The Science of Life Lecture Series

So, there has been a debate going around social media as of late.  It deals with the order of operations, and the fact that the vast majority of people seem to forget that each step of the order of operations ends with the phrase "from left to right".  That phrase is irrelevant most of the time, but when it's not irreverent, it's crucial. Damn you PEMDAS! So what is 9!/8!(3^2)?  Is it 81 or 1?  Or is it something else entirely?  Now I am going to tread lightly here so as to not enrage too many hearts. Before I answer this question, it would be a good idea to review the algebraic order of operations , or PEMDAS: Perform all operations inside parentheses using the remainder of the order of operations as your guide to the order.  Any parentheses within parentheses are to be performed from the inside out and from left to right. Perform any and all exponent from left to right. Perform all multiplication and division from left to right. Perform all ad

Typically, problems involving at least two unknowns are solved by translating the problem to two or more equations, such as the slope-intercept form and/or the standard form of the line. Developing Equations from Sentence Form When deciphering word problems, we typically try to take a word or phrase which explains what a variable is and represent that word or phrase as a single letter instead. For instance, the energy consumed by your household so far this billing cycle can be represented by the letter E, and the total cost so far in that pay cycle can be represented by the letter C. It is also useful to translate commonly used words into mathematical operations. For example, the product of two things m and c represents multiplication, while the square of c represents squaring the letter c. So the product of the two values of m and the square of c would be $m \times c^2$. I will leave a table of some common and uncommon phrases and their mathematical translations here . Outs

The process of problem solving - commonly known as solving word problems - tends to give students of Algebra the most trouble. Part of the issue is the lack of intuitive understanding; a bigger issue is the lack of good explanations from both text books and teachers. There tends to be less explicit explanations available for for how to set up word problems to equation form than for any other section of Algebra. Once the issue of setting up problems is resolved, solving them becomes much easier. This chapter deals with the mechanism of setting up problems in order to solve them. This is necessary for all physical, life, and social sciences as well as all forms of accounting and economics. Basically, anything which is fundamentally numerical in nature tequires this skill. I will try my best to explain how to set up a word prolem to the best of my ability, so sit back, relax, and get ready to understand. Section 1: Systems of Equations in Two Equations Section 2: Solvin

When interpreting word problems as math equations, it is a good idea to keep in mind that certain phrases will always represent a certain mathematical operation.  Here is a list of some of these words for the basic operations. Addition Subtraction Multiplication Division Equals Exponent Parenthases Add Subtract Multiply Divide Is To the power of Quantity Sum Difference Product Quotient Yields Raised to the Increased by Decreased by Times As much Set as Plus Minus Double ($\times 2$) Halve ($\frac{x}{2}$) Equal to More Less Triple ($\times 3$) A third ($\frac{x}{3}$) Determined to be Combined Change Twice ($\