0.12 x 150 = 18
So that 150 + 18 = 168
The patient’s new weight is 168 kg
Method 2
Notice that if we add 12% to the original
We now have 112%
1.12 x 150 = 168
As above the patient’s new weight is 168 kg
Decreasing by a percentage
Example
The dose of a drug given to a patient is to be reduced by 15%. If the patient had
been originally prescribed 300 mg of drug A what is the new dosage in mg?
Method 1
Find out what 15% of 300 is and subtract that from the original dose
15% =
= 0.15
And 0.15 x 300 = 45
24
So that 300 – 45 = 255
The new dosage is 255 mg
Method 2
Notice that if we reduce the dosage by 15%
We have 85% left
85% = 0.85
0.85 x 300 = 255
As above, the new dosage is 255 mg
Always check that your answer makes sense. A good check is to perform your
calculation in reverse, so if you’ve found 25% of something, multiply it by 4 and you
should have your original quantity back.
25
Percentages Exercise 1
1. Express as i) a fraction (simplify if possible), ii) a decimal
a) 20%
b) 30%
c) 45%
e) 9%
f) 12%
g) 84%
d) 95%
h) 29%
2. Using the method of your choice, evaluate the following:
a) 20% of 15
b) 30% of 10
c) 45% of 200
d) 95% of 100
e) 9% of 300
f) 12% of 50
g) 84% of 25
h) 29% of 300
3.
A baby’s weight has increased since
birth by 10%. When it was born it weighed 3kg. What is its new weight?
4.
A young adult’s height was measured
and found to be 1.3m. They grow by 10% over the next year. What is their new
height?
5.
A patient loses 7% of their body weight
after surgery. If they originally weighed 195 kg what is their new weight?
For extra help with Percentages consult Mathematics leaflets ‘Fractions, Decimals
and Percentages: how to link them’ and ‘Percentages’ available on the web at
www.hull.ac.uk/studyadvice
Percentages Exercise 1 - Answers
1. a)
e)
20
100
9
100
2. a) 3
e) 27
 102  15  0.2
 0.09
b)
f)
30
100

b) 3
f) 6
12
100
 103  0.3
6
50

3
25
c)
g)
 0.12
3. New weight is 3.3kg or 3300g
4. 1.43m
26
45
100

9
20
 
c) 90
g) 21
84
100
42
50
 0.45
21
25
 0.84
d)
h)
95
100
29
100
d) 95
h) 87
 19
20  0.95
 0.29
5. 181.35 kg
Percentage increase/decrease
We often need to find the percentage increase or decrease in a patient’s weight. To
do this we use the formula:
Change in Weight x 100
Original Weight
Example:
A patient who originally weighed 50kg loses 2 kg. What is her percentage weight
loss?
Her change in weight is 2 kg and her original weight is 50 kg.
So we have 2_ x 100 = 4
50
This represents a 4% weight loss.
A patient who originally weighed 125 kg now weighs 135 kg. What is his percentage
weight gain?
Here the change in weight is 10 kg and the original weight is 125 kg.
So that we have 10__ x 100 = 8
125
This represents an 8% weight gain.
27
Percentages Exercise 2
Find the weight gain/loss of the following patients.
a) Weight originally 80 kg, final weight
92 kg
b) Weight originally 60 kg, final weight
63 kg
c) Weight originally125 kg, final weight
120 kg
d) Weight originally 200 kg, final weight
195 kg
e) Weight originally 250 kg, final weight
245 kg
Percentages Exercise 2 – Answers
a)15% weight increase
b) 5% weight increase
c) 4% weight decrease
d) 2.5% weight decrease
e) 2% weight decrease
28
Body Mass Index (BMI)
The BMI provides a simple numeric measure of a person’s ‘fatness’ or ‘thinness’
which allows healthcare professionals to discuss over and underweight problems
objectively.
The current settings are:
BMI < 20 – Underweight
20 < BMI < 25 – Optimum weight
25 < BMI < 30 – Overweight
BMI > 30 – Obese
BMI > 40 – Morbidly obese
BMI is calculated by dividing the person’s weight (in Kg) by their height 2 (in metres).
