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Essential Skills and Apprenticeship
Trades Math Workbook
The Trades Math Workbook will help you improve
your numeracy skills and increase your success in
an apprenticeship program. It includes a variety of
exercises to help you practise your numeracy skills
and learn how these skills are used in the trades.
Now and TomorrowExcellence in Everything We Do
Human Resources andSkills Development Canada
Ressources humaines etDéveloppement des compétences Canada
WP-145-03-10E
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For more inormation on essential skillsand to provide us with your eedback, visit hrsdc.gc.ca/essentialskills
For more inormation on the InterprovincialStandards Red Seal Program, visit www.red-seal.ca
You can order this publication by contacting:
Publications ServicesHuman Resources and Skills Development Canada140 Promenade du PortagePhase IV, 12th FloorGatineau, QuebecK1A 0J9
Fax: 819-953-7260Online: http://www.hrsdc.gc.ca/publications
This document is available on demand in alternativeformats (Large Print, Braille, Audio Cassette, Audio CD,e-Text Diskette, e-Text CD, or DAISY), by contacting1 800 O Canada (1 800 622 6232). If you have a hearingor speech impairment and use a teletypewriter (TTY),
call 1 800 926 9105.© Her Majesty the Queen in Right of Canada, 2010
PaperCat. No.: HS18-11/2010EISBN: 978-1-100-14722-2
PDFCat. No.: HS18-11/2010E-PDFISBN: 978-1-100-14842-7
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Introduction
Working in the trades requires strong numeracy skills to help you succeed on the jobThis workbook includes questions and learning material to help you:
• learmoreabouttheumeracyskillsrequiredtoworkithetrades;
• discoverhowjoureypersosuseumeracyothejob;
• practiseyourumeracyskills;ad
• doutwhichumeracyskillsyoumayeedtoimprove.
The workbook is divided into four sections, each of which highlights different numeracy skillsthat journeypersons use on the job
1 Measurement and calculation:Skills used to measure and describe the physical world, for example by taking measurementsand calculating area and volume
2 Money math:Skills used in paying and receiving money on the job, for example in handling cash, makingchange, preparing bills or making payments
3 Scheduling, budgeting and accounting: Skills used to manage time and money, for example in planning and keeping track of how youuse your time and money, in choosing the products or services that offer the best value and in
using your time and money wisely
4 Data analysis: Skills used to solve problems by analyzing and comparing numerical data
An answer key is provided at the end of the workbook to help you review your answers anddoutwhichareasofumeracyyoumayeedtoimprove.
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Math foundation skills Workplace examples
Whole numbers e.g.: 3, 14
Read, write, count, round off,add, subtract, multiply and dividewhole numbers
•Ordersupplies. •Takestockivetory. •Coutparts. •Readserialumbers.
Integers e.g.: -5, 0, 11
Read, write, add, subtract,multiply and divide integers
•Readtemperatures.•Usesurveytools.•Setupcomputerumericalcotrol
programs•Measureairpressure.
Fractions e.g.: 1 /8, 1 /4
Read, write, round off, add,subtract, multiply or divide
fractions Multiply or divideby a fraction
•Takeadrecordimperial measurements
•Determietoolor material sizes
•Calculatequatities.
Decimals e.g.: 8.50, 0.00375
Read, write, round off, addor subtract, multiply or dividedecimals Multiply or divideby a decimal
•Hadlemoey.•Takeadrecordmetric
measurements•Measuretoleraces.•Selecttoolsizes.
Percentages e.g.: 10%, 42%
Read and write percentagesCalculate the percentage onenumber is of another Calculate
a percentage of a number
•Calculatetax.•Readadwritetoleraces.•Adjustmachieloads.
•Describeitermsofaproportioofmaximum capacity or an amount ofprogress towards completion
Equivalent numberse.g.: 1 /2 = 0.5 = 50%
Convert between fractions,decimals and percentages
•Covertdecimalreadigso gauges to percent of output
•Covertdecimalstofractiosto select the correct part or size of tool
•Covertquatitiesofigredietstodecimals to calculate cost
Other real numberse.g.: √ 36, 92 ,
2.2 x 103, p
Use square roots, powers,scieticotatioad sigicatdigits.
•Calculatepoweradcurreti three-phase motors
•Usesquarerootstocalculate
dimensions for a staircase•Usepowerstoexpressthevolume of tanks
Equationsand ormulas
Solve problems using equationswith one unknown quantity Useformulas by inserting quantitiesSolve quadratic equations
•Determiewheretoplaceholes.•Calculatethecorrectaglesfor
rigging loads•Setfoodprices.•UseOhm’slawtocheck
motor voltage
5
Math Foundations
Trades occupations require all or most of the math foundations listed below.
