Numeracy –
The Essentials
Tips to help you study effectively
Learning Development Service
Queen’s University Belfast
The following guide will provide an overview of the basic numeracy skills required for Nursing and
Midwifery students.
The Learning Development Service have created an online interactive resource to equip you with essential
numeracy skills and help you with exam preparation. Each section has a multimedia presentation followed
by randomly generated questions for you to practise; you may also check correct answers and past papers,
solutions and mock exams.
The e-learning resource is available via the LDS website, by googling “Qub numeracy”, or directly
accessing: www.qub.ac.uk/elearning/public/NumeracySkillsforDrugCalculations/
If you require any additional assistance, free one-to-one appointments are available by contacting the
Learning Development Service: [email protected], 028 9097 3618, www.qub.ac.uk/lds.
We wish you all the very best in your studies and for your time here at Queen’s.
CONTENTS
1. Place Value......................................................................................................................................................... 2
2. Times Tables...................................................................................................................................................... 3
3.Addition.............................................................................................................................................................. 4
4.Multiplication..................................................................................................................................................... 4
5.Subtraction......................................................................................................................................................... 5
6.Division............................................................................................................................................................... 5
7. Combined Functions......................................................................................................................................... 6
8. Converting Weights.......................................................................................................................................... 6
9. Fractions & Decimals ....................................................................................................................................... 7
10.Basic Drug Calculations .................................................................................................................................. 7
11.Percentages ..................................................................................................................................................... 8
12. Sample Paper ................................................................................................................................................... 9
Learning Development Service – 2012/13 1 1.
Place value
x 10
H
T
U
.
t
h
12 3. 45
÷ 10
In any number each digit has a different place value. Going
from left to right we have Hundreds, Tens, Units, tenths, and
hundredths.
There are 10 hundredths in 1 tenth,
10 tenths in 1 unit,
10 units in 1 ten, and
10 tens in 1 thousand
hundred
The numbers AFTER a decimal point represent a fraction of 1
To multiply a number by 10 move the decimal point to the right.
To divide a number by 10 move the decimal point to the left.
Example: if we multiply the following number by 10
HT U. t h
23. 45
it becomes:
HT U. t h
234. 5
Note what has happened to the decimal point. From 23.45 it has
become 234.5, moving 1 place to the right.
You may need to ‘add zeros’ to the left of the number or after the decimal point before moving the decimal
point:
1234 x 10 = 1234.0 x 10 = 12340
Add a zero
0.22 ÷ 10 = 00.22 ÷ 10 = 0.022
The decimal point moves The decimal point moves The decimal point moves 1
2
3
place to the right when multiplying by places to the right when multiplying by places to the right when multiplying by 10
100
1000
The decimal point moves The decimal point moves The decimal point moves 1
2
3
place to the left places to the left places to the left 10
100
1000
when dividing when dividing
when dividing
If you find this difficult to remember, then think of L for less, L for Left.
123.3 x 1000 = 123.30000 x 1000 = 123300.00 = 123300
Add as many zeros as you like
2 Numeracy – The Essentials
by by by Ordering Numbers
To determine the highest number, line up the decimal points, then start from the left and go through
each place value selecting the highest digit(s) until just one number is left.