The formula is written W
H2
Example
Find the BMI of a patient who weighs 75 kg and is 1.42 m tall
BMI = 75 / (1.42 x 1.42) = 34.72
To the nearest whole number this is 35, therefore this patient is in the obese range.
Find the BMI of a patient who weighs 93 kg and is 1.95m tall
BMI = 93 / (1.95 x 1.95) = 24.46
To the nearest whole number this is 24, therefore this patient is in the optimum
weight range.
Body Mass Index Exercise with answers
Find the BMI of the following patients to the nearest whole number
a) Weight 80 kg, height 1.83m
b) Weight 115 kg, height 2.00m
c) Weight 78 kg, height 1.54m
(24)
(29)
(33)
d) Weight 62 kg, height 1.8m
e) Weight 132 kg, height 1.64m
29
(19)
(49)
Averages
The average or the mean of a set of numbers is just the value you get after adding
the set of numbers up and dividing by how many numbers you have.
Examples
1. Find the average of 2, 6, 4, 8, 5
2+6+4+8+5 = 25
=5
The average is 5
2. If a patient’s oral fluid intake on successive days is 120 mL, 200 mL 140 mL
and 260 mL, what was the average intake over 4 days?
120+200+140+260 = 720
= 180
The average intake is 180 mL
Averages Exercise
1. A patient’s pulse was taken every 30 minutes over 2 hours
It was found to be 110, 105, 95 and 90
What is the average pulse rate over the 2 hours?
2. A patient’s temperature was taken every 30 minutes over 4 hours.
It was 38°C, 38°C, 38.5°C, 39.1°C, 38.4°C, 38.1C°, 37.4°C, and 42.1°C
What is the average temperature over:
a) The first two hours
b) The second two hours
Averages Exercise
1. 100
2. a) 38.4°C
b) 39.0°C
30
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
Kilogram
Gram
Milligram
Microgram
Nanogram
Abbreviation
kg
g
mg
mcg
ng
Notes
Approx. the weight of a litre of water
One thousand grams to a kilogram
One thousand mg to the gram
One million mcg to the gram
One thousand ng to the mcg
Conversion Chart
Number of
Kilograms
÷1000
x 1000
Number of
Grams
÷1000
x 1000
Number of
Milligrams
÷1000
x 1000
Number of
Micrograms
÷1000
x 1000
Number of
Nanograms
31
As we move down the
diagram the arrows are
on the right and we
move the decimal point
three places to the right.
As we move up the
diagram the arrows are
on the left and we move
the decimal point three
places to the left.
Metric Measurements of Liquids
Name
Litre
Millilitre
Abbreviation
Notes
L
An upper case L
mL
One thousand millilitres to a
litre
Conversion Chart
Number of
Litres
÷1000
x 1000
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 10mL. Centilitres are normally used to measure
wine.
DO NOT USE A LOWER CASE L AS AN ABBREVIATION FOR LITRES. There is a
chance of misreading 3l as thirty one (31) when it should be 3L. Always use L even
in mL!
Examples
1. Convert 575 millilitres into litres.
From the diagram, we see that to convert millilitres to litres, we divide the number of
millilitres by 1000.
So we have 575÷1000=0.575 litres
2. Convert 2.67 litres into millilitres.
To convert litres to millilitres we multiply the number of litres by 1000.
So we have 2.67×1000=2670 millilitres
Estimation
Always look at the answers you produce to check they are sensible. A good way to
do this is to estimate the answer.
32
In Example 1 above we can use our knowledge of litres and millilitres to estimate the
result. We have 575 millilitres. If we had 1000 millilitres we would have a litre. Half a
litre would be 500 millilitres, so our result will be a little over half a litre.
Conversions of lbs ⇾ kg, kg ⇾ lbs
It is sometimes necessary to change from imperial units to metric units and vice
versa. The method is shown below:
Weights in kg x 2.2 = weights in pounds.
A patient weighs 124 kg, what is this in pounds (lbs)?
124 x 2.2 = 272.8 lbs
Weights in pounds ÷ 2.2 = weights in kg.
A patient weighs 212 lbs, what is this in kg?