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Math foundation skills Workplace examples
Rates, ratios andproportions
Use a rate comparing twoquantities with different unitsUse a ratio comparing twoquantities with the same units
Use a proportion comparingtwo ratios or rates
•Adjusttirepressure.•Mixgasolieadditives.•Adjustigredietsiarecipe
to make more servings
•Calculatespeedadfeed rates of a machine
•Readascaledrawig.•Calculateairowrates.
Measurementconversions
Convert between imperialand metric (SI) measurementsConvert to another unit within ameasurement system
•Covertuitstoselectwrechsizes.•Cutlegthsofwire.•Mixcolourigagets.•Meetproductspecicatios.•Calculateairow.•Usescaledrawigs.
Areas, perimetersand volumes
Calculate areas, perimetersand volumes
•Calculatetheareaorperimeter of a work surface to be painted,
sodded or caulked•Calculatethevolumeofgasolie
additives or concrete required•Calculatethecapacityofa
storage tank
Geometry Apply geometric conceptssuch as parallelism,perpendicularity and tangents
•Fidthecetreofaroomto istallxtures.
•Cuthairusigagles.•Cutslopestofabricateramps.•Useaglestolayoutpatters
for materials
Trigonometry Use trigonometry to determine
the size of an unknown side orangle of a triangle
•Calculateaglesfora
circular staircase•Placeholesoapart.•Makeboltpattersfordrillig
or machine installation•Fidoffsets.
Summarycalculations
Calculate averages andrates other than percentages,proportions or ratios
Calculate averages for:•fuelorpowercosumptio;•toollifespa;•speedadfeedrates;•materialproductio;ad•timeeededtoperformtasks.
Statistics and
probability
Use statistics and probability
to draw conclusions
•Estimatehowmuchof
something clients use•Predictsalestreds.•Determietheprobabilityof
equipment and parts failure•Describetheprogressoffabricatio
and installation tasks
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Section 1:
Measurement and Calculation
Measurement is the way that numbers are used most often in the trades Measurementand calculation are used to measure and describe the physical world, for example bytaking measurements and calculating area and volume The following are three typicalworkplace examples of measurement and calculation:
• Construction electricians take measurements and perform calculations to makesure that electrical installations meet electrical code requirements
• Carpenters take precise measurements using survey equipment
• Plumbers perform calculations using trigonometry to design, fabricate and installpipe that needs to go around an obstacle
Using Measuring Tools
Journeypersons who build things in their work use measuring tapes, laser surveyequipment, micrometers, scales and other tools to measure on a daily basis They workwith both imperial and metric measurements on the job
1 Enter the correct length beside each arrow on the measuring tape Remember to includethe correct unit (inches or centimetres) Two examples are provided for you
21 / 2"
3cm
Metric (SI)
1 cm 17 mm
0
23 cm 35 cm0 1"
Imperial Measures
1 / 16" 1 / 8" 3 / 8" 3 / 4"1 / 2"
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2 Label the following measurements (a–f) on the measuring tape with an arrow and the letter of thequestion Two examples have been done for you
x. 37 1 /2 "
a 391 / 8 in
b 3 ft 43
/ 4 inc 35 ft
3 Carpenters take readings of elevations, directions and lengths of property lines using a levellingrod The red numbers on the rod represent the number of feet, and the black numbers representtenths of a foot
Recordthereadigsbelow.Therstoehasbeedoeforyou.
Note: The red numbers are larger than the black numbers when they mark an even number oeet (e.g., 3.0 eet), but smaller when they appear as “reminders” in between.
y. 1.01m
d 93 cm
e 0992 mf 1075 cm
5 feet
a ___________ b ___________
x
y
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Using Formulas
The formulas in the box below will help you solve the workplace problems in this section
Whether you are in a classroom or on the job, it is helpful to develop your own method for solvingmath problems involving measurements The steps below can help you do this
Use your calculator to completethe questions in this workbook.
Note: Whenyou’r eonthe job, using a calculator saves time Become f amiliar with your calculator so that you can use all of its f eatur es
Steps:
1 Draw a diagram and label it with measurements
•Idetifytheiformatioyoueed.
•Thikabouttheuitsyouareworkigwith(e.g.,squaremetres,loads,feet).