1 5 . 1 8
1 5 . 1 8
1 4 . 9 4
14 .94
15.3
1 5. 3
1 4 . 0 9
14.09
1 5 . 1 8
1 5 . 3
15.3 is the highest number
Examples to try; find the lowest number in the following questions:
(1) (i) 87.87
(2)
(i) 0.23
(3) (i) 624.01
(ii) 87.97
(ii) 0.2
(ii) 642.01
(iii) 88.07
(iii) 0.32
(iii) 624.0
(iv) 88.1(iv) 0.3(iv) 624.1
2. Times Tables
X
1
2
3
4
5
6
7
8
9
10
11
12
1
1
2
3
4
5
6
7
8
9
10
11
12
2
2
4
6
8
10
12
14
16
18
20
22
24
3
3
6
9
12
15
18
21
24
27
30
33
36
4
4
8
12
16
20
24
28
36
36
40
44
48
5
5
10
15
20
25
30
35
40
45
50
55
60
6
6
12
18
24
30
36
42
48
54
60
66
72
7
7
14
21
28
35
42
49
56
63
70
77
84
8
8
16
24
32
40
48
56
64
72
80
88
96
9
9
18
27
36
45
54
63
72
81
90
99
108
10
10
20
30
40
50
60
70
80
90
100
110 120
11
11
22
33
44
55
66
77
88
99
110
121 132
12
12
24
36
48
60
72
84
96
108
120
132 144
TIPS
Learning your times tables off now will help prepare you for future nursing calculations exams.
5 times tables always end in either 5 or 0
You can use your fingers for 9 times tables:
•
•
•
•
Hold your hands in front of you with your fingers spread out.
For 9 X 3 bend your third finger down (9 X 4 would be the fourth finger etc.)
You have 2 fingers in front of the bent finger and 7 after the bent finger
Thus the answer must be 27!
One of the best interactive web resources for times tables is BBC Skillswise:
http://www.bbc.co.uk/skillswise/game/ma13tabl-game-tables-grid-find
Examples to try; using the table above, calculate the following:
(1) 9 x 8 (2) 7 x 12
(3) 6 x 9
(4) 4 x 7
(5) 5 x 11 (6) 3 x 8
(7) 11 x 12
Learning Development Service – 2012/13 3 3.Addition
• Line up the decimal points directly above each other, keep the decimal point in the answer
in the same place.
• If you get a number greater than 10 then write down the number of units and carry the
number of tens over to the next column on the left.
e.g.
8 9
+ 11 5
10 4
9 + 5 = 14
write down 4 and carry the 1 over
A patient is given 1300 units of I.V. fluids and 275 units of oral fluids. Find out how many total
units were given?
1300
+ 27 5
1575
Examples to try:
(1)
(2)
37.4
+ 78.9
(3)
1344
+ 385
+ 7 .9
1250
100
+
45
Keep decimal
point in same
place
More questions to try:
(4) 37.4 + 78.9
(7) 2301.65 + 145.201
(5) 285.6 + 568.4
(8) 1404 + 501.01
(6) 123.58 + 1458.42
(9) 12.58 + 56.89
4.Multiplication
• Ignore the decimal point until the end. The rule is that you count the number of decimal
places in your question and apply the same number to the answer.
• Carry over tens as before.
• If multiplying by a number with two or more digits, treat them separately, remembering to
put one zero on the far right column when multiplying by tens, two zeros for hundreds etc.
Example 1:
4.2
x 8 1
4 2
3 3 6 0
3 4 0. 2
4 Numeracy – The Essentials
one zero is put down when multiplying by the 8
since there is one decimal place in the question, there should be one
decimal place in the answer.
Example 2:
4 4. 6 2
x 3.7
31234
133860
1 6 5.0 9 4
2 numbers after the decimal point here
1 number after the decimal point here
We need 2 + 1 = 3 numbers after the decimal point in the answer
Exercises
(1) A patient is to receive 2.5 micrograms per kilogram. What dose is required if the patient weighs
79 kilograms?
(2) If one tablet contains 20 milligrams, how many milligrams would 4 tablets contain?
(3) If one tablet contains 20.5 milligrams, how many milligrams would 8 tablets contain?
(4) A patient is to receive 1.6 micrograms per kilogram. What dose is required if the patient weighs
79.5 kilograms?
(5) A patient is to receive 2.05 micrograms per kilogram. What dose is required if the patient weighs
58.8 kilograms?
5.Subtraction
• Keep the decimal point in the same place.
• Borrow 1 from the column on the left if necessary.
e.g.
7 112 . 16
- 2 4 . 9
4 7 . 7
6
Examples to try:
(1) What is the difference between 1.6 kg and 0.825 kg?