212 ÷ 2.2 = 96.37 (2dp) kg
33
Unit Conversion Exercise 1
1. Copy and complete the following, using the tables and diagrams
a) 1 kilogram = ____ grams
b) 1 gram = ____ milligrams
c) 1 gram = ____ micrograms
d) 1 microgram = ____ nanograms
e) 1 litre = ____ millilitres
2. Convert the following into milligrams
a) 6 grams
b) 26.8 grams
c) 3.924 grams
d) 405 grams
3. Convert the following into grams
a) 1200mg
b) 650mg
c) 6749mg
d) 3554mg
4. Convert the following into milligrams
a) 120 micrograms b) 1001 micrograms
d) 12034 mcg
c) 2675 micrograms
5. Convert the following: (you may find it easier to work out the answers in two
stages):
a) 1.67grams into micrograms
b) 0.85grams into micrograms
c) 125 micrograms into grams
d) 6784 micrograms into grams
e) 48.9 milligrams into nanograms f) 3084 nanograms into milligrams
6. Convert the following into litres
a) 10 millilitres
b) 132 millilitres
c) 2389 millilitres
d) 123.4 millilitres
7. Convert the following into millilitres
a) 4 litres
b) 6.2 litres
c) 0.94 litres
d) 12.27 litres
8. A patient needs a dose of 0.5 g of medicine A. They have already had 360mg.
a) How many more mg do they need?
b) What is this value in grams?
c) A dose of 1400 mcg has been prepared. Will this be enough?
34
Unit Conversion Exercise 1 - Answers
1 a) 1kg=1000g
d) 1 mcg=1000ng
b) 1g=1000mg
e) 1 litre=1000Ml
c) 1g=1000000mcg
2 a) 6g=6000mg
b) 268g=26.800mg
d) 405g=405000mg
3 a) 1200mg=1.2g
d) 3554mg=3.554g
b) 650mg=0.65g
c) 3.924g=3924mg
c) 6749mg=6.749g
4 a)120mcg=0.12mg b) 1001mcg=1.001mg c)2675 mcg= 2.675mg
d) 12034mcg=12.034mg
5 a) 1.67g=1670000mcg
c) 125 mcg=0.000125g
e) 48.9mg=48900000ng
b) 0.85g=850000mcg
d) 6784mcg=0.006784g
f) 3084ng=0.003084mg
6 a) 10mL=0.01litres
b) 132mL=0.132litres
d) 123.4mL=0.1234 litres
c) 2389mL=2.389litres
7 a) 4litres=4000mL
b) 6.2litres=6200mL
d) 12.27litres=12270mL
c) 0.94litres=940mL
8 a) 140 milligrams
b) 0.14 grams
c) no, the correct dose would be 140000mcg
35
Dosage Calculations
Working out a dosage in either tablets or liquids is straightforward. The formula used
is always the same.
What you want x What it’s in
What you’ve got
When working with tablets what it’s in is always one tablet.
To calculate a dosage you must write down 3 numbers.
They are:
What you want – this is what is prescribed/ordered/required/needed by the patient.
What you have got – this is what is available.
What it’s in – this is either 1 when we are working with tablets or in mL when working
with liquids.
The order in which you write these down is not difficult to remember, if you think ‘The
patient always comes first’ ie. What you want.
Note: In order to use this formula, the units of ‘What you want’ and ‘What you’ve
got’ must be the same, ie. both in mcg, or both in mg, or both in g.
Examples
1. A patient needs 500mg of drug X per day. X is available in 125mg tablets. How
many tablets per day does he need to take?
What you want = 500mg
What you’ve got = 125mg
What it is in = one tablet
}
}
The units are both the same
So our calculation is
x1=4
The patient needs 4 tablets a day.
2. We need a dose of 500mg of Y. Y is available in a solution of 250mg per 50mL.
In this case,
What you want = 500mg } both in mg
36
What you’ve got = 250mg }
What it’s in = 50mL
So our calculation is
500 ×
250
50 =100
We need 100mL of solution.
3. We need a dose of 250mg of Z. Z is available in a solution of 400mg per 200mL.
In this case,
What you want = 250mg } both in mg
What you’ve got = 400mg }
What it’s in = 200mL
So our calculation is
250 ×
400
200 = 125
We need 125mL of solution.
4. A patient is prescribed 250mg of erythromycin IV.
Stock on hand contains 1g in 10mL once diluted.