2 Decide which formula or formulas you will need to use
3 Calculate the answer
Formulas for Perimeter, Area and Volume
Perimeter Area Volume
1 - Dimensional 2 - Dimensional 3 - Dimensional
L
W
P = 2(L + W)
L
W
A = LW
H
L
W
V=LWH
radius
diameter
C = pd or C = 2pr
radius = diameter2
diameter = 2 x radius A = pr2
LA = pdh or
LA = 2prhSA = LA + area
of both bases V = pr2h
V =pr2h3
Pythagorean Theorem(3-4-5 Method)
a2 + b2 = c2
a2 = c2 - b2
b2 = c2- a2
b
ac If your calculator
doesn't have a p key,use 31416
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1 A carpenterisbuildigatemporaryfecearoudabuildigsite.Howmaymetresoffecigare required for a site that is 478 m × 303 m? Round your answer up to the nearest metre
Use the problem-solving steps:
1 Draw
2 Decide
3 Calculate
2.Howmaystudswillacarpenter need to frame the exterior walls of the building below? Use theformula given below to estimate the number of studs
Number of studs = perimeter
2
3.Howmay3.7Lcotaiersofbodigproductdoesaoorcovering installer need to install vinylsheetoorigiaroommeasurig9.2m×7.8m?
Olyfullcotaierscabeordered.
Typical Recommended Trowel Approximate Coverage Trowel(depth, width, space)
Fibrous felt-backed vinyl sheet goods: 185–245 sq ft/US gal1 / 32" × 1 / 16" × 1 / 32" (45–60 m2 /L)
(08 mm × 16 mm × 08 mm)
52'
30' 8"
28'
14'
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4 A bricklayer is covering a playground surface with rubber tiles Each 2-ft2 tile costs $1329Calculate how much it will cost to cover the playground
Note: Only whole tiles can be ordered, so you will need to round your answer up when youcalculate how many tiles are needed.
5 A landscape horticulturalist needs to order enough sand to create a border 152 mm deep around
asquaresurface,asshowbelow.Howmaycubicmetresofsadareeeded?
Sand
925 m
14 m
r=82 ft
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6 A construction crat worker needs to know how much material is in the cone-shaped pile shownbelow Calculate the approximate volume of the pile in cubic yards
Use this formula to calculatethe radius of a pile of material:
r = ¾ × height
27 ft3 = 1 yd3
7 Heat and rost insulators coverpipestokeepsubstaceshotorcold.Howmaysquaremetresofmaterial are needed to insulate a pipe that is 6 m long and has a diameter of 2 m?
Think of the cylinder as beinglaidoutatsothatthecircumferece becomes the width measurement
Use this formula: pdh
8 Electricians calculate the total resistance of parallel electrical circuits Use the formula below tocalculate the total resistance for the circuit shown
Total resistance = resistance of one resistor (ohms)
number of resistors
r
16 ft
h
C = p d
d
6 m
2 m
R1 R2 R4R38 ohm 8 ohm 8 ohm 8 ohm
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9 Plumberstpiecesofpipeforcustomjobs.Whatisthecetre-to-cetre(c–c)legthofthepipe shown below?
10 Carpenters perform calculations to help them lay out and construct wooden stairs Calculate thelength of the stringer (c) for the stairs shown below
11 Rerigeration and air conditioning mechanics and sheet metal workers build and installtransition elbows to connect different sizes of ducts Calculate the length of the diagonal side ofthe transition elbow shown below
?
c - c
22 cm
18 cm
T o t a l R i s e
Total Run
Total Run
1 255 mm
Total Rise
1 000 mma
b
c
transition elbow
8"
12"
15"
?
S t r i n g e r
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12 Plumbers calculate water pressure in pounds per square inch (psi) What is the water pressurefor a 28-foot vertical pipe full of water?
Use this formula:
Water pressure (psi) = h × 0433
13 Sheet metal workers install ducts in buildings
The equation below shows the relationship between:
•airowvolumeicubicfeetpermiute(V); •airvelocityifeetpermiute(v);ad •areaofacross-sectioofductisquarefeet(A).
V = A × v
a Calculate the area in square feet of a cross-section of an 8 in × 24 in duct
1 ft2 = 144 in2
b. Calculatetheairowvolumeiftheairvelocityithesameductis1200feetpermiute.
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Using Drawings
Joureypersosworkigoacostructiositefollowspecicatiosfromasetofdrawigsorpritsthatshowdifferetviewsoftheishedbuildigproject.Joureypersosialltradesscathedrawings for the detailed information they need
Look at the drawings for a residence on the next page to complete the questions below
1 The walk-in closet measures 1¼ in × 1½ in on the drawing What are the actual dimensions of thecloset?
2. Howmaypocket(slidig)doorsareeeded?
Pocket door
3 What is the exterior length from A to B ?
4 Carpet costs $2850 per square yard What is the cost of carpet for the master bedroom and
closet?
