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Cool math Pre-Algebra Help Lessons: Properties - The Distributive Property

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This prealgebra lesson defines and explains the distributive property.

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The best source for free properties of addition and properties of multiplication worksheets. Easier to grade, more in-depth and best of all... 100% FREE! Kindergarten, 1st Grade, 2nd Grade, 3rd Grade, 4th Grade, 5th Grade and more!

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Learn about and practice the properties of multiplication

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Learn about and practice the properties of multiplication

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Properties and patterns for multiplication

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Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere.

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Cool math Pre-Algebra Help Lessons: Properties - The Associative Property of Multiplication

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This prealgebra lesson defines and explains the associative property of multiplication

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There are four properties involving multiplication that will help make problems easier to solve. They are the commutative, associative, multiplicative identity and distributive properties.

Commutative property: When two numbers are multiplied together, the product is the same regardless of the order of the multiplicands. For example 4 * 2 = 2 * 4

Associative Property: When three or more numbers are multiplied, the product is the same regardless of the grouping of the factors. For example (2 * 3) * 4 = 2 * (3 * 4)

Multiplicative Identity Property: The product of any number and one is that number. For example 5 * 1 = 5.

Distributive property: The sum of two numbers times a third number is equal to the sum of each addend times the third number. For example 4 * (6 + 3) = 4*6 + 4*3

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There are four properties involving multiplication that will help make problems easier to solve. They are the commutative, associative, multiplicative identity and distributive properties. Commutative property: When two numbers are multiplied together, the product is the same regardless of the order of the multiplicands.

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Learn about Properties of Multiplication

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Learn about Properties of Multiplication

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So if you look at each of these 4 by 6 grids, it's pretty clear that there's 24 of these green circle things in each of them. But what I want to show you is that you can get 24 as the product of three numbers in multiple different ways. And it actually doesn't matter which products you take first or what order you actually do them in. So let's think about this first. So the way that I've colored it in, I have these three groups of 4. If you look at the blue highlighting, this is one group of 4, two groups of 4, three groups of 4. Actually, let me make it a little bit clearer. One group of 4, two groups of 4, and three groups of 4. So these three columns you could view as 3 times 4. Now, we have another 3 times 4 right over here. This is also 3 times 4. We have one group of 4, two groups of 4, and three groups of 4. So you could view these combined as 2 times 3 times 4. We have one 3 times 4. And then we have another 3 times 4. So the whole thing we could view as-- let me give myself some more space-- as 2 times-- let me do that in blue-- 2 times 3 times 4. That's the total number of balls here. And you could see it based on how it was colored. And of course, if you did 3 times 4 first, you get 12. And then you multiply that times 2, you get 24, which is the total number of these green circle things. And I encourage you now to look at these other two. Pause the video and think about what these would be the product of, first looking at the blue grouping, then looking at the purple grouping in the same way that we did right over here, and verify that the product still equals 24. Well, I assume that you've paused the video. So you see here in this first, I guess you could call it a zone, we have two groups of 4. So this is 2 times 4 right over here. We have one group of 4, another group of 4. That's 2 times 4. We have one group of 4, another group of 4. So this is also 2 times 4 if we look in this purple zone. One group of 4, another group of 4. So this is also 2 times 4. So we have three 2 times 4's. So if we look at each of these, or all together, this is 3 times 2 times 4, so 3 times 2 times 4. Notice I did a different order. And here I did 3 times 4 first. Here I'm doing 2 times 4 first. But just like before, 2 times 4 is 8. 8 times 3 is still equal to 24, as it needs to, because we have exactly 24 of these green circle things. Once again, pause the video and try to do the same here. Look at the groupings in blue, then look at the groupings in purple, and try to express these 24 as some kind of product of 2, 3, and 4. Well, you see first we have these groupings of 3. So we have one grouping of 3 in this purple zone, two groupings of 3 in this purple zone. So you could do that as 2 times 3. And we have one 3 and another 3. So in this purple zone, this is another 2 times 3. We have another 2 times 3. Whoops. I wrote 2 times 2. 2 times 3. We have another 2 times 3. And then finally, we have a fourth 2 times 3. So how many 2 times 3's do we have here? Well, we have one, two, three, four 2 times 3's. So this whole thing could be written as 4 times 2 times 3. Now, what's this going to be equal to? Well, it needs to be equal to 24. And we can verify 2 times 3 is 6 times 4 is, indeed, 24. So the whole idea of what I'm trying to show here is that the order in which you multiply does not matter. Let me make this very clear. Let me pick a different example, a completely new example. So let's say that I have 4 times 5 times 6. You can do this multiplication in multiple ways. You could do 4 times 5 first. Or you could do 4 times 5 times 6 first. And you can verify that. I encourage you to pause the video and verify that these two things are equivalent. And this is actually called the associative property. It doesn't matter how you associate these things, which of these that you do first. Also, order does not matter. And we've seen that multiple times. Whether you do this or you do 5 times 4 times 6-- notice I swapped the 5 and 4-- this doesn't matter. Or whether you do this or 6 times 5 times 4, it doesn't matter. Here I swapped the 6 and the 5 times 4. All of these are going to get the exact same value. And I encourage you to pause the video. So when we're talking about which one we do first, whether we do the 4 times 5 first or the 5 times 6, that's called the associative property. It's kind of fancy word for a reasonably simple thing. And when we're saying that order doesn't matter, when it doesn't matter whether we do 4 times 5 or 5 times 4, that's called the commutative property. And once again, fancy word for a very simple thing. It's just saying it doesn't matter what order I do it in.

