Download MEM12024A

Perform
Computations
(MEM12024A)
(Light & heavy fabrication version)
LEARNING RESOURCE
MANUFACTURING, ENGINEERING, CONSTRUCTION
AND TRANSPORT CURRICULUM CENTRE
Metal Fabrication & Welding
⅞
÷
×
$
10
√
%
52.75
16
23.2
10.2235
8.168
3.142
2356
¼
½
¾
MEM12024A/3
Second Edition
MEM12024A Perform Computations
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MEM12024A
PEFORM COMPUTATIONS
Unit Purpose
When you have completed this unit of competency you will be able to estimate
approximate answers to arithmetical problems, carry out basic calculations involving
percentages and proportions, and determine simple ratios and averages. The unit
includes producing and interpreting simple charts and graphs.
Elements of Competency and Performance Criteria
Elements are the essential
outcomes of the unit of
competency.
1.
2.
3.
Determine work
requirement
Perform
calculations
Produce charts and
graphs from given
information
MEM12024A Perform Computations
Together, performance criteria specify the requirements for
competent performance. Text in italics is explained in the
range statement following.
1.1
Required outcomes are established from job
instructions
1.2
Data is obtained from relevant sources and
interpreted correctly
1.3
Required calculation method is determined to
suit the application, including selection of
relevant arithmetic operations and/or formulae
1.4
Expected results are estimated, including
rounding off, as appropriate
2.1
Calculation method is applied correctly
2.2
Correct answer is obtained
2.3
Answer is checked against estimation
3.1
Data is transposed accurately to produce charts
or graphs
3.2
Charts or graphs accurately reflect data on which
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they are based
STUDENT ASSESSMENT GUIDE
Perform computations
Unit of competency name
Unit of competency number
MEM12024A
Unit Purpose
When you have completed this unit of competency you will be able to estimate approximate answers to
arithmetical problems, carry out basic calculations involving percentages and proportions, and determine
simple ratios and averages. The unit includes producing and interpreting simple charts and graphs.
Reporting of assessment outcomes
Your result will be recorded and reported to you as Competent or Not yet
Competent.
Requirements to successfully complete this unit of competency
To achieve this unit of competency, you will need to provide evidence of having achieved each of the
elements of this unit. These are as follows:



determine work requirement
perform calculations
produce charts and graphs from given information
Assessment for this unit of competency may require you to provide a range of evidence which may include
reports from your employer, written tests, assignments and practical class exercises. The actual assessment
details will be provided to you by your teacher.
Occupational health and safety
The laws protecting the Health and Safety of people at work apply to learners who attend TAFE Colleges,
either part time or full time. These laws emphasise the need to take reasonable steps to eliminate or control
risk at work (this includes a TAFE College). TAFE NSW has the responsibility for the control, and where
possible, the elimination of health and safety risk at the college. You are encouraged to help in eliminating
hazards by reporting to your teacher or other College staff, anything that you think may be a risk to you or
other people.
Your teacher will encourage you to assist in hazard identification and elimination, and to devise control
measures for any risks to yourself and other people that may arise during practical exercises. The OHS Act
2000 and OHS Regulation 2001 require that teachers and learners take reasonable steps to control and
monitor risk in the classroom, workshop or workplace.
What you will need
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You must provide the following items to complete this Unit of Competency:






MEM05 TAFE NSW Unit Resource Manual for this unit of competency
a calculator with scientific functions
stationery as per college requirements
drawing instruments and equipment as per college requirements
pencils as per college requirements
trade tools as per college requirements
More about assessment
For information about assessment in TAFE please see "Every Student's Guide to
Assessment in TAFE NSW" which is available on the TAFE internet site at:
http://www.tafensw.edu.au/courses/about/assessment_guide.htm
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Section 1
Basic Mathematical Operations
There are four common mathematical operations these are: addition, subtraction,
multiplication and division.