1 yd2 = 9 ft2
5 Estimate the number of drywall sheets needed for the walls of the ensuite bathroom
Drywall sheets: 4 ft × 8 ftHeightofroom:8ft. Width of pocket door: 3 ft
Journeypersons often convert inches to fractions or decimals of a foot
3 in = ¼ ft or 025 ft 6 in = ½ ft or 05 ft 9 in = ¾ ft or 075 ft 12 in = 10 ft
Adding and subtracting eet and inches:
Step 1: Line up the measurements so that like units are under like unitsStep 2: Add or subtract the inches Add or subtract the feetStep 3: Change the inches to feet (divide by 12)Step 4: Add your answer from step 3 to the number of feet from step 2
Example:
Step 1 Step 2 Step 3 Step 4
7 ft 11 in 7 ft 11 in 20 in = 1 ft 8 in 9 ft+ 2 ft 9 in + 2 ft 9 in + 1 ft 8 in
9 ft 20 in 10 ft 8 in
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2'10"
1'0"
5'4"
2'2" 2'2"8' 2'8" 2'8"
4 ' 2 "
7 ' 6 "
3 ' 2 "
8 ' 4 "
6 ' 6 "
5 ' 0 " x 7 '
8 " E n s u
i t e
5 ' 0 " x 7
' 8 "
W a l k - i n
3 0 0 0 S F
Window Seatmi18"fromoor
M a s t e r R
o o m
1 2 ' 0 " x 1
4 ' 0 "
2X 2650
2 6 6 8
2 6 6 8
2 6 6 8
2036OBSSafety
2668
Job
2K1–09271
Date
SEPT 20
S h e et
Of
–––
s h e et
Scale
1/4" = 1'0"
DrawnF
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3 / 8"18"4'
Estimating Weight Loads
Mobile crane operators estimate weight loads Calculating safe loads protects the equipment, thematerials it carries, the workers on the job site and the general public
1 Boilermakers and ironworkers estimate the weight of materials used in fabricationCalculate the approximate weight of a 2 ft × 18 ft steel plate ¾ in thick
1" steel plate weighs about 40 lb/ft2
2 A mobile crane operator estimates the weight of a concrete panel to make sure that the crane canlift it safely Calculate the approximate weight of the panel shown below
Reinforced concrete weighs about 150 lb/ft3
3017 '
26 ' 05 '
b)
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Working with Quantities
1 A sewer line slopes at ¼" per foot Calculate the total fall in 30 feet
Use this formula:Total fall = length × grade
2 Automotive service technicians occasionally need to convert kilometres to miles for Americancustomers An oil change is due at 35 000 km What is the same distance in miles?
1 km = 06214 mi
3 A hairstylist is mixing a hair treatment The client has long hair, so the hairstylist starts with 1¼scoops of powder lightener
Mixing: Measure 1 level scoop of powder lightener into a non-metallic bowl or bottle Add1oz.(30g)oftheboosterad2.oz.(60mL)ofcoditioigcreme.Mixthoroughly to achieve a creamy consistency
a Calculate the number of grams of booster needed
b Calculate the number of millilitres of conditioning creme needed
Rates and ratios are used to compare two quantities Both can be expressed in the followingforms: 1 to 2, 1:2 or ½
Rates compare two quantities with different units For example, a rate can be used to describetheowofaliquidilitrespersecod.
Example:1tablespooofour:1cupofmilk
Ratios compare two quantities with the same units For example, a ratio can be used todescribe the number of parts of water and colouring agents to combine
Example: 1 part water2 parts cement
Proportions compare two ratios or two rates
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4 Cooks often change the yield of recipes to serve more or fewer customers The following recipemakes 30 pancakes Adapt the recipe to make 75 pancakes
Useproportiostocalculatehowmuchofeachigredietiseeded.Therstigredietisdoeforyou using two different methods
Ingredient Amount or 30 Amount or 75
Flour 625 g 15625 g
Sugar 60 g
Baking powder 30 g
Eggs 4
Milk 1 L
Melted butter 125 g
5 Product labels provide information about quantities to mix Use the label to answer thequestions below it
= bag of concrete
a.Acarpeterisbuildigafecewith9posts.Howmaybagsofcocretearerequiredto set the posts?
b Calculate the number of bags of concrete mix required for a slab measuring 5' × 2'4" × 6"
c Tube forms are used to form concrete columns The concrete is mixed at a ratio of 25 litres ofwater per bag of concrete mix Calculate the amount of water needed for a 15-foot column with adiameter of 8 inches
Method 1: Method 2:
625 g = ? g 625 ÷ 30 = 2083330 75
625 × 75 = 46875 ÷ 30 = 15625 g 75 × 20833 = 15625 g30
POSTS (Standard fence)25 x
= 1 Post
COnCRETESLAB4"
2'3'
5 x = 6 sqft
TUBEFORMS (For each 4' length)
55 x = 10" Diameter
35 x = 8" Diameter
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Section 2:
Money Math
Money math is used in paying and receiving money on the job, for example in handlingcash, preparing bills or making payments The following are three typical workplaceexamples of money math
• Cooks use petty cash to purchase small quantities of supplies that are neededimmediately
• Hairstylists prepare bills and collect cash, debit and credit card payments for theirservices They charge a set rate for each service and add applicable taxes, suchas the GST
• Automotive service technicians calculate the total cost of repair jobs includingparts,labour,markupadtaxes,adetertheseamoutsoestimatesorishedwork orders
Calculating Increases and Decreases
Calculating increasesIn some shops, products are bought at wholesale prices and marked up to sell tocustomers.Hereisoewaytocalculatemarkupadsalestax.
