Auto Shop Math

SalisburySalisbury

The reason we need Math

You will need to do math problems every day if you You will need to do math problems every day if you plan on working in a auto shop. Here are some plan on working in a auto shop. Here are some basic formulas that you will use. Time is money so basic formulas that you will use. Time is money so learn how to use a calculator, it can be one of your learn how to use a calculator, it can be one of your best friend’s. Learn it, you cannot depend on best friend’s. Learn it, you cannot depend on someone else to do the math for you.someone else to do the math for you.

Scott SalisburyScott Salisbury

Writing out fractionsWrite out the fractions from 1/64 to 64/64’sShould look like this;1/642/64 1/323/64 You cannot reduce a odd Number4/64 2/32 1/16 But you can reduce a even Number5/646/64 3/327/648/64 4/32 2/16 1/8Write them all out you should have columns of 64 - 32 - 16 - 8 - 4 - 2

Cubic Centimeters to Cubic Inches:

CC X .06102 = CICC X .06102 = CI

Liters to Cubic CentimetersLiters to Cubic Centimeters 1 Liter = 1000 Cubic Centimeters1 Liter = 1000 Cubic Centimeters

So a 2200 is a 2.2 liter engine.So a 2200 is a 2.2 liter engine.

Cubic Inches to Cubic Centimeters:

CI X 16.387 = CCCI X 16.387 = CC

CI X .01639 = LitersCI X .01639 = Liters

So is a 350 cubic inch Chevrolet a 5.7Liter?So is a 350 cubic inch Chevrolet a 5.7Liter?

Cubic Inches to Liters:

Liters to Cubic Inches:

Liters X 61.024 = CILiters X 61.024 = CI

What is the Cubic inch of that 3.3 Dodge What is the Cubic inch of that 3.3 Dodge Caravan?Caravan?

Cubic Inch DisplacementHow to figure out the size or your engine

Bore X Bore X .7854 X stroke X # of Bore X Bore X .7854 X stroke X # of cylinderscylinders or or

BoreBore22 X .7854 X stroke X # of cylinders X .7854 X stroke X # of cylinders

What is the size of your engine after you What is the size of your engine after you bore it out .060?bore it out .060?

Cubic Inch Displacement

OK, I lied on the last slide. I did not show you all OK, I lied on the last slide. I did not show you all the steps first off where did I get the .7854. Was the steps first off where did I get the .7854. Was it just a random number I pulled out of the Air.it just a random number I pulled out of the Air.

Remember we are finding out the engine size in Remember we are finding out the engine size in Cubic inch’s. The engine piston are round. How Cubic inch’s. The engine piston are round. How do you turn a round cylinder into a square.do you turn a round cylinder into a square.

Remember pi Remember pi

Cubic Inch Displacement pi pi Is usually thought of as 3.14pi Is usually thought of as 3.14 Some people round it to 3.14159Some people round it to 3.14159 My TI Calculator says 3.141592654My TI Calculator says 3.141592654 My computer says 3.14159265358979323846My computer says 3.14159265358979323846 Pi is an infinite decimal. That means it goes on forever. Not like Pi is an infinite decimal. That means it goes on forever. Not like

my class that comes to an end.my class that comes to an end. Most of the time I just use the CalculatorMost of the time I just use the Calculator

Cubic Inch Displacement

So the .7854 I got by taking the Pi/4 So the .7854 I got by taking the Pi/4

3.141592654/4 = .785398163 3.141592654/4 = .785398163 So unless I am building my race engine I round it So unless I am building my race engine I round it

off to .7854off to .7854 So that is how you find out the cubic inch’s of a So that is how you find out the cubic inch’s of a

round cylinder.round cylinder.

/ means to divide / means to divide ÷÷

Cubic Inch Displacement

The real formula should read like thisThe real formula should read like this Pi/4 X BorePi/4 X Bore22 X stroke X # of cylinders X stroke X # of cylinders

Celsius to Fahrenheit F = (1.8 X C) + 32F = (1.8 X C) + 32

C = Celsius F = Fahrenheit C = Celsius F = Fahrenheit 1.8 X 12 =21.6 + 32 = 53.6

You can also come close by just rounding it off by take the Celsius reading doubling it and add 32.12 + 12 = 24 plus 32 = 56

Sometimes you will see it written out as F = (C × 9/5) + 32 What’s the difference between 9/5 and 1.8 take the 9 and divide by 5 and guess what, you come up with 1.8.

