• Unit 2: Order of Operations

    In life, we often have procedures that everybody uses to avoid problems. When driving a car, for example: if you want to change lanes, you have to first look to make sure the lane is clear, activate your turn signal, check the lane again, move into the lane, and deactivate your turn signal. You do not move into the lane, activate your signal, make sure the lane is clear, and deactivate your signal. That can, and eventually will, cause a serious accident. In order to avoid costly errors, mathematicians had to agree on the series of steps that are needed to simplify expressions involving the four basic operations, grouping symbols, and exponents. This series of steps is known as the "order of operations" and is more commonly known as either PEMDAS or "Please Excuse My Dear Aunt Sally, she Left to Right." This tells us in which order to simplify the expression. (Tip: it is multiply OR divide and add OR subtract - whichever you see first.)

    Mathematicians also needed a way to quickly write out a repeated multiplication problem, like 2 x 2 x 2 x 2 x 2, so they invented the use of exponents. This unit will introduce you to the process of working with basic exponents. As you go higher, you will learn more about exponents.

    Another topic you will learn about in this unit is the concept of "greatest common factor." Mathematically, the greatest common factor (GCF) is the largest number you can divide two or more numbers by. In real life, it also makes appearances, both mathematical and non-mathematical. A detective trying to make connections between an arrested criminal and a suspected accomplice is going to be less interested in the facts that they have both eaten at McDonald's and both like strawberry milkshakes than in the fact that the suspected accomplice has been the criminal's best friend for twenty years. That fact is far greater to the investigation.

    The last topic you will cover is related to greatest common factor but is different. It is known as "least common multiple." Here, you are trying to determine the smallest number that two numbers can both divide into. Again, it appears in life. Let's say your favorite radio station is running a promotion: every fifth caller receives free concert tickets, and every twelfth caller receives a free gas card. How long will it take before they have a caller who receives both prizes on the same phone call? This is an example of using the least common multiple. (In case you are wondering, it would be the 60th caller who won both prizes.)

    Completing this unit should take you approximately 22 hours.