Method Examples
Markup100% + markup = total %change % to a decimal
total decimal × unit price = selling price
An item with a wholesale price of $1435 ismarked up 22% Calculate the selling price
100% + 22% = 122%122 / 100 = 122122 × $1435 = 17507 = $1751
Salestax
100% + tax = % including taxchange % to a decimaltotal decimal × cost = after-tax total
Calculate the after-tax cost of 2 hours oflabour at a rate of $45/hour
2 hours × $4500 = $9000 labour cost100% + 7% = 107%107 / 100 = 107107 × $9000 = 963 = $9630
Calculating discountsProducts are sometimes discounted when they are discontinued or when the supplierhasapromotio.Hereisoewaytocalculateadiscout.
Method Example
100% – % discount = new %change % to a decimaldecimal × unit price = sale price
An item with a regular price of $1089 isdiscounted 15% Calculate the sale price
100% – 15% = 85%85 / 100 = 085085 × $1089 = 9257 = $926
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1 In a hair salon, products are marked up for resale Calculate the selling prices of the itemslisted below
Wholesale price Markup Selling price
a $9725 10%
b $24999 15%
c $650 8%
2 Calculate the after-tax cost of the items listed below
Cost Tax Total
a $7350 12%
b $1,84700 13%
c $8675 8%
3 In a hair salon, products are discounted for promotions Calculate the sale prices of the itemslisted below
Price Discount Sale price
a $8540 10%
b $1,34800 33%
c $45975 40%
Invoicing or Services
Journeypersons who install, maintain and repair equipment often make invoices for servicesand are paid in cash, by cheque or by credit card on the job Calculating tax is a typical task inthese situations
1 a) Complete the invoice on the next page for the following services:
•Repairdishwasher
•Model#MDB7601AWW
•Cleapumpassembly,TestOK
•Labour1.2hoursat$88.25perhour(5%GST)
•Parts$2.80(5%GST+6%PST)
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b) The customer pays the bill in cash using the following amounts:
1 × $1001 × $201 cent
Howmuchchageshouldthetechiciagivethecustomer?Etertheamoutsofmoeythatcouldbe given as change in the table below (There are several correct answers)
$50 $20 $10 $5 $2 $1 25¢ 10¢ 5¢ 1¢
McLea’sAppliaceadRefrigeratioLtd.
1529 Leopold St
Woodstock,Onn4S1L2
Invoice No B0051441
Date: Nov 15
Bill to: John B WalkerPhone: 519-555-22221250 Cloverley StWoodstock,Onn4S8M3
Hours Hourlyrate Description of work Amount
Subtotal
GST(#39706)Total
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Section 3:
Scheduling, Budgeting and Accounting
Comparing Values
Use a table structure to compare items
Points o comparison Item 1 Item 2 Item 3
Cost 1
Cost 2Cost 3
The problems in this section require you to locate and understand information indocuments
Scheduling, budgeting and accounting are used to manage time and money, for examplein planning and keeping track of how you use your time and money, in choosing theproducts or services that offer the best value and in using your time and money wiselyThe following are three typical workplace examples of scheduling, budgeting andaccounting
• Industrial mechanics (millwrights) schedule tasks for construction, repair andmaintenance projects They also create maintenance schedules for equipment inmanufacturing plants
• Machinists adjust daily work schedules to accommodate rush jobs or jobs that takelonger than estimated For example, they may change machining processes or theorderofjobs.Theycosiderwhetherothersareaffectedbychagesitheworkowand try to minimize the disruption
• Cooks establish weekly budgets that include the cost of fresh food, shelf itemsand kitchen staff requirements They also establish separate budgets for each ofthe catering events for the week The costs included in the catering budgets varydepending on the menu items, number of courses and number of people served
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Roll-on Method
COMPOnEnT 929 m2 (100 sq ft)
1858 m2 (200 sq ft)
2787 m2 (300 sq ft)
3716 m2 (400 sq ft)
nOPRIMERREQUIRED
Step 1: Roll-onstone coat$8900/ 92 L
1 × 92 L 2 × 92 L 3 × 92 L 4 × 92 L
Step 2: Protectivetop coat$2678/946 mL
1 × 946 mL 2 × 946 mL 1 × 378 L 1 × 378 L
Trowel-on Method
COMPOnEnT 929 m2 (100 sq ft)
1858 m2 (200 sq ft)