(2) Clare weighed 4.85 kg at birth. By week 3 her weight had dropped to 3.8 kg. How much weight
had she lost?
(3) Jonny weighed 4500g at birth. By week 3 her weight had dropped to 3526 g. How much weight
had she lost?
6.Division
• Keep the decimal point in the same place.
• Divide into each digit in turn, from left to right.
• Carry over the remainder to the next digit.
• Fractions are just another way of writing division. The following are all the same:
666 divided by 7 = 666 ÷ 7 =
666
7
=
7 666
=
7 666
Simplifying fractions
• Express a fraction in its simplest form by dividing top and bottom by the same number, for
example if we have: 3 this can be simplified by dividing top and bottom by 3 to give us: 1
9
3
Learning Development Service – 2012/13 5 • Simplify fractions by halving (if even), or try dividing by 3, 5, or 7. This should reduce the need for
long division. It is almost always easier to simplify the fraction as much as possible before dividing.
45
9
3
=
=
= 3
15
3
1
• You can always remove the same number of zeroes from the end of the number on top and
bottom. This is the same as dividing top and bottom by 10:
300
3
=
2500
25
• If the bottom number is a decimal you should remove this by multiplying top and bottom numbers
by 10:
36
360
=
1.2
12
• In drug calculations and percentage calculations it is almost always easier to simplify the fraction
as much as possible before doing the division or multiplication.
Examples to try:
(1) 225 ÷ 6
(4) 1235 ÷ 5
(7) 251 ÷ 9
(2) 1500 ÷ 250
(3) 1000 ÷ 8
(10) 1298 ÷ 8.1
(13) 245 ÷ 2.5
(5) 1080 ÷ 8
(6) 568 ÷ 7
(11) 598 ÷ 4.9
(14) 354 ÷ 2.4
(8) 357 ÷ 2
(9) 1224 ÷ 8
(12) 8940 ÷ 450
(15) 980 ÷ 2.7
7.Combined
A baby is to be fed 75mL every 3 hours. How much is this per day?
24 ÷ 3 = 8
8 x 75 = 600mL
Examples to try:
(1)
(2)
(3) (4) (5) If 5mL contains 100mg, how many milligrams would there be in 20mL?
If a patient is to receive 1500ml over 24hrs, how much is this in mL/hr?
A patient is to receive 1000mL over 8 hours. Calculate the rate in mL/hour?
If a patient is to receive 750mL over 5 hours. Calculate the rate in mL/min?
A baby is to be fed 100mL every 4 hours. How much is this per day?
8. Converting weights
The following diagram can help remind you whether to multiply or divide.
Put in order from smallest to largest, and then draw an arrow up with x 1000 beside it, and an arrow
down with ÷ 1000 beside it.
÷ 1000
nanograms
micrograms
milligrams
x 1000
grams
kilograms
to convert milligrams to micrograms, multiply by 1000
to convert grams to kilograms divide by 1000
6 Numeracy – The Essentials
e.g. 568 milligrams to grams = 568 ÷ 1000 (move 3 d.p. to left) = 0.568 grams
Examples to try:
(1) Convert 360 micrograms to mg
(2) Convert 500 mL to L
(3) Convert 70.5 mg to g
(4) Convert 1.08 kg to g
(5) Convert 390 g to kg.
(6) Convert 500 micrograms to mg.
(7) Convert 40 mL to L.
(8) Convert 55 L to mL.
9. Fractions and decimals
Learn the following fractions:
1/10 = 0.1
1/5 = 0.2
1/4 = 0.25
1/3 = 0.33
1/2 = 0.5
Therefore
6/10 = 6 x 0.1 = 0.6
4/5 = 4 x 0.2 = 0.8
3/4 = 3 x 0.25 = 0.75
2/3 = 2 x 0.33 = 0.66
Sometimes it is useful to convert to a decimal before calculating, here are 2 ways of doing the same
question:
Question: Find two fifths of 250.
