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Lesson 4: Multiplication with arrays

# Multiplication with arrays

Let's explore this video about representing 12 with multiplication. It shows 12 as 4x3, 3x4, 2x6, 6x2, 1x12, and 12x1. This helps students understand multiplication and different group arrangements. Created by Sal Khan.

## Want to join the conversation?

• Is addition the same thing as multiplication?
• In a way, yes.

Multiplication is simply a faster method of addition. When you multiply a number by another number, you are basically adding a number the same amount of times as the other number calls for, e.g: 5*3 = 5+5+5 and 3*5 = 3+3+3+3+3.

Hope this helps!
• Multiplication is basically the other way of division,right?
• Yes. We call these inverse operations. When you multiply any number a by b, and then divide that by b, the answer will be a gain. The same goes for adding and subtracting, and exponents and logarithms.
• is this like a start to multiplication? If it is, why is it for third grade?
• Yes, groups of objects is the basic meaning of multiplication. Multiplication is taught in 3rd grade.

You don’t always have to draw groups of objects to multiply numbers, but it is good to mentally visualize groups of objects.

Have a blessed, wonderful day!
• I wonder, is there a formula that will determine, by plugging in the product number that will tell you how many ways you can arrive at the product. For example, 12 has six ways of reaching 12. Is there a formula? Is there a pattern that can be discerned?
• why is this in 5th grade tho-
• because they think the covid severely held students back and even if it didnt you still need practice
• hi you guys are cool
• should i memorize the whole multiplication table ?
to make it easier and faster for me to calculate things
• You could if you wanted to. Memorizing the table it would make it easier in the long run. In algebra, you have to do lots of multiplying.
• Can you do the nines please 🙏
• 9 18 27 36 45 54 63 72 81 90 99 108
• can you multiply without arrays
• Yes!You can multiply without arrays.
• what about division is it the same with that strategy?
• yes. it is the same x = to division

## Video transcript

So, I have several groups of these ball-looking things. And let's think about how many balls are in each group. We have 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 12. And what I want to do is think about the different ways of dividing these 12 balls into different numbers of groups. So, for example, I could view these 12 balls as one, so that's 1 group of 3, 2 groups of 3, 3 groups of 3, 4 groups of 3. So I could view 12 as being 4 groups of 3. And the way that we would write that is that 12 is equal to 4 groups of 3. Or another way of reading this is that 12 is equal to 4 times 3. If I have 1, 2, 3, 4 groups, and in each of those groups I have 1, 2, 3, objects, I'm going to have a total of 12 objects. But that's not the only way we can get to 12. We could also view it as 3 groups of 4. So, let's look at that. So we could have it as 1 group of 4, 2 groups of 4, 3 groups of 4. So now we could view 12 as being 3 groups of 4. Or we could say-- let me get the right tool out-- that 3 times 4 is equal to 12. So, whether we're doing 4 times 3 or 3 times 4, they're both going to be equal to 12. 4 groups of 3 is 12, 3 groups of 4. But we don't have to stop there. We could also view 12 as, well, we could view it as 2 groups of 6. Let's look at that. So this is 1 group of 6 right over here. So, that's one 1 of 6. That's another group of 6. So, once again, we could view this as 2 times 6. 2 times 6 will also get us a 12. Well, what about doing it as 6 groups of 2? Well, we can draw that out, too-- 6 groups of 2. So that's 1 group of 2. Let me do that in a different color. Let me do it in this purple color. We have 1 group of 2, 2 groups of 2, 3 groups of 2, 4 groups of 2, 5 groups of 2, and 6 groups of 2. So once again, this is all different ways of writing 12, something equivalent to 12. We could write 6 times 2-- 6 groups of 2-- 6 times 2 is also equal 12. But we don't have to stop there. We could also literally view 12 as 1 group of 12. So how would that look? So 1 group of 12. So this whole thing is just 1 group of 12 here. So we could literally say 1 times 12 is equal to 12. We have one entire group of 12. 1 times 12 is equal to 12. And we could think of it the other way around. We could view this as 12 groups of 1. Let me draw that. So 12 groups of 1. This is 1 group of 1, 2 groups of 1, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12-- 12 groups of 1. So we could also write 12. 12 groups, and in each one, I have 1. Well, that's still going to get me to 12.