2787 m2 (300 sq ft)
3716 m2 (400 sq ft)
Step 1:Primer coat$4820/378 L
1 × 378 L 1 × 378 L+1 × 946 mL
2 × 378 L 3 × 378 L
Step 2: Trowel-onstone coat$11507/151 L$5325/378 L
1 × 151 L+2 × 378 L
3 × 151 L 4 × 151 L+2 × 378 L
6 × 151 L
Step 3: Protectivetop coat
$2678/946 mL
1 × 946 mL 2 × 946 mL 1 × 378 L 1 × 378 L
Coating products can be applied by either atrowel-on or a roll-on method
1 A concrete fnisher estimates the cost ofresurfacing the sidewalk pictured using twodifferent methods for placing concrete Thetrowel-on method lasts longer but costs more
Estimate the cost difference given:
• Thecocreteishercharges$37.50perhour;
• Eachcoattakesapproximately1hourad 30 minutes to apply
3 ft
32 ft
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Accounting or Cost
1.Joureypersoscompareestimateswithactualcosts.Whethecustomerselectsthespecicitemthey want to purchase, the journeyperson can point out how much higher or lower than estimatedthe actual cost will be
Use the renovation invoice on the next page to answer the following questions
a.Comparetheallowacefortheoorcoverigswiththeactualcost.Eterthediffereceo the invoice
b A contractor is bidding on apartment renovations and needs to submit an estimate for installingthe same bathroom mirror, wall tile and toilet in 5 units Use the actual costs from the invoice to
calculate the estimate the contractor should provide Add 10% to account for rising costs
Many journeypersons give estimates to customers This involves telling the customer approximatelyhow much he or she should expect to pay for a certain item
In the example below, a journeyperson estimates that a sink will cost $100 If the sink is not
purchased or costs less than $100, the savings are shown in brackets This means the actual cost isless than budgeted
Item Allowance ($) Actual ($) Dierence +/- ($)
Sink 10000 7599 (2401)
If the sink costs more than $100, the extra cost is shown without brackets This means the actualcost is more than budgeted
Item Allowance ($) Actual ($) Dierence +/- ($)
Sink 10000 12367 2367
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Livingston Renovations
2709 Glenridge Avenue Abbotsford, BC, V2S 4J5
604-123-4444
December 6
InVOICE–AllowacesadExtras
Item Allowance ($) Actual ($) Difference +/– ($)
Exterior French doors 80000 81820 1820
Fireplace & gas piping 1,80000 1,85000 5000
Bathtub 25000 15300 (9700)Fireplace wall unit 4,00000 5,58500 1,58500
Bathtub faucet & showerhead 15000 0 (15000)
Toilet 25000 19910 (5090)
Sink 10000 0 (10000)
Faucet for sink 8000 0 (8000)
Bathroom vanity & countertop 45000 1,02000 57000
Lightxtures&potlights 65000 65000 0
Wall tile 15000 14512 (488)
Floor tile & carpet 3,05000 6,35603Bathroom mirror 5000 0 (5000)
Extra reframe around ducting 0 15000 15000
Extra install laundry cabinet 0 6750 6750
Surround speaker wire 0 3500 3500
Extra pot lights n/c
ALLOWAnCEBALAnCEOWInG $5,24895
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Section 4:
Data Analysis
Calculating Tolerances
1 Sheet metal workers, machinists, rerigeration and air conditioning mechanics and othersworktoverytighttoleraces.Decideifthemeasuresithefollowigtablearewithispecicatios.If they are, place aaithetable;iftheyareotacceptable,placeax
± means plus or minus
Specifcation Measure a /xa 225° ± 2° 201°
b 0850 m ± 0020 m 0827 m
c 0750 L ± 0015 L 0761 L
Data analysis is used to solve problems by analyzing and comparing data The need forthese skills is increasing as computer programs make data more available The following arethree typical workplace examples of data analysis
• Automotive service technicians analyze readings from tests of vehicle electrical systemsto diagnose problems such as an engine that will not start
• Machinists review quality control data to examine trends in machine performance Forexample,theymaycomparetheisheddimesiosofpartsproducedatdifferetpoitsin the machining cycle to decide when to replace tooling or recalibrate machinery
• Construction electricians use the results of electrical measurements (eg, draw, voltage,torque and temperature) taken at several points in a circuit to analyze circuit operation, totroubleshootelectricalproblemsadtoicreaseelectricalefciecy.