What you want = 250mg
What you’ve got = 1g
What it’s in = 10mL
The units of What you want are mg and the units of What you’ve got are g. They
must be the same units.
Both in mg
1g = 1000mg
So:
What you want = 250mg
What you’ve got = 1000mg
What it’s in = 10mL
Both in g
250mg = 0.25g
Our calculation is
250 x 10 = 2.5
1000
We need 2.5mL
Our calculation is
0.25 x 10 = 2.5
1
We need 2.5mL
= 0.25g
=1g
=10mL
Medicine over Time
Tablets/liquids
This differs from the normal calculations in that we have to split our answer for the
total dosage into 2 or more smaller doses.
Example A child weighing 12.5kg is prescribed a drug which is to be given in four
equally divided doses. The dosage the child requires is 100mg/kg body weight.
The child requires 12.5 x 100mg = 1250mg of the drug.
37
So for four equally divided doses
1250 = 312.5
4
They need 312.5mg four 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
A patient is receiving 500mg of medicine X over a 20 hour period.
X is delivered in a solution of 10mg per 50mL.
What rate should the infusion be set to?
Here our total dosage required is 500mg
Period of time is 20 hours
There are 10mg of X per 50mL 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:
500
10 ×50=2500 so the patient needs to receive 2500mL.
We now divide the amount to be given by the time to be taken:
2500
20
=125
The patient needs 2500mL to be given at a rate of 125mL per hour
Note: Working out medicines over time can appear daunting, but all you need to do
is work out how much medicine is needed in total, and then divide it by the amount of
doses needed or the time over which it is to be given.
Drugs labelled as a percentage
Some drugs may be labelled in different ways from 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 15% V/V means for every 100mL of solution, 15mL 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 15% W/V means that for every 100mL of solution there are
15 grams of the drug.
38
If we are converting between solution strengths, such as diluting a 20% solution to
make it a 10% solution, we do not need to know whether the solution is V/V or W/V.
Examples
1. We need to make up 1 litre of a 5% solution of A. We have stock solution of 10%.
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 5% solution. This is the same as
5
100
We’ve got a 10% solution. This is the same as
or 201 .
10
100
or
1
10
.
We want our finished solution to have a volume of 1000mL.
Our formula becomes
1
20
1
10
×1000
= 201 × 101 ×1000 (using the rule for dividing fractions)
= 12 ×1000=500 . We need 500mL of the A solution.
Which means we need 1000-500=500mL of water.
(Alternatively you can use the fact that a 5% solution is half the strength of a 10%
solution to see that you need 500mL of solution and 500mL of water)
2. You have a 20% V/V solution of drug F. The patient requires 30mL of the drug.
How much of the solution is required?
20% V/V means that for every 100mL of solution we have 20mL of drug F.
Using our formula:
What you want × What it’s in
What you’ve got
This becomes
30
20
×100=150
We need 150mL of solution.
3. Drug G comes in a W/V solution of 5%. The patient requires 15 grams of G. How
many mL of solution are needed?
39
5% W/V means that for every 100mL of solution, there are 5 grams of G.
Using the formula gives us
15
5 ×100=300
300mL 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.
Dosage Calculations Exercise 1
1. How many 30mg tablets of drug B are required to produce a dosage of:
a) 60mg
b) 120mg
c) 15mg
d) 75mg
2. Medicine A is available in a solution of 10mg per 50mL. How many mL are needed
to produce a dose of:
a) 30mg
b) 5mg
c) 200mg
d) 85mg
3. Medicine C is available in a solution of 15 micrograms per 100mL. How many mL
are needed to produce a dose of:
a)150mcg
b) 45mcg
c)30mcg
d) 75mcg
4. Medicine D comes in 20mg tablets. How many tablets are required in each dose
for the following situations:
a) total dosage 120mg , 3 doses b) total dosage 60mg, 2 doses
c) total dosage 100mg, 5 doses d) total dosage 30mg, 3 doses
5. At what rate per hour should the following infusions be set?
a) Total dosage 300mg, solution of 25mg per 100mL, over 12 hours
b) Total dosage 750mg, solution of 10mg per 30mL, over 20 hours
c) Total dosage 450mg, solution of 90mg per 100mL, over 10 hours
6. Drug B comes in a 20% V/V stock solution.
i) How much of the solution is needed to provide:
a) 50mL of B
b) 10mL of B
c) 200mL of B
ii) How would you make up the following solutions from the stock solution?
