Order of Operations: Using PEMDAS to Simplify Expressions
Using the order of operations (PEMDAS) is a very important skill for any math student starting in pre-algebra. Take the time to learn this skill well since you’ll be using it in nearly every math problem you do!
PEMDAS tells us the order in which to simplify an expression. There are four steps.
Parentheses — this includes all grouping symbols such as brackets and absolute value.
Multiplication and Division — do these from left to right.
Addition and Subtraction — also do these from left to right.
In the video I explain how the order of operations works, why we use it, and go over four helpful examples. Take a look for yourself, or share it with a classmate who could benefit.
As an online math tutor, I love teaching my students helpful shortcuts! Algebra 2 and Precalculus students, this one is for you. Let’s learn a binomial expansion shortcut. Let’s say we want to expand .
Without knowing a shortcut, we would start out by first writing this as . Then we could FOIL the first two terms.
Which gets us closer, but now we need to multiply these together (by multiplying everything in the first polynomial by everything in the second polynomial).
Phew, we’re done. But what if we wanted to expand a binomial that has an exponent of 4 or 5? Multiplying all of those terms together can really make your head start spinning.
Luckily, there’s an easier way. We can use Pascal’s Triangle to expand binomials. Check out my video for four examples of using Pascal’s triangle to expand binomials.
I took a few minutes last week to make a video for anyone struggling or needing a refresher on simplifying complex fractions. Usually this is covered during the first few weeks of precalculus, but it will come up in Calculus and even College Algebra.
The key, as you’ll see, is to think of these complex fractions as the division of two fractions. Dividing two fractions, you say? That’s easy! We just flip and multiply.
Watch the video yourself, and share with a friend. We could all use some more simplicity (even if it’s complex fractions) in our lives.