Range of AcceptableValues for 52 ± 3
518489 out of range 551 out of range
–3 +3
46 47 48 49 50 51 52 53 54 55 56 57
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Using Numbers in Patterns1 Automotive service technicians use diagnostic equipment to analyze problems in exhaust
systems When the system is operating correctly, the Y or vertical axis on the graph should showsignals that constantly change from under 02 volts to over 08 volts
Thegraphbelowshowstwosetsofumericaldata.Thetopsetshowsthereadigfromthedriver’ssideoftheegieadthebottomsetshowsthereadigfromthepasseger’sside.
Howarethetwosetsofgraphliesdifferet?
WORKInGLOADSFORWIREROPES
VerticalLit
ChokerHitch
BasketHitch
Rope Size Tons (2 000 lb)
1/43/8
1/2
5/8
3/4
7/8
1
060134
240
350
540
700
910
045100
180
260
400
520
680
120265
480
700
1080
1400
1820
2 An ironworker rigging a load plans to use a ¾-inch wire-rope choker hitch to lift a beam thatweighs 46 tons Use the table below to make a recommendation for a safer lift (There are severalcorrect answers)
Note: This capacity table isor this workbook only. On
the job you should use themanuacturer's table.
1.00
0.50
0.001.00
0.50
0.00
98 1998 2098 2198 2298
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Answer Key
Use this answer key to gain a better understanding of your numeracy skills Compare your answers tothose provided below to identify your strengths and areas for improvement
Note: There may be more than one method o arriving at the right answer. Answers may alsovary depending on how you round o your numbers.
Section 1: Measurement and Calculation
Pg 7 Using Measuring Tools Math Foundation Skills
Q1 31 / 4" 41 / 2" 63 / 16"
45 cm 97 cm 144 cm
Whole numbers, fractions,
decimals (imperial, metric)
Q2 a b c
d fe
Whole numbers, fractions,
decimals (imperial, metric)
Q3a 732 feet Whole numbers, decimals
Q3b 512 feet Whole numbers, decimals
Pg 9 Using Formulas
Q1 2 (478 m + 303 m) = 1562 = 157 m Perimeter (metric)
Q2 52' + 14' + (52' – 30' 8") + (28' – 14 ‘) +
30' 8" + 28' = 160'
160 ÷ 2 = 80 studs
Perimeter (imperial)
Q3 92 m × 78 m = 7176 m2
7176 m2 ÷ 45 m2 /L = 1595 L
1595 L ÷ 37 L = 431 = 5 containers
Area (metric)
Q4 31416 (82 ft × 82 ft) = 21124 ft2
(21124 ft2 ÷ 2 ft2 /tile) = 10562 = 106 tiles
106 tiles × $1329/tile = $1,40874
Area (imperial)
Q5 (14 m)2 – (925 m)2 = 11044 m2
11044 m2 × 0152 m = 1679 m3
Volume (metric)
Q6 r = ¾ × 16 ft = 12 ft
(31416 × (12 ft)2 × 16 ft) ÷ 3 = 2 41275 ft3
2 41275 ft3 ÷ 27 ft3/yd3 = 8936 yd3
Volume (imperial)
Q7 31416 × 2 m × 6 m = 376992 = 377 m2 Area (metric)
Q8 8 ohms ÷ 4 resistors = 2 ohms Equations and formulas
Q9 222 + 182 = 808
√ 808 = 2843 cm
Trigonometry
Q10 1 0002 + 1 2552 = 2 575 025
√ 2 575 025 = 1 605 mm
Trigonometry
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Q11 152 + (12– 8)2 = 241
√ 241 = 1552 inches
Trigonometry
Q12 28 × 0433 = 1212 psi Equations and formulas
Q13 8 in × 24 in = 192 in2
192 in2 ÷ 144 in2/ft2 = 133 ft2
Area (imperial)
Q13b 133 ft2 ×1 200 ft/min = 1 596 ft3 /min Equations and formulas
Pg 15 Using Drawings
Q1 5 / 4 × 1 ft = 5 ft
3 / 2 × 1 ft = 6 ft
Dimensions = 5 ft × 6 ft
Rates, ratios and
proportions
Q2 3 Whole numbers
Q3 2' 2" + 8' + 2' 2" = 12' 4" Measurement conversions
Q4 A = 12 ft ×14 ft = 168 ft2
168 ft2 + 30 ft2 = 198 ft2
198 ft2 ÷ 9 ft2/yd2 = 22 yd2
$2850/yd2 × 22 yd2 = $62700
Area, measurement
conversions
Q5 Method 1:
