Trades Math Workbook[1]

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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



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





4

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.



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.



6

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



7

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"



8

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



9

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



10

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'



11

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



12

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



13

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



14

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.



15

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



16

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



17

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)



18

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



19

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



20

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



21

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)



22

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



23

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



24

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



25

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



26

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



27

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



28

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



29

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



30

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



31

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



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

Documents

Trades Math Workbook[1]