# Making Pre-Algebra fun *tolerable*

# Chris is a Stanford-educated tutor with over 10 years experience tutoring Pre-Algebra to students of all abilities, from students struggling to get from a C to a B, to go-getters trying to move an A- up to an A, to struggling students just hoping to pass. In that time he got a lot of experience learning how to explain this stuff in a way it actually makes sense to non-math people. Through his videos he has helped countless students, and he can do the same for you.

# Pre-Algebra

# I. Numbers & Calculations:

#### By request, this chapter video covers the most important skill you'll need for Algebra and beyond: addition and subtraction of negative numbers using the number line. You can add and subtract any number with the number line, but negatives are where it's really great.

#### In this chapter we'll get into the basics of prime numbers and "prime factoroization", which we'll use in fractions and roots throughout Algebra and Algebra 2. I also get into divisibility rules, which show up -- among other places -- on the SAT.

#### Everything you need to know about fractions: reducing, least common denominators, addition, subtraction, multiplication, division, converting improper fractions to mixed numbers, converting to decimals. Also the tricky problem of converting repeating decimals to fractions.

#### Adding, subtracting, multiplying and dividing decimals (without a calculator) are all covered here.

#### Sig figs. This chapter will teach them to you, but it's your job to remember to use them in every answer for the rest of the year or you'll lose half your points. Seriously.

#### In this chapter we'll introduce the concept of exponents, as well as rules for combining and canceling exponents. Also, we'll talk about the special cases of exponents of 0 and 1, and what happens with negative exponents.

#### This chapter covers the basics of scientific notation, both converting it to regular numbers and back again. Decimals, huge numbers, multiplying scientific notation numbers together, positive exponents, negative exponents, "base 10", etc. it's all covered.

#### In this chapter we'll learn how to reduce radicals using a couple different methods. If you have a tough teacher and you have to know how to rationalize denominators and deal with variables under the root, then you'll need our Algebra 2 Roots & Radicals page.

#### In this chapter we'll introduce Order of Operations, often referred to simply by its ultra-useful acronym PEMDAS. We'll also get into how to do PEMDAS on your calculator, and a few common calculator mistakes to avoid.

#### We'll start by comping percentages using basic ratios, then we'll move on to using a decimal-based approach since that's what you'll need for more advanced problems. I also point out the most common types of trick questions about percents, including common types of SAT questions, and computing interest. And if you're super-advanced, "compound interest", where you have to calculate how interest builds over n weeks, months, years, etc.

# II. Intervals & Set Notation:

#### This is the thing where you use ( )'s and [ ]'s and ( ]'s and [ )'s to write down a chunk of the number line.

#### These videos cover everything about sets: elements, subsets, intersection, union, Venn diagrams, R, Z, Q, N. And set builder notation such as {x E R|x<5}.

#### More fun with sets. Also included in this topic: how to use weighted averages to figure out what grade you need on the final!

#### This chapter covers Venn diagrams in all their glory: two-circle, three-circle, complements, universes, intersections, unions, shading problems, numbers, members. Even covers the Common Core question about Venn diagrams!

# III. Geometry:

#### This chapter covers the basic formula and how to use it on right triangles, as well as the most common mistake students make with it. Also included is a video about simplifying radicals, since that comes up a lot with Pythagorean.

#### The videos in this topic introduce you to the X-Y plane (aka "rectangular coordinate system"), explain what the "origin" is, explain how to graph points, explain "the four quadrants", and tell you how to plot points.

#### If you're new to X-Y graphs, this is the place for you. We'll start with segments and lines without equations (for equations of lines from algebra, click here). Then we'll look at graphs of circles and rectangles, and x- and y-intercepts.

#### This chapter teaches you the formulas for finding the distance and midpoint between two points on the X-Y plane, as well as word problems using these formulas.

# IV. Variables & Equations:

#### In this chapter I explain what "x" is, what expressions are, how to plug in values to "evaluate" expressions, and how to turn word problems into equations so you can solve them. We'll also go over how to check whether a number is a solution of an equation or not.

#### These videos explain the process of solving algebraic equations by addition/subtraction, multiplication/division, combining like terms, and any combination of the three (multi-step problems like 3x-5=7).

#### Combining "like terms", adding and subtracting polynomials and monomials. Also covered: distribution (a.k.a. "multiplying stuff out"), where you have a number or variable in front of a set of parentheses that has to get multiplied by each term, such as 2(x-5).

#### Cross "multiplication" refers to what you do when you have two fractions across an equal sign from each other. You cross "cancel" when you are multiplying fractions. Confused yet? This chapter will sort you out.

#### Ratios are mostly word problems that lead to cross multiplication equations, and most students find them pretty basic. In this chapter we'll work some typical problems about marbles and pizzas, and I'll emphasize the one trick they always pull on the SAT.

#### Slope-Intercept Form, Point-Slope Form, Standard Form, Vertical Lines, Horizontal Lines, Perpendicular Lines: in this chapter, we experience the splendor of all the different types of linear functions, and master the equations and graphing of each.

# V. Advanced Stuff (really Algebra 1 topics):

#### When a word problem talks about two things being "proportional", this is what they're talking about. Or maybe they're "inversely proportional". "Joint" variation just refers to when you have three things that are proportional or inversely proportional instead of just the two, which is basically just ratios in disguise.

#### FOIL is an acronym that helps you multiply out parentheses in problems like (x-5)(x+2), and you've got to be able to do this before you can factor. This chapter covers the easier 2-by-2 FOIL problems, as well as 2-by-3 and beyond.

#### In this chapter we'll learn factoring, which is basically "reverse FOIL," including special cases like difference of squares and lead coefficients.

#### "Quadratic" means "squared", for some reason, so this chapter is about solving equations with x

^{2}'s in them. You'll have to learn several tricky techniques -- square rooting, factoring, completing the square, and/or the Quadratic Formula -- but I give you tips to make them easier, and to decide which to use in different situations.#### The above list probably already has more topics than almost any Pre-Algebra class covers, overlapping a bit with Algebra. But if you have one of those crazy Pre-Algebra teachers who's really throwing some advanced topics in there, click here for the Algebra class page.

##### (There's lots more geometry on the Geometry page.)