Light & Heavy Fabrication Version

Perform

Computations

(MEM12024A)

(Light & heavy fabrication version)

LEARNING RESOURCE

manufacturing, engineering, construction

and transport curriculum centre

Metal Fabrication & Welding

⅞ ÷ 10 16 2356

× √ 23.2 10.2235

$ % 8.168 ¼

52.75 3.142 ½ ¾

MEM12024A/3

Second Edition

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. / Together, performance criteria specify the requirements for competent performance. Text in italics is explained in the range statement following.
1. / Determine work requirement / 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. / Perform calculations / 2.1 / Calculation method is applied correctly
2.2 / Correct answer is obtained
2.3 / Answer is checked against estimation
3. / Produce chartsand graphs from given information / 3.1 / Data is transposed accurately to produce charts or graphs
3.2 / Charts or graphs accurately reflect data on which they are based

STUDENT ASSESSMENT GUIDE

Unit of competency name / Perform computations
Unit of competency number
MEM12024A

Unit Purpose

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

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

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

4 + 3 =

6 + 5 =

73 + 22 =

1243 + 345 + 45.5 =

354 + 78.9 =

178.9 + 2256 + 37.3 =

234 – 123 =

4789 – 3267 =

367 + 678 – 234 =

87.96 – 22.4 + 32 =

96.7° ÷ 6 =

180° × 3 ÷ 45 =

33.3 ÷ 3 =

910 ÷ 14 ÷ 5 =

525174 ÷356 ÷ 68 =

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

(4 × 6) + 2 =

4 × (6 + 2) =

23 – (6 +4) =

(367 × 67.8) + (56 × 93) =

33.7 – (8 ÷ 73) =

[(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

Exercise 1.3

Do the following calculations

14 – 5 + 3 =

36 – 5 + 14 – 12 =

13 + 2 × 4 – 6 =

15 + 8 × 3 – 20 ÷ 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

23² =

105³ =

√87 =

√226.7 =

289 × ∏ =

475 × ∏ =

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 Improper Fractions

1/4 2/4 3/4 4/4 5/4 6/4 7/4 8/4

0 1 2

1¼ 1½ 1¾

Mixed Numbers

Equivalent fractions are when two fractions are equal at the same point on the number scale.

1/8 2/8 3/8 4/8 5/8 6/8 7/8 8/8

1/4 2/4 3/4 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 5

28 ÷4 7

Exercise 1.5

Reduce the following fractions to equivalent fractions in their lowest terms

Write the following as equivalent fractions using the denominators shown

1 ___

4 16

7 ___

16 32

4 ____

25 100

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 1 7

5 9 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 multiplied by 8

8 5

Exercise 1.6

WORKING OUT

Mathematical Formulas

Area and Perimeter formulas for common shapes

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

Exercises 1.4

Calculate the area and perimeter of the following shapes.

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?

2.5 Calculate the cutting size for the following allowing for all material thicknesses.

Cutting Size =

2.6 Calculate the volume of the following

Volume =

2.7 Calculate the missing measuremenents

A = ______

B = ______

C = ______

D = ______

E = ______

F = ______

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

H = A + B Find B B = ?

C = D x 3.142 Find D D = ?

A = B x H x 2 Find B B = ?

A = B x H – 2 Find H H = ?

F = L x S x T Find L L = ?

2 x F x T = P x D x S Find S S = ?

2 x F x T = P x D x S Find F F = ?

A = D x 0.7854 Find D D = ?

V = D x 0.7854 x H Find H H = ?

V = D x 0.7854 x H x 1000 – 2 Find H H = ?

SECTION 4