a) Strength 20% volume 1 litre
b) Strength 10% volume 750mL
iii) What strength are the following solutions?
a) Volume 1 litre, made up of 600mL stock solution, 400mL water
b) Volume 600mL, made up of 300mL stock solution, 300mL water
7. Drug C comes in a 15% W/V stock solution.
i) How much of the solution is needed to provide:
40
a) 30g of C
b) 22.5g of C
c) 90g of C
ii) How would you make up the following solutions from the stock solution?
a) Strength 5% volume 900mL
b) Strength 10% volume 750mL
iii) How many grams of C are in the following solutions?
a) Volume 1 litre, made up of 400mL stock solution, 600mL water
b) Volume 800mL, made up of 450mL stock solution, 350mL water
Dosage Calculations Exercise 1 – Answers
1. a) 2 tablets
b) 4 tablets
c)
1
2
tablet
d)
2 12 tablets
2. a) 150mL
b) 25mL
c) 1000mL
d) 425mL
3. a) 1000mL
b) 300mL
c) 200mL
d) 500mL
4. a) 2 tablets
b) 1 12 tablets
c) 1 tablet
d)
5. a) 100mL per hour
b) 112.5 mL per hour
1
2
tablet
c) 50mL per hour
6. i) a) 250mL
b) 50mL
ii) a) 1 litre stock, no water
iii) a) 600mL stock contains 120mL B
120
So 120mL in 1000mL= 1000
=12%
c) 1 litre
b) 375mL stock, 375mL water
b) 300mL stock contains 60mL B
60
So 60mL in 600mL= 600
=10%
7. i) a) 200mL
b) 150mL
ii) a) 300mL stock, 600mL water
iii) a) 60g
b) 67.5g
c) 600mL
b) 500mL stock, 250mL water
Dosage Calculations Exercise 2
A drug is available in 1 mg, 2 mg, 5 mg and 10 mg tablets.
What is the best combination of these (i.e. the smallest number of tablets) to give the
following dosages?
Dosage
1
3 mg
2
7 mg
3
8 mg
4
10mg
5
11 mg
Tablets required
Number of tablets
41
6
14 mg
Dosage Calculations Exercise 2 – Answers
Tablets
required
Number of
tablets
Tablets
required
Number of
tablets
1
1 mg & 2
mg
2
2
2 mg & 5
mg
2
3
1 mg, 2
mg & 5
mg
3
4
5 mg & 5
mg
2
5
5 mg, 5
mg & 1
mg
3
6
5 mg, 5
mg, 2 mg
& 2 mg
4
Dosage Calculations Exercise 3
1. A solution contains furosemide (frusemide) 10 mg/mL. How many milligrams of
frusemide are in
a 2 mL
b 3 mL
c 5 mL of the solution?
2. A solution contains morphine hydrochloride 2 mg/mL. How many milligrams of
morphine hydrochloride are in
a 3 mL
b 5 mL
c 7 mL of the solution?
3. Another solution contains morphine hydrochloride 40 mg/mL. How many
milligrams of morphine hydrochloride are in
a 2 mL
b 5 mL
c 10 mL of this solution?
4. A suspension contains phenytoin 125 mg/5 mL. How many milligrams of
phenytoin are in
a 20 mL
b 30 mL
c 40 mL of the suspension?
42
5. A solution contains fluoxetine 20 mg/5 mL. How many milligrams of fluoxetine
are in
a 10 mL
b 25 mL
c 40 mL of the solution?
6. A suspension contains erythromycin 250 mg/5 mL. How many milligrams of
erythromycin are in
a 10 mL
b 20 mL
c 30 mL of the suspension?
7. A syrup contains chlorpromazine 25 mg/5 mL. How many milligrams of
chlorpromazine are in
a 10 mL
b 30 mL
c 50 mL of the syrup?
8. A mixture contains penicillin 250 mg/5 mL. How many milligrams of penicillin are
in
a 15 mL
b 25 mL
c 35 mL of the mixture?