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Properties of multiplication (video) | Khan Academy

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Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere.

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Number Bubble: Skip Counting is an educational game for kids to practice counting by multiples.

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Self-correcting Auto scored quizzes for multiplication facts

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Self-correcting Auto scored quizzes for multiplication facts

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Multiplication

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Multiplication Auto-Scored Quizzes Expanded reporting features Mobile friendly Picture hint option Large equation input box Automatically scored and timed Enter answer with keyboard or touch pad Click here for "Pin" Style Navigation MULTIPLICATION Equation Family Quizzes (All equation for the fact group) MULTIPLICATION Up Through Quizzes (All equation UP THROUGH the fact group) The "up-through" quizzes for the tens, elevens, and twelves do not include all of the equations.

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IXL | Identify multiplication expressions for arrays | 3rd grade math

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Improve your math knowledge with free questions in "Identify multiplication expressions for arrays" and thousands of other math skills.

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Worksheets and interactive resources to help children learn early multiplication skills.

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I have these three star patches, I guess you could call them, right over here. And so I could say, if I had one group of three star patches, how many star patches do I have? So I literally have one group of three star patches. Well, that means that I have three star patches. 1, 2, 3. This is my one group of three. Now let's make it a little bit more interesting. Let's say that I had two groups. Let's say that I had two groups of three. So that's one group, and then here's a second group. Here's two groups of three. So how many total star patches do I have now? Well, I have two groups of three. Or another way of thinking about it is this is 3 plus 3. This is equal to 3 plus 3, which is equal to 6. So we see 1 times 3-- one group of 3 is 3. Two groups of 3, which is literally two 3's, is 6. Let's make it even more interesting. Let's have three groups of 3. Now, what is this going to be equal to? Well, it's three groups of 3. So I could write this as three groups, 3 times 3. And how many of these star patches do I now have? Well, this is going to be 3 plus 3 plus 3. It's going to be 3 plus 3 plus 3. Notice I have three 3's. I have two 3's. I have one 3. So this is 3 plus 3 plus 3 is equal to 9. And you can count them. 1, 2, 3, 4, 5, 6, 7, 8, 9, or you could just count by 3's. 3, 6, 9. And I think you see where this is going. Let's keep incrementing it. Let's get four groups of 3. So let's think about what 4 times 3 is. 1, 2, 3, and 4. This right over here is four groups of 3. We could write this down as 4 times 3, which is the same thing as 3 plus 3 plus 3 plus 3. Notice I have four 3's. One 3, two 3's, three 3's, four 3's. One 3, two 3's, three 3's, four 3's. So we get 3, 6, 9, 12. So what I encourage you to do now, now that the video is almost over, is to keep going. I want you to figure out what 5 times 3 is, and 6 times 3, and 7 times 3, and 8 times 3, and 9 times 3, and 10 times 3. And I'll give you a little hint. You don't always have to draw the star patches, but it's nice to visualize it. We saw 4 times 3 is literally four 3's. Well, 5 times 3 is going to be five 3's. So 2, 3, 4, 5. Which is equal to 3, 6, 9, 12, 15. So I encourage you to think about what all of these are after this video is done.

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Multiplication as equal groups (video) | Khan Academy

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I have these three star patches, I guess you could call them, right over here. And so I could say, if I had one group of three star patches, how many star patches do I have? So I literally have one group of three star patches.