Heightofdrywallsheets=heightofroom
5 ft + 767 ft + 5 ft + 767 ft = 2534 ft
2534 ft – 3 ft = 2234 ft
2234 ft ÷ 4 ft/sheet = 5585 = 6 sheets
Method 2:
5 ft + 767 ft + 5 ft + 767 ft = 2534 ft
2534 ft – 3 ft = 2234 ft
2234 ft × 8 ft = 17872 ft2
4 ft × 8 ft = 32 ft2
17872 ft2 ÷ 32 ft2 = 5585 = 6 sheets
Decimals
Pg 17 Estimating Weight Loads
Q1 2 ft × 18 ft = 36 ft2
¾ × 40 lb/ft2 = 30 lb/ft2
36 ft2 × 30 lb/ft2 = 1 080 lb
Equations and formulas
Q2 26' × 3017' × 05' = 39221 ft3
39221 ft3 × 150 lb/ft3 = 58 8315 lb
Equations and formulas
Pg 18 Working with Quantities
Q1 Total fall = 30 ft × ¼ in/ft = 75 ft Rates, ratios andproportions
Q2 35 000 km × 06214 mi/km = 21 749 mi Rates, ratios and
proportions
Q3a 5 / 4 × 30 g = 375 g Rate, ratios and
proportions
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Q3b 5 / 4 × 60 mL = 75 mL Rate, ratios and
proportions
Q4 amount × 75 = quantity of ingredients
30
sugar–150g;bakigpowder–75g;
eggs–10;milk–2.5L:butter312.5g
Rate, ratios and
proportions
Q5a 9 posts × 25 bags/post = 225 = 23 bags Rate, ratios and
proportions
Q5b 5 bags = 3 ft × 2 ft × 33 ft = 198 ft3
5 ft × 233 ft × 05 ft = 5825 ft3
5825 ft3 ÷ 198 ft3 = 294
294 × 5 bags = 147 = 15 bags
Rate, ratios and
proportions
Q5c 15ft ÷ 4 ft = 375
375 × 35 = 13125 = 14 bags
14 bags × 25 L/bag = 35 litres of water
Rates, ratios and
proportions
Section 2: Money Math
Pg 20 Calculating Increases and Decreases Math Foundation Skills
Q1a (100 + 10 / 100 ) × $9725 = $10698 Percentages
Q1b 115 × $24999 = $28749 Percentages
Q1c 108 × $650 = $702 Percentages
Q2a 112 × $7350 = $8232 Percentages
Q2b 113 × $1,847 = $2,08711 Percentages
Q2c 108 × $8675 = $9369 Percentages
Q3a (100 – 10 / 100 ) × $8540 = $7686 Percentages
Q3b 067 × $1,348 = $90316 Percentages
Q3c 060 × $45975 = $27585 Percentages
Pg 21 Invoicing or Services
Q1a $10590 × 105 = $11120 (labour)
$280 × 111 = $311 (parts)
$11120 + $311 = $11431
Decimals
Q1b Change: $12001 – $11431 = $570 Decimals$50 $20 $10 $5 $2 $1 25¢ 10¢ 5¢ 1¢
1 2 2
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Section 4: Data Analysis
Pg 27 Calculating Tolerances Math Foundation Skills
Q1a X not acceptable
225° – 2° = 205°
201° is not between 205°
and 225° = not acceptable
Integers
Q1b X not acceptable0850 m – 0020 m = 0830 m
0827 m is not between 0830 m and 0850 m =
not acceptable
Integers
Q1c aacceptable
0750 L + 0015 L = 0765 L
0761 L is between 0750 L and 0765 L =
acceptable
Integers
Q2 •usea3 / 4" rope and a vertical lift (54 tons max)
•usea7 / 8" rope and a choker hitch (52 tons max)
Integers
Pg 28 Using Numbers in Patterns
Q1 Ithetopset,bothliesuctuatefromuder0.2
volts to over 08 volts In the bottom set, only one
line is showing this pattern The other line remains
almostataroud0.2volts.
Statistics and probability
Section 3: Scheduling, Budgeting and Accounting
Pg 23 Comparing Values Math Foundation Skills
Q1 Area of sidewalk = 32 ft × 3 ft = 96 ft2
Roll-on: (15 h × 2) × $3750/h = $11250
$8900 + $2678 = $11578$11250 + $11578 = $22828
Trowel-on: (15 h × 3) × $3750 = $16875
$4802 + $11507 + (2 × $5325) +
$2678 = $29655
$16875 + $29655 = $46530
$46530 – $22828 = $23702
The trowel-on method costs about $24000 more
Decimals
Pg 25 Accounting or Cost
Q1a $3,050 – $6,35603 = –$3,30603
Entry on invoice: (3,30603)
Integers
Q1b ($15300 + $14512 + $19910) × 5 = $2,48610
110 × $2,48610 = $2,73471
Integers, percentages