Basic Maths Session 1: Basic Arithmetic. Intended learning objectives At the end of this session...
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Transcript of Basic Maths Session 1: Basic Arithmetic. Intended learning objectives At the end of this session...
![Page 1: Basic Maths Session 1: Basic Arithmetic. Intended learning objectives At the end of this session you should be able to: add, subtract, multiply and.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649db55503460f94aa73c6/html5/thumbnails/1.jpg)
Basic Maths
Session 1: Basic Arithmetic
![Page 2: Basic Maths Session 1: Basic Arithmetic. Intended learning objectives At the end of this session you should be able to: add, subtract, multiply and.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649db55503460f94aa73c6/html5/thumbnails/2.jpg)
Intended learning objectives At the end of this session you should be able to:
add, subtract, multiply and divide fractions convert fractions to decimals and decimals to
fractions, multiply and divide decimals by multiples of 10
change a fraction to a percentage, find a percentage of a number, increase/decrease a number by a percentage
round whole numbers and decimals use ratio and dividing in proportion understand the order of arithmetic operations
and use some basic calculator functions
![Page 3: Basic Maths Session 1: Basic Arithmetic. Intended learning objectives At the end of this session you should be able to: add, subtract, multiply and.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649db55503460f94aa73c6/html5/thumbnails/3.jpg)
‘expanding’
(x top and
bottom by 2)
‘simplifying’ or ‘cancelling down’
(÷ top and
bottom by 3)
§ 1. Fractions (simplifying and expanding)
If we multiply (or divide) BOTH numerator and denominator by the same number we don’t change the value of the expression
rdenominato
numerator
3
2
9
6
8
6
4
3
![Page 4: Basic Maths Session 1: Basic Arithmetic. Intended learning objectives At the end of this session you should be able to: add, subtract, multiply and.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649db55503460f94aa73c6/html5/thumbnails/4.jpg)
§ 1. Fractions (multiplying and dividing)
Multiplying fractions
multiply numerators multiply denominators simplify
Dividing fractions
invert second (to get the ‘reciprocal’) and multiply by first
4
3
7
2 1
9 5
2
2 3 6
7 4 28
3
14 29 1
51 5
8
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§ 1. Fractions (adding and subtracting)
Find ‘common denominator’ Expand both fractions Add or subtract numerators
2
5 7
1
2 1 5
5 5
7
7 7
35
5
35
14
35
19
35
514
![Page 6: Basic Maths Session 1: Basic Arithmetic. Intended learning objectives At the end of this session you should be able to: add, subtract, multiply and.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649db55503460f94aa73c6/html5/thumbnails/6.jpg)
§ 1. Fractions (rewriting)
You may need to rewrite any mixed fractions as improper fractions BEFORE performing these operations
‘mixed fraction’ to ‘improper fraction’
‘improper fraction’ to ‘mixed fraction’
214
7
3
4
1 2
1
(2 )3 1
3
(4 ) 1
(
2
1 2 2)
(4 )2 1
2
8
2
1
9
2
3
3
(2 ) 1
3
1
33
2 12
1
![Page 7: Basic Maths Session 1: Basic Arithmetic. Intended learning objectives At the end of this session you should be able to: add, subtract, multiply and.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649db55503460f94aa73c6/html5/thumbnails/7.jpg)
Converting decimals to fractions:
Convert fractions to decimals by dividing numerator by denominator:
Multiplying a decimal by a multiple of 10:3.27x10 = 32.7, 3.27x100 = 327, 3.27x1000 = 3270
Dividing a decimal by a multiple of 10:43.1÷10 = 4.31, 43.1÷100 = 0.431, 43.1÷1000 = 0.0431
§ 2. Decimals
125.0818
1
1000949
10061 7949.7 ,461.4 ,
10
77.0
![Page 8: Basic Maths Session 1: Basic Arithmetic. Intended learning objectives At the end of this session you should be able to: add, subtract, multiply and.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649db55503460f94aa73c6/html5/thumbnails/8.jpg)
§ 2. Fractions/Decimals in Pictures
1
1/2 1/2
1/3 1/3 1/3
1/4 1/4 1/4 1/4
1/6 1/6 1/6 1/6 1/6 1/6
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
1/10 1/10 1/10 1/10 1/10 1/10 1/10 1/10 1/10 1/10
833.06
5
25.04
1
![Page 9: Basic Maths Session 1: Basic Arithmetic. Intended learning objectives At the end of this session you should be able to: add, subtract, multiply and.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649db55503460f94aa73c6/html5/thumbnails/9.jpg)