Exercise 1.1
Do the following calculations
1. 4 + 3 =
2. 6 + 5 =
3. 73 + 22 =
4. 1243 + 345 + 45.5 =
5. 354 + 78.9 =
6. 178.9 + 2256 + 37.3 =
7. 234 – 123 =
8. 4789 – 3267 =
9. 367 + 678 – 234 =
10. 87.96 – 22.4 + 32 =
11. 96.7° ÷ 6 =
12. 180° × 3 ÷ 45 =
13. 33.3 ÷ 3 =
14. 910 ÷ 14 ÷ 5 =
15. 525174 ÷356 ÷ 68 =
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Order of Operations
It is important to follow the order of operation rules in order to get the correct answer.
A maths problem like 3 × 2 + 4 has two operations to be done. Depending on which
order the operation is done two answers are possible.
If the multiplication is done first,
3 × 2 + 4 = 10
If the addition is done first,
3 × 2 + 4 = 18
Grouping symbols are used to indicate the order of operations.
 ( ) parentheses
 [ ] brackets
These grouping symbols are used to enclose the parts of the maths problem to be done
first.
Exercise 1.2
Do the following calculations
1. (4 × 6) + 2 =
2. 4 × (6 + 2) =
3. 23 – (6 +4) =
4. (367 × 67.8) + (56 × 93) =
5. 33.7 – (8 ÷ 73) =
6. [(4 × 9) ÷ 3 ] × 4.3 =
When there are no grouping symbols the following rules apply,
When an expression has only addition and subtraction, work from left to right.
58 + 3 – 11 + 8
= 61 -11 +8
= 50 + 8
= 58
Where an expression has only multiplication and division, work from left to right.
4×5÷2×6
= 20 ÷ 2 × 6
= 10 × 6
= 60
Where an expression has multiplication and division as well as addition and
subtraction, do the multiplication and division first from left to right, then do the
addition and subtraction from left to right.
12 × 3 + 16 ÷ 4 -2
= 36 + 16 ÷ 4 – 2
= 36 + 4 – 2
= 40 – 2
= 38
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Exercise 1.3
Do the following calculations
1. 14 – 5 + 3 =
2. 36 – 5 + 14 – 12 =
3. 13 + 2 × 4 – 6 =
4. 15 + 8 × 3 – 20 ÷ 5 =
5. 35 + 25 ÷ 5 – 2 =
Other Mathematical Functions
Index notations
When the same number is to be multiplied by itself several times, instead of writing
the number down several times, a small numeral is written above the right of the
number. The numeral indicates the number of times the number is to be multiplied.
Example
2² means 2 × 2
2³ means 2 × 3 times
Square Root
The square root of a number is an amount that when multiplied by itself equals the
original number. Square root is indicated by the symbol √.
Example
√25 = 5 because 5 squared equals 25.
Pye
Pye is a number used to calculate circumference of a diameter. Pie is indicated by the
symbol ∏.The number of pie is 3.14672.
Exercise 1.4
Using the index notation, square root and pie key on your calculator calculate the
following
1. 23² =
2. 105³ =
3. √87 =
4. √226.7 =
5. 289 × ∏ =
6. 475 × ∏ =
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Fractions
There are a number of names given to different types of fractions.





Common or vulgar fractions, also called proper fractions
Improper fractions
Mixed fractions
Equivalent fractions
Decimal fractions
Common fractions are numbers smaller then one but greater than zero
1/5
1/5
1/5
1/5
1/55
Lots of 1/5th = 1 Whole
Improper fractions are fractions where the numerator is larger than the denominator
and so has a value greater than one.
1/5
1/5
1/5
1/5
1/5
1/5
5 Lots of 1/5th = 6/5th’s
Mixed numbers are made up from a whole number and a proper fraction
Proper/Common Fractions
1/4
2/4
3/4
0
Improper Fractions
4/4
5/4
6/4
7/4
1
8/4
2
1¼
1½
1¾
Mixed Numbers
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Equivalent fractions are when two fractions are equal at the same point on the number
scale.
1/8
2/8
3/8
4/8
1/4
5/8
2/4
6/8
3/4
7/8
8/8
4/4
1/2
1
On this number Scale the following are Equivalent Fractions: 2/8 and 1/4
4/8, 2/4 and 1/2
6/8 and 3/4
8/8 and 4/4
Reducing Equivalent Fractions
If both the numerator and denominator of a fraction are multiplied or divided by the
same number, the value of the fraction is unchanged.
