# The Student Success Commons at York County Community College: MAT 107: Technical Mathematics

## Technical Math Resources

#### Please keep in mind that any videos, calculators, and notes on this page are no substitute for attending class, whether it be in person or online. All the resources on this page are here to supplement the information from your instructor and textbook. First and foremost please be sure to follow any directions your teacher provides before using these resources to ensure you meet course requirements.

This page is under construction. New resources will be added and updated soon.

## Chapter 4-1

#### In other words, a ratio says how much of one thing there is compared to another thing.

GEAR RATIO = (number of teeth on the driven gear)/(number of teeth on the driving gear)

COMPRESSION RATIO= (expanded volume)/(compressed volume)

## Chapter 4-3 through 4-5

#### A percentage is a ratio, fraction, or portion of a whole (which is represented as 100) usually denoted with the percent symbol: %.

(Click to enlarge or print)

## Chapter 6

#### Another way to think about negative numbers with money. Which bank account is worse off: Overdrawn \$750.00 (-750) or overdrawn \$2.35 (-2.35)? The account overdrawn by \$750 would be much worse to have than an account overdrawn by a little over two dollars (and much harder to recover from). Thus, -750 is less than than -2.35.

 COMMON SIGN KEYWORDS POSITIVE NEGATIVE Profit Increase Add Above More than Surplus Debt Loss Decrease Lower Below Defecit Subtract

#### Remember: math is the only time that "two wrongs make a right"! When adding or subtracting, two successive negative symbols turn into a plus sign. You'll see that this applies to multiplication and division as well.

• You have \$4.00. An item you wish to purchase will cost you \$3.00. You will have \$1.00 remaining.
• You have \$7.00. An item you wish to purchase will cost you \$10.00. You do not have enough so are left with a defecit of \$3.00, or -\$3.00

## Chapter 7

#### All three of these examples represent the same expression: 4 is being multiplied by some unknown number.

##### SKILL CHECK: get into the habit of avoiding confusion with the multiplication symbol by practicing using one of the above methods to write out multiplication problems.

When evaluating mathematical expressions, be sure to follow the order of operations:

1) G: Groupings. These include parentheses, brackets, and braces.
2) E: Exponents. This includes roots and radicals.
3) M and D: Multiplication or Division. These both have the same "weight" so when you get to this step do whichever operation comes first when working from left to right.
4) A and S: Addition or Subtraction. These both have the same "weight" so when you get to this step do whichever operation comes first when working from left to right.

## PROPERTIES TO KNOW

 PROPERTY DESCRIPTION EXAMPLE Commutative Property of Addition When two numbers are added, the sum is the same regardless of the order in which the numbers are added. 2 + 3 =  5 3 + 2 = 5 Associative Property of Addition When three or more numbers are added, the sum is the same regardless of the way in which the numbers are grouped. 6 + (4 + 3) = 13 (6 + 4) + 3 = 13 Commutative Property of Multiplication When two numbers are multiplied together, the product is the same regardless of the order in which the numbers are multiplied. 3 • 5 = 15 5 • 3 = 15 Associative Property of Multiplication When three or more numbers are multiplied, the product is the same regardless of the way in which the numbers are grouped. 6 • (4 • 3) = 72 (6 • 4) • 3 = 72 Distributive Property The sum of two numbers times a third number is equal to the sum of each addend times the third number. 5(7 + 2) = 45 5 • 7 + 5 • 2 = 45 Identity Property of Addition Adding 0 to any number does not change the original value. 76 + 0 = 76 Identity Property of Multiplication Multiplying any number by 1 does not change the original value. 19 • 1 = 19 Inverse Property of Addition The sum of any number and its additive inverse is equal to 0. 5 + -5 = 0 Inverse Property of Multiplication The product of any number and its reciprocal is equal to 1. 4(1/4) = 1 Zero Property of Multiplication Any number multiplied by 0 is equal to 0. 123(0) = 0

### TYPES OF NUMBERS

• Natural Numbers (N), (also called positive integers, counting numbers, or natural numbers); They are the numbers {1, 2, 3, 4, 5, …}
• Whole Numbers (W). This is the set of  natural numbers, plus zero, i.e., {0, 1, 2, 3, 4, 5, …}.
• Integers (Z). This is the set of all whole numbers plus all the negatives (or opposites) of the natural numbers, i.e., {… , ⁻2, ⁻1, 0, 1, 2, …}
• Rational numbers (Q). This is all the fractions where the top and bottom numbers are integers; e.g., 1/2, 3/4, 7/2, ⁻4/3, 4/1 [Note: The denominator cannot be 0, but the numerator can be].
• Real numbers (R), (also called measuring numbers or measurement numbers). This includes all numbers that can be written as a decimal. This includes fractions written in decimal form e.g., 0.5, 0.75 2.35, ⁻0.073, 0.3333, or 2.142857. It also includes all the irrational numbers such as π, √2 etc. Every real number corresponds to a point on the number line

### EQUATION-SOLVING TIPS THAT MAY SAVE YOUR LIFE:

#### Be familiar with the rules.

Know the order of operations, basic mathematical properties, and how to use your calculator properly.

Know what you know and know what you don't--especially when solving a word problem. Clarify for yourself what it is you have and what you're being asked to find.

#### Write clearly.

Don't skimp on writing things down. Write down the problem simply, in your own words. Set aside space to list out the variables in your problem, what they stand for, and what values are known to be associated with them. Color code to help you keep track.

#### PRACTICE.

Practice, practice, practice. Practice so much that the word practice no longer feels like a real word. Repeat the same problem multiple times.

#### Show all your steps.

Avoid skipping steps and definitely avoid not writing things down. This goes along with writing clearly: write each step on a new line. Don't sacrifice clarity for the sake of saving paper.

#### Double check.

As you solve ensure you're following the correct steps and using the correct values. Your instinct might be to rush in order to get the pain over with as fast as possible but please resist this temptation.