Fahrenheit to Celsius C = (F - 32) X .556C = (F - 32) X .556

C = Celsius F = Fahrenheit C = Celsius F = Fahrenheit 75 – 32 = 43 X .556 = 23.9 Celsius 75 – 32 = 43 X .556 = 23.9 Celsius

You can also come close by just rounding it off. Take the Fahrenheit reading Subtract 32 and divide by 2 Practice doing this in your head if you need a calculator just do the whole problem the right way.

Sometimes you will see it written out as C = (F -32) X .556 What’s the difference between 5/9 and .556 take the 5 and divide by 9 and guess what, you come up with .556 Well not really it’s .555555556

Tap drill size

Tap drill size = Major diameter - (.975 ÷ N)Tap drill size = Major diameter - (.975 ÷ N) N = Number of threads per inchN = Number of threads per inch Take a decimal chart and check your work.Take a decimal chart and check your work.

1 inch X 12tpi take .975 ÷ 12 = .08125 take the 1.000 - .08125 = ÷ 12 = .08125 take the 1.000 - .08125 = .9185 Look at the decimal chart.9185 Look at the decimal chart the closest one is 59/64 that is .9219 close enough.

Converting Decimal to Fractions

To convert a decimal fraction to a common To convert a decimal fraction to a common fraction, multiply the decimal fraction by the fraction, multiply the decimal fraction by the desired denominator and the result will be the desired denominator and the result will be the numerator. Examplenumerator. Example.25 X 4 = 1 .25 X 4 = 1 1 1 (numerator) (numerator) 4 (denominator) 4 (denominator)

The only problem with this is that if it is not the The only problem with this is that if it is not the exact fraction it will not work out. See next pageexact fraction it will not work out. See next page

Converting Decimal to Fractions To convert a decimal to a fraction. Take the To convert a decimal to a fraction. Take the

decimal and put it over a 1 plus the same decimal and put it over a 1 plus the same number of Zeros that there are #’s past the number of Zeros that there are #’s past the decimal place. Remove the decimal decimal place. Remove the decimal ExampleExample.25 = .25 = 2525 reduces reduces 1 1 (numerator) (numerator) 100 to 4 (denominator) 100 to 4 (denominator)

1.2 = 1.2 = 1212 reduces reduces 66

10 to 510 to 5

Decimal to Percent

Move the decimal two places to the right.Move the decimal two places to the right. Example .40 = 40%Example .40 = 40% Example 1.50 = 150%Example 1.50 = 150%

Fractions to Decimal

To convert a fraction to a decimal divide the To convert a fraction to a decimal divide the numerator by the denominator. numerator by the denominator. (Top number divided by the bottom number.)(Top number divided by the bottom number.)Example ¼ 1 ÷ 4 = .25Example ¼ 1 ÷ 4 = .25

Percent to a Fraction Percent means out of a hundred.Percent means out of a hundred. 60% = .60 = 60% = .60 = 6060 = = 33 100 = 5100 = 5Take the largest number that you can divide Take the largest number that you can divide

into both numbers. In this example use 20.into both numbers. In this example use 20.

To make it easier get rid of the Zero and make it To make it easier get rid of the Zero and make it 66 = = 33

10 = 5 got the same answer and you could 10 = 5 got the same answer and you could figure it out in your head.figure it out in your head.

In this example use 2.In this example use 2.

Percent to a Fraction cont. Not all are that easy. Maybe your coach tells Not all are that easy. Maybe your coach tells

you to give 110% how much more is that.you to give 110% how much more is that.

110% 110% .110.110 = = 1111 That is 1/10 more That is 1/10 more

100 = 10100 = 10

What about a very small number like .5%What about a very small number like .5%

.5% = .005 .5% = .005 5 5 = = 1 1

1000 2001000 200

Do you understand why I put 3 zero’s on that?Do you understand why I put 3 zero’s on that?

Fraction to a Percent

To convert a fraction to a Percent. First To convert a fraction to a Percent. First divide the numerator by the denominator. divide the numerator by the denominator. (Top number divided by the bottom (Top number divided by the bottom number.) Then you move the decimal over number.) Then you move the decimal over to the right two places.to the right two places.