Example
5 ×3
15
7 ×3
21
20 ÷4
28 ÷4
5
7
Exercise 1.5
Reduce the following fractions to equivalent fractions in their lowest terms
1. 12
16
2. 30
32
3. 56
64
4. 48
36
5. 44
48
Write the following as equivalent fractions using the denominators shown
1
4
___
16
7
16
___
32
4
25
____
100
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Adding and Subtracting Fractions
Before fractions can be added or subtracted together, they must have the same
common denominator. This is referred to as the least common denominator, and is the
smallest number that each of the denominators will divide into. To add or subtract
fractions first find the least common denominator and express each fraction in
equivalent form with LCD.
Example Find the value of
2
5
1
9
7
15
As the denominators are five, nine and fifteen, the smallest number that each will
divide into is forty-five.
Multiplying of Fractions
Multiplication of fractions is carried out by multiplying all the numerators and all the
denominators together.
A multiplication of fractions may be expressed in several ways.
Division of Fractions
The rule for dividing fractions is to invert the fraction and multiply.
Eg:
5
8
multiplied by
8
5
Exercise 1.6
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WORKING OUT
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Mathematical Formulas
Area and Perimeter formulas for common shapes
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Volume formulae for common shapes
Litre Conversion Factor
There being 1000 litres in a cubic metre, to calculate the volume in litres enter a 1000
factor in the formula
Eg: V = L × B × H × 1000
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Exercises 1.4
Calculate the area and perimeter of the following shapes.
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Section 2
Practical Mathematical Applications
Using the functions and formulas you have learnt in section 1 complete the following
exercises.
2.1 Calculate the total cost of the replacement parts below.
Working Out
3 Bearings @ $42.65 each
34 10mm bolts @ $15.80 per 100
34 10mm nuts @ $4.65 per 100
13 spring clips @ $0.14 each
100 seals @ $22.64 per 7
TOTAL = $
2.2 Calculate the material required to manufacture 5 of the hoppers below and the
volume of each
2.3 Estimate the cost of 3 cabinets if the material is $37 per cabinet and labour is $75
per hour and it will take a total of 4 hours to manufacture.
Material =
Labour =
TOTAL = $
2.4 If 1 tonne of steel costs $1687 and each sheet is 2400×1200 and weighs 2.1kg per
square metre how much would each sheet cost?
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2.5 Calculate the cutting size for the following allowing for all material thicknesses.
Cutting Size =
Cutting Size =
Cutting Size =
2.6 Calculate the volume of the following
Volume =
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Volume =
2.7 Calculate the missing measuremenents
A = ________________
B = ________________
C = ________________
D = ________________
E = _________________
F = ______________
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SECTION 3
Transposition of Formula
All equations must balance so the correct answer can be calculated out. Sometimes
the unknown symbol is not in an isolated position eg. 5 = C – 4 + 1 The unknown
must be isolated keeping the formula balanced before you can attempt to find the
answer. All numbers or letters are + unless it has a – in front of it.
5 =C–4+1
C is positive so the – 4 and + 1 must be removed. We can change
the formula around by doing exactly the same to both sides.
If we add four to both sides the – 4 cancels out the + 4
5+4=C–4+1+4
5+4=C+1
We can do the same for the + 1 by minusing 1 from both sides 5 + 4 – 1 = C + 1 – 1
5+4–1=C
C=5+4–1
therefore C = 8 lets try the answer in the original formula 5 = C – 4
+1 5=8–4+1
5 = 5 therefore the formula is balanced.
Transpose the following formula
1. H = A + B
Find B
B=?
2. C = D x 3.142
Find D
D=?
3. A = B x H x 2
Find B
B=?
4. A = B x H – 2
Find H
H=?
5. F = L x S x T
Find L
L=?
6. 2 x F x T = P x D x S
Find S
7. 2 x F x T = P x D x S
Find F F = ?
8. A = D x 0.7854
Find D
D=?
9. V = D x 0.7854 x H
Find H
H=?
10. V = D x 0.7854 x H x 1000 – 2
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S=?
Find H
Version 3
H=?
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SECTION 4
Estimating & Costing
The main benefit of estimating an answer to a mathematical problem is to be able to
know what the answer should be. Calculators give an accurate answer to a problem
with the information entered. If this information is entered incorrectly the answer will
not be the correct answer to the problem. By estimating we can get a good idea of
what the answer should be.