Percentages are fractions out of 100 and can be written as decimals
Converting a fraction to a percentage:
Percentage of a number:
Increase/decrease a number by a percentage:
e.g. To increase 5 by 60%
§ 3. Percentages
0.09,100
9%9
1004
3
4
3
60 of %30
6060% of 5 5
100
61.1100
161%161
3 100
4
3 25
75%1
60100
30 3 3 6060
10 10
18
1
63
10
56
,32
6 835
510
63 5
3, 5
5 3 8
or
![Page 10: Basic Maths Session 1: Basic Arithmetic. Intended learning objectives At the end of this session you should be able to: add, subtract, multiply and.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649db55503460f94aa73c6/html5/thumbnails/10.jpg)
§ 4. Rounding
Thousands Hundreds Tens Units
7 2 8 4
7284 rounded to the nearest ten is 7280 7284 rounded to the nearest hundred is
7300
Rounding decimals is similar e.g. 3.854 rounded to 1 decimal place is 3.9
![Page 11: Basic Maths Session 1: Basic Arithmetic. Intended learning objectives At the end of this session you should be able to: add, subtract, multiply and.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649db55503460f94aa73c6/html5/thumbnails/11.jpg)
A and B are in the ratio 1:2 1 + 2 = 3
15ml in ratio 1:2
§ 5. Ratios and proportion
1 2 of and
3 3of A B
1 1515ml ml 5ml
3 3of A
2 2 1515ml ml
3 3
5
10
B of ml10ml1
52
A
B
![Page 12: Basic Maths Session 1: Basic Arithmetic. Intended learning objectives At the end of this session you should be able to: add, subtract, multiply and.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649db55503460f94aa73c6/html5/thumbnails/12.jpg)
§ 6. Order of operations
Do calculation from left to right obeying ordering: Brackets (innermost 1st) Exponents Multiplication and Division Addition and Subtraction
))312((5405 E.g.20405
257
)45(405
![Page 13: Basic Maths Session 1: Basic Arithmetic. Intended learning objectives At the end of this session you should be able to: add, subtract, multiply and.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649db55503460f94aa73c6/html5/thumbnails/13.jpg)
§ 7. Applied problems 30ml of drug solution consists of two thirds drug A
(costing 10p per ml), a sixth of drug B (costing 50p per ml) and rest of volume made up with water (no cost)
How much does the whole solution cost? A
B
Total cost =
How much water is required?
00.2£/10.0£20 mlml
mlmlml 56
30130
6
1
6
1
6
1
3
21
50.2£/50.0£5 mlml
mlmlmlml 552030 or
50.4£50.2£00.2£
22
330 0ml ml
01
63 5ml ml
![Page 14: Basic Maths Session 1: Basic Arithmetic. Intended learning objectives At the end of this session you should be able to: add, subtract, multiply and.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649db55503460f94aa73c6/html5/thumbnails/14.jpg)
§ 8. Topics in Term 1 modules using basic maths skills
STATISTICS: Frequency Relative (percentage)
frequency Arithmetic mean Standard deviation Confidence intervals p-values …etc
EPIDEMIOLOGY: Incidence Point prevalence
(proportion) Risk ratio Rate ratio Odds ratio Mortality rates …etc
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Intended learning objectives (achieved?)
You should be able to: add, subtract, multiply and divide fractions convert fractions to decimals and decimals to
fractions, multiply and divide decimals by multiples of 10
change a fraction to a percentage, find a percentage of a number, increase/decrease a number by a percentage
round whole numbers and decimals use ratio and dividing in proportion understand the order of arithmetic operations
and use some basic calculator functions
![Page 16: Basic Maths Session 1: Basic Arithmetic. Intended learning objectives At the end of this session you should be able to: add, subtract, multiply and.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649db55503460f94aa73c6/html5/thumbnails/16.jpg)
Key messages If we multiply or divide BOTH numerator and denominator
by the same number then the value of the fraction stays the same
To multiply fractions together we multiply the top numbers together and _______ the bottom numbers together
To divide one fraction by another we invert the one we are dividing by and then _______ by it
To add and subtract fractions we first need to rewrite the fractions so that they have the same ____________
Percentages are fractions out of ____N.B. For next session: http://www.lshtm.ac.uk/edu/studyskills.html
(subheading ‘Maths and Numeracy Skills’)
multiply
multiply
denominator
100