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Using associative property to simplify multiplication

Sal uses the associative property to multiply 2-digit numbers by 1-digit numbers.

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  • blobby green style avatar for user Oz F
    Can't we do like that 3*21 = (3*20)+(3*1)=60+3=63
    For me it is much more easier to do them
    like 83 *4 =(80*4)+(3*4)=320+12=332?
    (11 votes)
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  • duskpin sapling style avatar for user Banana boi
    i dosent know how to do this very well can i has some help?
    (9 votes)
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  • duskpin sapling style avatar for user SerraO
    There was so many numbers and number sentences I couldn't understand anything. Why are we doing so much things?
    (6 votes)
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  • starky tree style avatar for user IsaiahR
    why does the teachers make math so hard
    (5 votes)
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  • blobby green style avatar for user xedevel
    Does it matter, if you wrote the answer to be 15 x 3 = (3x3) x 5 = 9 x 5 = 45. / video time.
    (5 votes)
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  • stelly blue style avatar for user adaggubati
    why does 3x1=3?
    (2 votes)
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  • blobby green style avatar for user Trish
    What does intuitive mean ?
    (3 votes)
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  • female robot ada style avatar for user riderbri56
    I am very confused I realy need some help.If you help i will give you an up vote.Thank you.
    (3 votes)
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  • leafers sapling style avatar for user wfosso30
    what are the energy points for?
    (3 votes)
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  • aqualine sapling style avatar for user hamiltonpn
    Can some one help me?
    (2 votes)
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    • hopper cool style avatar for user Philip
      Okay. So, when multiplying a value of two digits or longer, by a value of one digit, you are making a one-digit by one-digit multiplication at each place value, but since they are of higher place values, each also needs to have their appropriate place values.
      The video has five times 18. So first you do 5 times 8. That equals 40. Then you have a 5x1, which equals 5. But since the 1 is in the ten's place, the value of this product is 50.
      After you finish the multiplication of the individual digits, you add them according to their place values. Previously, you were pretending that every value was of the one'a place, but for the correct product you will now need to add each to their actual place values. Both the 5 and 4 are in the ten's place, and is why there is 90.

      Sometimes, you may have a digit on a line that, when added to digit below, gives a sum greater than 10. In this case, the next higher place value needs to be increased by the  so the 10s are not forgotten (that is what occurred when the 5 times 8 was done).
      For example, if you have 27x9, you first multiply the 7 by the 9 for a 63. Write a 3 in the one's place, and a 6 above the digits in the ten's place so it will be added later.
      Next, you multiply the 2 by the 9. This equals 18, so write an 8 in the ten's place and a 1 in the next higher place value.
      Now, you add the 6 with the 8 and get a 14. The 4 goes into a row in the ten's place, and the 1 goes to the next higher place value.
      Since there are two 1s, you get a 2. These are in the hundreds place, so there are two hundreds (for the hundreds themselves), and a final value 243.

      The long multiplication is done this way. As I said before, at first you are doing a one-digit by one-digit multiplication at each step, which should not be difficult if you have memorized your one-digit times tables. So as you do the multiplication you are lining them up to their respective place values in advance.

      Here is an example when there are higher place values for both digits:
      If you have something like a two-digit multiplied by a two-digit, such as 14x32, when you multiply the 3 in the ten's place by each single digit, those are multiples of 10. And when you do the 3x1, both are in the ten's place, so the 3 gets multiplied by two 10s for a multiple of 100 in the final value.

      Hope this helps in better understanding and clears things up.
      (2 votes)

Video transcript

- [Instructor] In this video, we're gonna think about how we can use our knowledge of multiplying single digit numbers to multiply things that might involve two digits. So for example, let's start with, what is five times 18? And you can pause the video and see how you might try to approach this, and then we'll do it together. All right, so if we're trying to tackle five times 18, one strategy could be to say, hey, can I re-express 18 as the product of two numbers? And the one that jumps out at me is that 18 is the same thing as two times nine, and so I could rewrite five times 18. This is the same thing as five times, instead of 18, I can write two times nine. Now, why does this help us? Well, instead of multiplying the two times nine first to get the 18, and then multiplying that by five, what we could do is we could multiply the five times the two first. And you might be thinking, wait, wait, wait, hold on a second. Before, you did the two times nine first, and now, you're telling me that you're going to change the order? That you're going to say, hey, let's multiply the five times two first, is that okay? And the simple answer is, yes, it is okay. If you are multiplying a string of numbers, you can do them in any order that you choose, and so this is often known as the associative property of multiplication. We can associate the two with the nine first. We can multiply those first, or we can have an association with the five and the two. We can multiply those two first. Now, why is that helpful? Well, what is five times two? Well, that's pretty straightforward. That's going to be equal to 10. So this is going to be equal to 10. We're doing that same color. 10 times nine. Now, 10 times nine is a lot more straightforward for most of us than five times 18. 10 times nine is equal to 90. Let's do another example. Let's say we wanna figure out what three times 21 is. Pause this video and see if you can work through that. There's multiple ways to do it, but see if you can do it the way we just approached this first example. Well, as you could image, we want to re-express 21 as the product of smaller numbers. So we could rewrite 21 as three times seven maybe? And so if we rewrite it as three times seven, and now, we do the three times three first. So I'm just gonna put parenthesis there, which we can do because the associative property of multiplication. Fancy word for something that is hopefully a little bit intuitive. Well then, this is going to be equal to, what's three times three? It is nine, and then times seven, which you may already know is equal to 63. Let's do another example. This is kinda fun. Let's say we wanna figure out what 14 times five is. Pause this video and see if you can figure that out. Well, we could once again try to break up 14 into the product of smaller numbers. 14 is two times seven, so we can rewrite this as two times seven or as seven times two, and I'm writing it as seven times two, because I want to associate the two with the five to get the 10 times five, and then I can multiply the two times five first. And so this is going to give us seven times 10, seven times 10, which is of course equal to 70. One more example. Let's say we want to calculate 15 times three. How would you tackle that? Well, we can break up 15 into five times three. Five times three, and then we can multiply that, of course, by this three, and then we can multiply the threes together first, and then this amounts to five times nine. And five times nine, you might already be familiar with this. This is going to be equal to 45. Another way to get to 45, you can say, hey, five times 10 is 50. So five times 9 is going to be five less than that, which is also 45.