Auto Shop Math Salisbury

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

Writing out fractions Write out the fractions from 1/64 to 64/64’s Should look like this; 1/64 2/64 1/32 3/64 You cannot reduce a odd Number 4/64 2/32 1/16 But you can reduce a even Number 5/64 6/64 3/32 7/64 8/64 4/32 2/16 1/8 Write them all out you should have columns of 64 - 32 - 16 - 8 - 4 - 2

Cubic Centimeters to Cubic Inches: CC X .06102 = CI Liters to Cubic Centimeters 1 Liter = 1000 Cubic Centimeters So a 2200 is a 2.2 liter engine.

Cubic Inches to Cubic Centimeters: CI X 16.387 = CC

Cubic Inches to Liters: CI X .01639 = Liters So is a 350 cubic inch Chevrolet a 5.7Liter?

Liters to Cubic Inches: Liters X 61.024 = CI What is the Cubic inch of that 3.3 Dodge Caravan?

Cubic Inch Displacement How to figure out the size or your engine Bore X Bore X .7854 X stroke X # of cylinders or Bore2 X .7854 X stroke X # of cylinders What is the size of your engine after you bore it out .060?

Cubic Inch Displacement OK, I lied on the last slide. I did not show you all the steps first off where did I get the .7854. Was it just a random number I pulled out of the Air. Remember we are finding out the engine size in Cubic inch’s. The engine piston are round. How do you turn a round cylinder into a square. Remember pi 

Cubic Inch Displacement pi pi Is usually thought of as 3.14 Some people round it to 3.14159 My TI Calculator says 3.141592654 My computer says 3.14159265358979323846 Pi is an infinite decimal. That means it goes on forever. Not like my class that comes to an end. Most of the time I just use the Calculator

Cubic Inch Displacement So the .7854 I got by taking the Pi/4 3.141592654/4 = .785398163 So unless I am building my race engine I round it off to .7854 So that is how you find out the cubic inch’s of a round cylinder. / means to divide ÷

Cubic Inch Displacement The real formula should read like this Pi/4 X Bore2 X stroke X # of cylinders

Celsius to Fahrenheit F = (1.8 X C) + 32 C = Celsius F = Fahrenheit 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 .556 C = Celsius F = Fahrenheit 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) N = Number of threads per inch Take a decimal chart and check your work. 1 inch X 12tpi take .975 ÷ 12 = .08125 take the 1.000 - .08125 = .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 fraction, multiply the decimal fraction by the desired denominator and the result will be the numerator. Example .25 X 4 = 1 1 (numerator) 4 (denominator) The only problem with this is that if it is not the exact fraction it will not work out. See next page

Converting Decimal to Fractions To convert a decimal to a fraction. Take the decimal and put it over a 1 plus the same number of Zeros that there are #’s past the decimal place. Remove the decimal Example .25 = 25 reduces 1 (numerator) 100 to 4 (denominator) 1.2 = 12 reduces 6 10 to 5

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

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

Percent to a Fraction Percent means out of a hundred. 60% = .60 = 60 = 3 100 = 5 Take the largest number that you can divide into both numbers. In this example use 20. To make it easier get rid of the Zero and make it 6 = 3 10 = 5 got the same answer and you could figure it out in your head. In this example use 2.

Percent to a Fraction cont. Not all are that easy. Maybe your coach tells you to give 110% how much more is that. 110% .110 = 11 That is 1/10 more 100 = 10 What about a very small number like .5% .5% = .005 5 = 1 1000 200 Do you understand why I put 3 zero’s on that?

Fraction to a Percent To convert a fraction to a Percent. First divide the numerator by the denominator. (Top number divided by the bottom number.) Then you move the decimal over to the right two places. Example ¼ 1 ÷ 4 = .25 = 25% Example 5/4 5 ÷ 4 = 1.25= 125%

Kilometers to Miles Kilometers ÷ 1.60935 = Miles Kilometers X .62137 = Miles Some times we round it off to be; Kilometers ÷ 1.61 = Miles Miles to Kilometers Miles X 1.60935 = Kilometers or Miles ÷ .62137 = Kilometers

Inches and millimeters Inches X 25.4 = Millimeters (mm) Millimeters (mm) X .03937 = inches

Quarts and liters Quarts X .94635 = Liters Liters X 1.0567 = Quarts

Gallons and liters Gallons X 3.7854 = Liters Liters X .2642 = Gallons

Cups, Pints & Quarts 2 Cups = 1 pint 2 Pints = 1 quart 4 Quarts = 1 gallon

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

How fast is your car going Take 3600 ÷ by the seconds it takes to go 1 mile = Miles per hour 3600 ÷ 50 seconds = 72 mph If your going 1 mile in 60 seconds what’s your mph?

Tire Size If you switch tire size on a car you can mess up the speedometer to figure out how close you are do the math to figure out the diameter. For a 205/75R15 tire it would look like this 205 X .75 x 2 ÷ 25.4 + 15= 27.106 Tire size X Aspect ratio X 2 ÷ 25.4 + Rim size 100

Adding a Percent This would be useful when adding sales tax to your work order or how much tip to leave. The first way is to take the total and multiply the percentage you need to add. 20.00 X .083 1.66

Adding a Percent The other way is to use the % Key on the calculator. 20.00 X8.3% 1.66

Rounding a Percent You need to be able to come up with a close estimate with percentages by doing the quick math in your head. For example 10% of 100 is 10. 10% of 10 is 1. with that information you should be able to quickly figure out different percentages. 20% of 42 is what? 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 that is .20, the total is 4.20 so just double it to get the 20% 8.40 Was that hard???

The End for now. More math coming