Author Archives: admin
Converting REPEATING Decimals to Fractions
You need equations and variables to convert repeating decimals to fractions, so if you're not there yet in class, skip this video. But if you're ready for this topic, it's definitely one of the only fun things you'll do in algebra. Most of my students, even ones who hate math, enjoy working these problems because... I don't know why, maybe because it feels like you're outsmarting your calculator?7.NS.1, 7.NS.2, 7.NS.3
Multiplying & Dividing Fractions
Even though students start fractions in elementary school, multiplying and dividing them gets a little bit "interesting" in Algebra with triple-deck fractions. In this video we cover the basics, but we also look at the algebraic nightmares which are "complex" fractions (fractions within fractions).7.NS.1, 7.NS.2, 7.NS.3
Adding & Subtracting Fractions
You're probably surprised we got this far down the page before mentioning Least Common Denominator (LCD), eh? In this video we cover adding and subtracting fractions with different denominators using the LCD method (similar to least common multiple), or LCM. I also show you a great trick for coming up with a common denominator when you're having trouble thinking of a number that both denominators go into. 7.NS.1, 7.NS.2, 7.NS.3
How to Reduce Fractions (free)
There are a few different methods of reducing fractions -- prime factorization, factor trees, "pulling stuff out" -- and we'll cover them all in this video. We'll also talk about common mistakes and how to avoid them.7.NS.1, 7.NS.2, 7.NS.3
Fractions & Mixed Numbers on Calculator
Students these days love calculators! So in this video we'll talk about how to do the same basic fraction stuff we covered in the last video, except this time on your calculator. We'll also cover converting fractions and mixed numbers to decimals, and how different calculator types (four-function, scientific, graphing) treat fractions differently.7.NS.1, 7.NS.2, 7.NS.3
Improper Fractions and Mixed Numbers
In this video we'll learn about the basics of fractions in Algebra, and how in algebra fractions are all about division. We'll also review what improper fractions are, how to convert improper fractions to mixed numbers, how to convert mixed numbers to fractions, and what to do if there's a zero in a fraction's numerator or denominator.7.NS.1, 7.NS.2, 7.NS.3
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.
Prime Numbers, Factors & Factorization (free)
In this video I get into what prime numbers are, and how to do a prime factorization, all of which will be key when you're working on simplifying roots and fractions in later chapters. Also just two reminders: 1) one is not a prime number, since most people forget that, and 2) memorize your times tables!
Divisibility Rules (free)
In this video I cover the divisibility rules which help you figure out if a number is divisible by 2, 3, 4, 5, 6, 7, 8, 9 or 10. They're the next best thing to actually, you know, memorizing your times tables. Did you get that hint? Memorize your times tables already! Gotta be a good app for that.
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.
Basic Trig Proofs Using "Reciprocal Properties"
"Reciprocal Properties" is just a fancy way math teachers use to describe these three equations you already know: csc=1/sin, sec=1/cos, tan=sin/cos, and cot=cos/sin. Not so bad, right? The easiest trig proofs are the ones where you have a string of things multiplied together, so that if you turn them all into sin's & cos's, they'll cancel out. In this video I work a bunch of them, and show you how to spot this type.
Solving Systems: Matrix Row Operations (Gauss Jordan or Gaussian Elimination)
This is a slow and tedious way of solving systems, but then again, what isn't? In this rather long video we'll solve a system of 2 equations 2 unknowns, and 3 equations 3 unknowns. elimination, substitution and Cramer's Rule are all better choices.
Inverse & Identity Matrices
The identity matrix is the one - either 2x2, 3x3, or 4x4 - with a diagonal of 1's and everything else 0's. What's it got to do with inverse matrices? If you multiply a matrix by its inverse, you get the identity matrix, kind of like if you multiply a function by its inverse you get x.
Cramer's Rule
You've known for while how to solve a system of equations using elimination or substitution. But if you get tired of those, welcome to Cramer's Rule, which uses matrices and determinants to solve for x, y, and any other letters you've got!
The Determinant
In this video we'll cover how to calculate the determinant of 2x2 and 3x3 matrices, the latter requiring you to break the 3x3 into a bunch of 2x2's. If your teacher lets you use calculators for 3x3's, you're in luck; otherwise you're going to get tired of me telling you not to forget the minus sign in front of the second term!
Multiplying Matrices
To multiply matrices they don't have to be the exact same size, but they do have to obey certain guidelines that I cover in this video. I'll also take you through the tedious process of actually multiplying them, which involves multiplying a row of the first matrix by a column of the second in what's basically a glorified FOIL technique.
Basic Matrix Operations
This video covers the most basic things you can do to matrices which are the same size: adding and subtracting them. We'll also learn how to multiply them by a scalar, which is another word for constant.
This chapter covers the basics - matrix addition, subtraction, multiplication, and determinants - along with advanced moves like solving systems with row operations and Cramer's Rule.
Binomial Probability Formula
Finally, all that work on combinations will pay off (as if it hadn't already) when you get to use your nCr knowledge again, finding such amazing probabilities as: "In a family with 8 kids, what's the chance at least 2 are boys" and "If you flip a weighted coin 5 times, what's the probability of getting exactly 4 heads?"