Dosage Calculations Exercise 3 – Answers
All answers are in mg
1
a)
20
b)
30
c)
50
2
a)
6
b)
10
c)
14
3
a)
800
b)
200
c)
400
4
a)
500
b)
750
c) 1000
5
a)
40
b)
100
c)
6
a)
500
b)
1000
7
a)
50
b)
150
8
a)
750
b)
1250
160
c) 1500
c)
250
c) 1750
43
Dosage Calculations Exercise 4
In each example, you are given the prescribed dosage and the strength of stock on
hand. Calculate the volume to be given:
1. Ordered: penicillin 500 mg
On hand: syrup 125 mg/5 mL
2. Ordered: furosemide (frusemide) 40 mg
On hand: solution 10 mg/mL
3. Ordered: morphine hydrochloride 100 mg
On hand: solution 40 mg/mL
4. Ordered: paracetamol 180 mg
On hand: suspension 120 mg/5 mL
5. Ordered: phenytoin 150 mg
On hand: suspension 125 mg/5 mL
6. Ordered: erythromycin 1250 mg
On hand: suspension 250 mg/5 mL
7. Ordered: fluoxetine 30 mg
On hand: solution 20 mg/5 mL
8. Ordered: penicillin 1000 mg
On hand: mixture 250 mg/5 mL
9. Ordered: chlorpromazine 35 mg
On hand: syrup 25 mg/5 mL
10. Ordered: penicillin 1200 mg
On hand: mixture 250 mg/5 mL
11. Ordered: erythromycin 800 mg
On hand: mixture 125 mg/5 mL
Dosage Calculations Exercise 4 - Answers
All answers are in mL
1.
20
5.
6
9.
7
2.
4
6.
25
10.
24
3. 2.5
7. 7.5
11.
32
4. 7.5
8.
20
44
Dosage Calculations Exercise 5
Dosages of oral medications
1. A patient is ordered paracetamol 1 g, orally. Stock on hand is 500 mg tablets.
Calculate the number of tablets required.
2. Ordered: codeine 15 mg, orally. Stock on hand: codeine tablets, 30 mg. How
many tablets should the patient take?
3. A patient is ordered furosemide (frusemide) 60 mg, orally. In the ward are 40
mg tablets. How many tablets should be given?
4. How many 30 mg tablets of codeine are needed for a dose of 0.06 gram?
5. 750 mg of ciprofloxacin is required. On hand are tablets of strength 500 mg.
How many tablets should be given?
6. A patient is prescribed 150 mg of soluble aspirin. On hand we have 300 mg
tablets. What number should be given?
7. 450 mg of soluble aspirin is ordered. Stock on hand is 300 mg tablets. How
many tablets should the patient receive?
8. 25 mg of captopril is prescribed. How many 50 mg tablets should be given?
9. The stock on hand of diazepam is 5 mg tablets. How many tablets are to be
administered if the order is diazepam 12.5 mg?
10. Digoxin 125 mcg is ordered. Tablets available are 0.25 mg. How many
tablets should be given?
Check that you have used the same unit of weight throughout a calculation.
Are both weights in milligrams (mg)? Or are both weights in micrograms
(mcg)?
45
Dosage Calculations Exercise 5 - Anwers
All answers are in tablets
1.
2
5.
2.
1
6.
3.
1
7.
4.
2
8.
9.
1
or 0.5
1
or 0.5
46
10.
or 0.5
Dosage Calculation Exercise 6
Calculate the volume of stock required. Give answers greater than 1 mL correct to
one decimal place; answers less than 1 mL correct to two decimal places.
Ordered
Stock ampoule
1. Morphine
12 mg
15 mg/mL
2. Calciparine
7000 units
25 000 units in 1 mL
3. Benzylpenicillin
1500 mg
1.2 g in 10 mL
4. Heparin
3000 units
5000 units/mL
5. Phenobarbitone
70 mg
200 mg/mL
6. Pethidine
80 mg
100 mg/2 mL
7. Buscopan
0.24 mg
0.4 mg/2mL
8. Digoxin
200 mcg
500 mcg in 2 mL
9. Furosemide (frusemide)
150 mg
250 mg in 5 mL
10. Ondansetron
5 mg
4 mg in 2 mL
11. Capreomycin
800 mg
1 g in 5 mL
12. Tramadol
120 mg
100 mg in 2 mL
13. Gentamicin
70 mg
80 mg in 2 mL
14. Vancomycin
800 mg
1 g in 5 mL
15. Morphine
7.5 mg
10 mg in 1 mL
16. Ceftriaxone
1250 mg
1 g/3 mL
17. Buscopan
25 mg
20 mg in 1 mL
18. Dexamethasone
3 mg
4 mg/mL
19. Vancomycin
1.2 g
1000 mg/5 mL
20. Naloxone
0.5 mg
0.4 mg/mL
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Dosage Calculations Exercise 6 – Answers
All answers are in mL
1.