Answer 1:
2
2
250
500
100
of 250 =
×
=
=
= 100
5
5
1
5
1
Answer 2:
2
= 0.4
5
so two fifths of 250 is the same as 250 x 0.4:
250
2
x 0.4
1000 of course both methods give the same answer.
0000
100.0
When rounding a number to one decimal place, look at the second decimal point and if it is 5 or
above then round up, if less than 5 then keep it the same.
For example: 1.274 = 1.3
1.234 = 1.2
Examples to try:
(1) Find 4/10 of 42
(4) 3.333
(2) Find ¾ of 420
(5) 0.657
(3) Find 1/3 of 39.6
(6) 23.97
[Write q 4, 5 & 6 correct to 1d.p.]
10. Basic drug calculations
Use the following formula:
Dose required
Volume
×
Dose available
1
e.g. 240 milligrams is prescribed. The stock dose is 120 milligrams/5mL
Learning Development Service – 2012/13 7 What volume would you give?
240
5
24
×
=
120
1
12
8
=
4
2
=
1
10
=
1
5
1
5
×
1
5
×
1
×
= 10 ml
Examples to try:
(1) 6 milligrams is required. Stock is 10 milligrams/4mL. What volume is required?
(2) A patient required 10000 units. Stock is 25000 units/mL. What volume is required?
(3) A patient is prescribed 720mg of a drug. The Stock dose is 100mg / 3mL. What volume will you
require?
(4) A patient is prescribed 900mg of a drug. The Stock dose is 20mg / 1mL. What volume will you
require?
11.Percentages
• Always out of 100
• As a decimal, 0.10 = 10% 0.60 = 60%
(use the hundredths column to determine value)
Find 30% of 150:
30
150
×
100
1
3
150
=
×
10
1
450
45
=
=
10
1
30% of 150 =
= 45
What percentage of 250 is 50? To answer this we first need to write as a fraction then multiply by 100:
50
250
5
=
25
1
=
5
100
=
5
=
100
1
100
×
1
100
×
1
×
= 20%
Examples to try:
(1) Work out 20% of 65 mL
(2) A patient is to receive IV Fluids over 8 hours. What percentage would be administered after 6hrs?
(3) How long would it take to administer 50% in the above question?
(4) A patient is prescribed 700mL over 5 hours. What percentage would be administered after 2 hr?
(5) A patient has a daily fluid allowance of 800mL. The patient has taken 30%. How many mL is this?
8 Numeracy – The Essentials
12 Sample Paper
Please use this column to show
working out
ANSWER
Question 1
Calculate the following:
4.5
6.2 – 1.7
Question 2
Calculate the following:
34 multiplied by 25
850
Question 3
Calculate the following:
1521
6084 divided by 4
Question 4
Calculate the following:
9.89
3.19 + 0.7 + 6
Question 5
8.05
Write in order of size, starting with the
smallest:
8.5
8.05
8.57
8.92
Question 6
If bananas cost £1 for 4, how many can
you buy for £3.50?
8.5
8.57
8.92
£1 = 4
50p = 2
£3 = 4 × 3 = 12
14
1 banana costs 25 p
Jim’s fluid balance chart for 24 hours
shows:
INTAKE
OUTPUT
IV Fluids 1500 mL
Urine 980mL
Oral Fluids 250 mL
Drain 45mL
Calculate the total
Question 7 - Intake
Question 8 - Output
Q7 Answer
1750mL
Q8 Answer
1025mL
Learning Development Service – 2012/13 9 Question 9
Convert the following percentage into a
decimal:
0.75
75%
Question 10
Convert the following percentage into a
decimal:
0.15
15%
Question 11
What is 2/5 of 800?
