Sal uses arrays and repeated addition to multiply. Created by Sal Khan.
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- hi sal, ive learnt soo much from you, I'm not that good with math but after joining khan academy I know how to multiply 10s, 100s, ect. add, subtract, and decimals, but I am really struggling to memorise the multiplication table, any tips?(73 votes)
- What if you have 0 group(20 votes)
- Why learn multiplication other ways? Like, it's harder memorizing other stratedies
why not just stick with one?(1 vote)
- if you know other ways,then it will be easier to figure the answer. For example,if one person knows long multiplication and another person knows long multiplication AND a mental strategy, the second person will be more successful in math because he knows a mental strategy,which makes the question easier to figure out.(2 votes)
- Is division the inverse of multiplacation?(1 vote)
- How do I study my multiplication tables?(1 vote)
- You could try setting out a grid of questions and answers on graph paper, so that you number the squares from 1 to 12 going down the left side of the paper and across the top. Then you can fill in the open squares based on multiplying the number on the far left of the row and the number at the top of the column. Practice with the grid and then occasionally try to recreate the grid from memory until you can do it all.(1 vote)
- How do you know which number represents the groups and which number represents how many groups?(1 vote)
- It's the same number, but Crazy Donutz's question is reasonable,. In real life it may matter. If you have 5 packet of biscuits with 6 biscuits in each, you can share the biscuits equally between 6 friends only if you open the packages. It is only for exercises with text that it will matter, though, and there you will be told what you need to know.. A typical example is an exercise where you need to find how many liters of paint you need to buy when you can only buy full liters, and each liter covers a certain number of square meters. In this example you usually end up buying more than you need for the paint job..(1 vote)
- so addition and multiplication are similar in a way. but what about subtraction and division? do they have some relation with each other like the others?(1 vote)
- No, multiplication is the opposite of division, and thats the only relation I know about division
sorry if this didnt help(1 vote)
- Does multiplication have reminders?(1 vote)
- Multiplication between two whole numbers cannot have a remainder. The remainder is a unique property of division. If I ask you how many times does 3 go into 14 (i.e. what is 14/3) you could say that 3 goes into 14 4 times. But 3*4 is only 12. Therefore the remainder of the quotient is 2. There is nothing analogous to this in multiplication.(1 vote)
- what if you don't know how to skip count by 8 than what do you do?(1 vote)
- Remember that 8 is the same as 2 groups of 4. (8 = 2 x 4) If you can't count by groups of 8, try counting by groups of 4. If that is still too hard, try counting by groups of 2 and work your way up to counting by larger numbers.(0 votes)
- how is multiplication like repeated addition(1 vote)
- If you do: 7 + 7 + 7 + 7 = 28
you get the same result as 4 x 7 = 28
Multiplication is shorthand for repetitive addition.(1 vote)
If we have 2 groups and in each group I have 4, so that's one group of 4, and then here is my second group of 4, we already know that we could write this as 2 times 4, which is the same thing as 4 plus 4. Notice I have two 4's here. I have 4 plus another 4. Well, if I have 4 plus 4, or if I have 2 groups of 4, either way, I'm going to have a total of 8 things. And you see that right over here. We have 1, 2, 3, 4, 5, 6, 7, 8 things. What I want you to do is pause the video now and try to group these same 8 things, but to group it in other ways so that we can represent 8 as the product of whole numbers. Here I've represented 8 as the product of 2 and 4. 2 times 4 is 8. See if you can represent 8 as the product of other whole numbers, or as whole numbers in different ways, grouping it in different ways. So I assume you've paused the video. So let's try it out ourselves. So one thing we could do, we could view this instead of as 2 groups of 4, we can view 8 as 4 groups of 2. So that's 1 group of 2, 2 groups of 2, 3 groups of 2, 4 groups of 2. So we could write that 4 times 2 is equal to 8. And we could view this as the same thing as, literally, 4 2's. We have one 1, 2, 3, 4 2's. Each of these have 2 in them. So we're going to say 1, 2, 3, 4 2's. 2 plus 2, plus 2, plus 2 is equal to 8. These are both equivalent. 4 times 2, literally 4 groups of 2. That's the same thing as taking 4 2's and adding them together. Notice, we have 2 2's right over here. We added them together, 1, 2. Here, we have 4 2's and we're adding them together, 1, 2, 3, 4. We take our 4 2's and we add them together. How else could we represent 8? Well, we literally could view it as 8 groups of 1. So let's do that. So 8 groups of 1 would look like this. That's 1 group of 1, 2, 3, 4, 5, 6, 7, 8. So we could write this down as 8 times 1. 8 times 1 is, once again, equal to 8. And if we wanted to write this down as repeated addition, well, this is literally 8 1's. So 1 plus 1, plus 1, plus 1, plus 1, plus 1. Let's see. That's 1, 2, 3, 4, 5, 6, 7, 8. 1, 2, 3, 4, 5, 6, 7, 8. 1 plus 1, plus 1, plus 1, plus 1, plus 1, plus 1, plus 1 is equal to 8. Now, you might be a little stumped. Well, what's another way of getting to 8? Well, you could literally view it as 1 group of 8. So let me view it that way. So this is just 1 entire group of 8, the whole thing. The whole thing is a group of 8. So let me scroll over to the right a little bit. We could write this down as 1 times 8. And 1 times 8 is equal to 8. And how would we view that? Well, we only have one 8 now. We don't have to add that one 8 to anything else. So if we wanted to do it the way we've done the last few, we could literally write it down as we just have one 8. Well, one 8 is clearly going to just be equal to 8. So now let me ask you another question. So far we've been focused on each of these groups, but what if we actually view this as 4 groups of 8. Then how many things are we actually going to have? So let me make this very clear. So we have 1 group of eight 8, 2 groups of 8, 3 groups of 8, and 4 groups of 8. So we would view this as 4 times 8, or which is going to be the same thing as 8 plus 8, plus 8, plus 8. 4 8's. What is this going to be equal to? A And I encourage you to pause the video and figure it out right now. Well, there's a couple of ways that you could have thought about this. You could have literally just counted these. Or you could say, well, let's see, you can skip count by 8. 8, 16, 24, 32. Or you could have said, 8 plus 8 is 16, plus 8 is 24, plus 8 is 32. Or you could have literally just counted the triangles here.