Eg: 485.50 × 52 =
If we were to use a calculator for this problem we would get an answer of 25246.00
but if the decimal point is accidentally left out we would get an answer of 2524600,
by estimating this problem before calculating with a calculator we would know the
answer would be somewhere around 25000.00.
Eg:
485.50 is close to 500.00 so we round it up
52 is close to 50 so we round it down
The problem for estimating now becomes 500 × 50 = 25000.00
Exercise 4.1
Estimate the following
1. 14 × 21 =
2. 497 × 213 =
3. 173 + 427 – 250 =
4. 4483 ÷ 87
5. Estimate the cost of 48 litres of fuel at 78.9 cents per litre
6. Estimate the cost of 11 items at 9.85 each
7. 173 + 427 + 250 =
8. 68.72 × 82.86 =
Estimating can be used in a manufacturing environment to estimate material
quantities and costs.
Costing
Estimating and costing plays a major part in every manufacturing workshop. The
principles are used for estimate the cost of jobs for tenders and quotes.
Costing may involve more than one mathematical operation. You may need to
calculate areas, volumes and cost of materials before being able to cost a job.
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Exercise 4.2
1. Calculate the cost of 3 S/S tanks if the tanks are 2500long 1500wide and 850high
3mm thick material. The S/S costs 19.30 per kg and 1sq/mtr weights 15kg.
2. Cost the following material required for a job using the chart on page 22
5 lengths of 25x25x3 RHS
5 sheets 8ftx4ftx3 mild steel
100 Alum rivets @ .02kg each
@ $2.20 per kg
@ $6.80 per kg
@ $1.20 per kg
3. Calculate the cost of 5 galvanised dipping tanks that measure 6000 long x 2000
wide and 1500 deep and 3mm thick. Cost per kg = $3.42
4 .Calculate the amount of welding required for the dipping tank above if the tanks
were made in 5 pieces.
5. From the drawing below calculate:
The cutting size/s
Total length of welding required
The mass of the pattern blanks using the mass chart on page 22
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Section 5
Graphs and Charts
Graphs and charts consist of three pieces of information. Two variable values and a
resultant value occur when the values meet.
The vertical and horizontal axes each represent one of the variable values. The
resultant values are shown in the body.
There are several types of charts and graphs,
 Bar graph
 Line graph
 Organisational chart
 Pie graph
90
80
70
60
50
40
30
20
10
0
East
West
North
1st Qtr 2nd Qtr 3rd Qtr 4th Qtr
Bar Graph
Organisational Chart
Line Graph
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There are 6 steps to follow to plot a graph.






Decide which variable values are going to be displayed on each horizontal and
vertical axis.
Determine the spacing on each of the axes so the largest value of each variable
will fit on the graph.
Draw the vertical and horizontal axis at 90º to each other.
Label each axis with the name or description of the variable.
Plot each point in the body of the graph.
Join the points with vertical or horizontal lines to enable the information to be
read from the graph.
Graphs and charts can be use in a manufacturing workshop to show machine speeds
for material thickness and press capacity for different material thickness.
Exercise 5.1
1. Using the information given plot the variables on the graphs below
Year
1980
Steel
Production 3.5
Million
Tonnes
1981
1982
1983
1984
1985
1986
1987
1988
1989
3.7
4.1
4.3
4.7
5.1
5.5
6
6.3
6.6
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2. Answer the following questions using the information in the graph below.
a) Which year was the maximum amount of apprentices employed?
b) Calculate the approximate increase in employment of apprentices in 1988,
compared to 1987
c) Which twelve-monthly period which showed the greatest increase in
apprentices employed.
d) Which year was the lowest amount of apprentices employed?
3. Produce a line graph and enter the information below.
Blast furnace temperatures taken at hourly intervals
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4. Use the information in the graph below to answer the following questions.
a) Select a preferred tapping drill size for the following metric screw threads
M22 x 1.5
M3 x 0.05
M7 x 1.00
M12 x 1.50
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SECTION 6
OTHER ENGINEERING FORMULAS
There are other formulas that may be used in the engineering environment these
formulas may be used to calculate duct size, fan capacities and press capacities. All
these formulas play an important part in engineering.
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