320
Question 12
Calculate the total weight, in kg, of the
following:
135g
0.05kg
0.69
kilograms
½ kg
5g
Question 13
Convert 250 microgram to milligrams
0.25
milligrams
Question 14
Convert 1.08 grams to milligrams
Question 15
Convert 50 mL to litres
1080
milligrams
0.05
litres
Question 16
Convert 2.1 litres to mL
2100
micrograms
Question 17
Convert 0.19 kg to grams
190 grams
Question 18
Convert 8 milligrams to grams
10 Numeracy – The Essentials
0.008
grams
Question 19
A patient has a daily fluid allowance of
1500 mL.
He has taken 300 mL.
20%
What percentage is this?
Question 20
A patient requires Risperidone 500
micrograms
The stock dose is 4mg / mL.
What volume is required?
0.125
millilitres
Question 21
A patient has been prescribed 20 mg
Ketamine
The stock available is 50mg / 5mL.
2 millilitres
What volume of Ketamine is required?
Question 22
Heparin is available as 2000 units/4mL.
What volume is needed to give 12000
units?
24 millilitres
Question 23
A 73kg adult requires
Enoxaparin 3mg / kg for treatment of a
DVT.
219
milligrams
What dose is required?
Question 24
A patient has been prescribed
Prednisolone 15 mg
The stock available is 5 mg
3 tablets
How many tablets will you administer?
Question 25
Digoxin 20 mg is prescribed
The stock available is 10 mg
How many tablets will you administer?
2 tablets
Learning Development Service – 2012/13 11 Question 26
A patient is prescribed 50 mg of
Pethidine
5 millilitres
The stock dose is 20mg / 2mL
What volume will you require?
Question 27
A patient is prescribed 75 mg of
Tramadol Hydrochloride injection
6 millilitres
The stock dose is 50mg / 4 mL
What volume will you require?
Question 28
Which is the largest fraction?
4/5 = 0.8
4/5
2/3 = 0.66
2/3
1/2 = 0.5
½
3/4 = 0.75
¾
Either learn or use short division
4/5
Question 29
Calculate the following:
12 x 9
108
Question 30
Please calculate the mL per hour that
should be administered.
720 mL Parenteral Nutrition over 24
hours
12 Numeracy – The Essentials
30 mL/hr
Or
11. Answers to exercises
1. Ordering numbers:
(1) (i) 87.87; (2) (ii) 0.2; (3) (iii) 624.0
2. Times tables:
(1) 72; (2) 84; (3) 54; (4) 28; (5) 55; (6) 24; (7) 132
3. Addition:
(1) 116.3; (2) 1729; (3) 1395; (4) 116.3; (5) 854; (6) 1582; (7) 2446.851; (8)1905.01; (9) 69.47
4. Multiplication:
(1) 197.5micrograms; (2) 80mg; (3) 164mg; (4) 127.2micrograms; (5) 120.54micrograms
5. Subtraction:
(1) 0.775kg; (2) 1.05kg; (3) 974g;
6. Division and simplifying fractions:
(1) 37.5; (2) 6; (3) 125; (4) 247; (5) 135; (6) 81.14; (7) 27.89; (8) 178.5; (9) 153; (10) 160.25;
(11) 122.04; (12) 19.87; (13) 98; (14) 147.5; (15) 362.96
7. Combined:
(1) 400 mg; (2) 62.5 mL/hr; (3) 125mL/hr; (4) 4.17 mL/min; (5) 600 mL
8. Converting weights:
(1) 0.36 mg; (2) 0.5 L; (3) 0.0705 micrograms; (4) 1080 g; (5) 0.39 micrograms; (6) 500000; (7) 0.4 L; (8)
55000 mL
9. Fractions & decimals:
(1) 16.8; (2) 315; (3) 13.2; (4) 3.3; (5) 0.7; (6) 24.0
10. Basic drug calculations:
(1) 2.4mL; (2) 0.4mL; (3) 21.6mL; (4) 45mL
11. Percentages:
(1) 13 mL; (2) 25%; (3) 4hr; (4) 40%; (5) 240mL
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