Example ¼ 1 ÷ 4 = .25 = 25%Example ¼ 1 ÷ 4 = .25 = 25% Example 5/4 5 ÷ 4 = 1.25= 125%Example 5/4 5 ÷ 4 = 1.25= 125%

Kilometers to Miles Kilometers ÷ 1.60935 = MilesKilometers ÷ 1.60935 = Miles Kilometers X .62137 = MilesKilometers X .62137 = Miles

Some times we round it off to be;Some times we round it off to be; Kilometers ÷ 1.61 = MilesKilometers ÷ 1.61 = Miles

Miles to Kilometers Miles to Kilometers

Miles X 1.60935 = Kilometers orMiles X 1.60935 = Kilometers or

Miles ÷ .62137 = KilometersMiles ÷ .62137 = Kilometers

Inches and millimeters

Inches X 25.4 = Millimeters (mm)Inches X 25.4 = Millimeters (mm) Millimeters (mm) X .03937 = inchesMillimeters (mm) X .03937 = inches

Quarts and liters

Quarts X .94635 = LitersQuarts X .94635 = Liters Liters X 1.0567 = QuartsLiters X 1.0567 = Quarts

Gallons and liters

Gallons X 3.7854 = Liters Gallons X 3.7854 = Liters Liters X .2642 = Gallons Liters X .2642 = Gallons

Cups, Pints & Quarts

2 Cups = 1 pint2 Cups = 1 pint 2 Pints = 1 quart2 Pints = 1 quart 4 Quarts = 1 gallon 4 Quarts = 1 gallon

Fluid Ounce’s

1 cup = 8 Fluid Ounce’s1 cup = 8 Fluid Ounce’s 1 pint = 16 Fluid Ounce’s1 pint = 16 Fluid Ounce’s 1 quart = 32 Fluid Ounce’s1 quart = 32 Fluid Ounce’s 1 gallon = 128 Fluid Ounce’s1 gallon = 128 Fluid Ounce’s

How fast is your car going

Take 3600 ÷ by the seconds it takes Take 3600 ÷ by the seconds it takes to go 1 mile = Miles per hourto go 1 mile = Miles per hour

3600 ÷ 50 seconds = 72 mph3600 ÷ 50 seconds = 72 mph

If your going 1 mile in 60 seconds If your going 1 mile in 60 seconds what’s your mph?what’s your mph?

Tire Size If you switch tire size on a car you can mess up the If you switch tire size on a car you can mess up the

speedometer to figure out how close you are do the math speedometer to figure out how close you are do the math to figure out the diameter.to figure out the diameter.

For a 205/75R15 tire it would look like thisFor a 205/75R15 tire it would look like this

205 X .75 x 2 ÷ 25.4 + 15= 27.106205 X .75 x 2 ÷ 25.4 + 15= 27.106

Tire size X Tire size X Aspect ratioAspect ratio X 2 ÷ 25.4 + Rim size X 2 ÷ 25.4 + Rim size 100100

Adding a Percent

This would be useful when adding sales tax This would be useful when adding sales tax to your work order or how much tip to leave.to your work order or how much tip to leave.

The first way is to take the total and multiply The first way is to take the total and multiply the percentage you need to add.the percentage you need to add.

20.0020.00X .083X .083 1.66 1.66

Adding a Percent

The other way is to use the % Key on the The other way is to use the % Key on the calculator.calculator.

20.0020.00X8.3%X8.3% 1.66 1.66

Rounding a Percent You need to be able to come up with a close You need to be able to come up with a close

estimate with percentages by doing the quick estimate with percentages by doing the quick math in your head. For example 10% of 100 math in your head. For example 10% of 100 is 10. 10% of 10 is 1. with that information is 10. 10% of 10 is 1. with that information you should be able to quickly figure out you should be able to quickly figure out different percentages. 20% of 42 is what? different percentages. 20% of 42 is what? You know that 10% of 10 is 1. So take 10% You know that 10% of 10 is 1. So take 10% of 40. (1-2-3-4) the 40 is 4. Then take the 2 of 40. (1-2-3-4) the 40 is 4. Then take the 2 that is .20, the total is 4.20 so just double it to that is .20, the total is 4.20 so just double it to get the 20% 8.40 get the 20% 8.40

Was that hard???Was that hard???

The End for now.

More math coming