Hey it’s Professor Dave, let’s learn some algebraic properties. Remember when we learned about a few different mathematical properties and how they pertained to numbers? Let’s learn how they will be important in algebra when manipulating variables. The most important of these properties will be the distributive property. This told us how a number could be distributed across a parenthetical sum or difference. This didn’t matter too much for arithmetic, because four times the quantity of two plus three is certainly equal to four times two plus four times three, but there was nothing stopping us from adding two and three first, and then multiplying by four. We should get…


The Distributive Property In Arithmetic
Hi, I’m Rob. Welcome to Math Antics! In this video, we’re going to talk about a really important math concept called “The Distributive Property”. Well… at least that’s what it’s was called sometimes. You may hear it referred to as “The Distributive Law” or even the “The Distributive Property of Multiplication over Addition” by people who want to sound really technical. But no matter what it’s called, the concept of the Distributive Property is the same. Before we actually dive into that concept, there are two quick things that will help make it easier to understand. The first is simply knowing what the word “Distribute” mean. To distribute something means…

Exponent properties 1  Exponent expressions and equations  Algebra I  Khan Academy
Simplify 3a times a to the fifth times a squared. So the exponent property we can use here is if we have the same base, in this case, it’s a. If we have it raised to the x power, we’re multiplying it by a to the y power, then this is just going to be equal to a to the x plus y power. And we’ll think about why that works in a second. So let’s just apply it here. Let’s start with the a to the fifth times a squared. So if we just apply this property over here, this will result in a to the fifth plus twoth…

Distributive property exercise examples  Arithmetic properties  PreAlgebra  Khan Academy
We’re asked to rewrite the expression 7 times open parentheses 5 plus 11 close parentheses as the sum of 35 and another whole number. So really what they’re asking us to do is just apply the distributive property. We have 7 times the quantity 5 plus 11. Now this is easy to calculate. You could just say 5 plus 11 is 16 and then 16 times 7 is what? That’s 70 plus 42 which would be 112. But that’s not what they’re asking us to do. They’re not saying just calculate this. They’re saying express this as a sum of 35 and another whole number. So let’s apply the distributive…

Using the distributive property when multiplying
– [Instructor] What we’re going to do in this video is dig a little bit deeper into our understanding of multiplication. And just as an example, we’re going to use four times seven. And some of you might know what four times seven is, but even in this case, I think you might get something from this video because we’re gonna think about how you can break down a multiplication question into simpler parts, and that’s going to be useful well beyond four times seven. It’s going to be useful in your future when you’re tackling more and more complicated things. Now there’s a couple of ways that we can…

Associative property of multiplication
– [Instructor] So, what we’re gonna do is get a little bit of practicing multiple numbers together and we’re gonna discover some things. So, first I want you to figure out what four times five times two is. Pause the video and try to figure it out on your own. Alright, so whatever your answer is, some of you might have done it this way, some of you might have said hey, what is four times five and then you multiplied it by two, so what you would really have done is you would have done four times five first, so that’s why I put parentheses around that and then…

Multiplying: 2 digits numbers (using distributive property)  4th grade  Khan Academy
In this video, I’m going to multiply 87 times 63. But I’m not going to do it just by using some process, just showing you some steps. Instead, we’re just going to use the distributive property to actually try to calculate this thing. So first, what I’m going to do– let me rewrite 87. So this is the same thing as 87. But instead of writing 63 like that, I’m going to write 63 as 60 plus 3. Now, what is this going to be equal to? Well, 87 times 60 plus 3, that’s going to be the same thing as– and let me actually copy and paste this. So…

Introduction to the Distributive Property
>>Professor Perez: Hey! This is Professor Perez again. Today we’re going to look an introduction to the distributive property. Of course, we’ve got to get Charlie out here. He better be ready! Hey, Charlie, you ready to go?>>Charlie: Ya…>>Professor Perez: All right, here we go. Right here. Introduction to the distributive property. So, what the distributive property is, is what we’re going to do, is we’re going to distribute a number across an addition or a subtraction using multiplication. Let me give you an example here. 2 times 5 plus 3. Notice the 5 plus 3 is in parenthesis. Before we get to the distributive property, what we could do…

Ex: Simplify Exponential Expressions Using Power Property – Products to Powers
We want to simplify the following expressions completely. The first expression is two x raised to the fourth power. Let’s first simplify this by expanding, and then we’ll simplify it again using the power property of exponents. Notice we have an exponent of four, which means we have four factors of the base, which is two x. So this is equal to two x, times two x, times two x, times two x. Once expanded, notice how we can see we have four factors of two and four factors of x, so we can write this as two to the fourth times x to the fourth, and we can evaluate…

How to use the distributive property with variables  6th grade  Khan Academy
We’re asked to apply the distributive property. And we have 1/2 times the expression 2a6b+8. So, to figure this out, I’ve actually already copy and pasted this problem onto my scratch pad. I have it right over here. 1/2(2a6b+8). So, lemme just rewrite it. So, I’m gonna take, and lemme color code it, too, just for fun, so it’s going to be 1/2 times, give myself some space, 1/2(2a6b), so, 2a6b, minus six, lemme write it this way – 6b, and then we have plus eight. Plus, and I will do eight in this color. +8. And so, i just need to distribute the 1/2. If I multiplying 1/2 times…