0.8
6.
1.6
11.
4
16.
3.8
2.
0.28
7.
1.2
12.
2.4
17.
1.3
3.
12.5
8.
0.8
13.
1.8
18.
0.75
4.
0.6
9.
3
14.
4
19.
6
5.
0.35
10.
2.5
15.
0.75
20.
1.3
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Dosage Calculations Exercise 7
Calculate the volume of stock to be drawn up for injection.
1. Pethidine 60 mg is ordered. Stock ampoules contain 100 mg in 2 mL.
2. An adult is ordered metoclopramide 15 mg, for nausea. On hand are ampoules
containing 10 mg/mL.
3. A patient is prescribed erythromycin 250 mg, I.V. Stock on hand contains 1 g in
10 mL, once diluted.
4. Tramadol hydrochloride 80 mg is required. Available stock contains 100 mg in 2
mL.
5. A patient is ordered benzylpenicillin 800 mg. On hand is benzylpenicillin 1.2 g in
6 mL.
6. An adult patient with TB is to be given 500 mg of capreomycin every second day,
I.M.I. Stock on hand contains 1 g in 3 mL.
7. Digoxin ampoules on hand contain 500 mcg in 2 mL. Digoxin 150 mcg is
ordered.
8. Stock Calciparine contains 25 000 units in 1 mL. 15 000 units of Calciparine are
ordered.
9. Penicillin 450 mg is ordered. Stock ampoules contain 600 mg in 5 mL.
Dosage Calculations Exercise 7 - Answers
All answers are in mL
1. 1.2
4. 1.6
7. 0.6
2. 1.5
5. 4
8. 0.6
3. 2.5
6. 1.5
9. 3.75 (3.8 to 1dp)
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Dosage Calculations Exercise 8
1. An injection of morphine 8 mg is required. Ampoules on hand contain 10 mg in 1
mL. What volume is drawn up for injection?
2. Digoxin ampoules on hand contain 500 mcg in 2 mL. What volume is needed to
give 350 mcg?
3. A child is ordered 9 mg of gentamicin by I.M.I. Stock ampoules contain 20 mg in
2 mL. What volume is needed for the injection?
4. A patient is to be given flucloxacillin 250 mg by injection. Stock vials contain 1 g
in 10 mL, after dilution. Calculate the required volume.
5. Stock heparin has a strength of 5000 units per mL. What volume must be drawn
up to give 6500 units?
6. Pethidine 85 mg is to be given I.M. Stock ampoules contain pethidine 100 mg in 2
mL. Calculate the volume of stock required.
7. A patient is to receive an injection of gentamicin 60 mg, I.M. Ampoules on hand
contain 80 mg/2 mL. Calculate the volume required.
8. A patient is prescribed naloxone 0.6 mg, I.V. Stock ampoules contain 0.4 mg/2
mL. What volume should be drawn up for injection?
Think about each answer. Does it make sense? Is it ridiculously large?
Dosage Calculations Exercise 8 - Answers
All answers are in mL
1. 0.8
4. 2.5
7. 1.5
2. 1.4
5. 1.3
8. 3.0
3. 0.9
6. 1.7
50
Suggested Reading
Drug Calculations for Nurses-A Step By Step Approach
Robert Lapham and Heather Agar
ISBN 0-340-60479-4
Nursing Calculations Fifth Edition
J.D. Gatford and R.E.Anderson
ISBN 0-443-05966-7
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.
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 Skills Adviser by email at skills@hull.ac.uk
The information in this leaflet can be made available in an alternative format on
request using the email above.
51