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# Patterns in multiplication tables

CCSS.Math:

## Video transcript

we are asked what number should replace the a and B in the multiplication table so let's just make sure we can read this multiplication table the way you think about it is if you wanted to figure out it goes up to six so if you want to figure out what any number up to six times another number up to six is this table will tell you so for example if you wanted to figure out what three times two is you say okay three let me take the row that has this three in it and then the column for the two so three times two so if you're in this row three the three row and you're in the two column three times two is going to be six here or another you can go the other way around this 12 this means that three times four is 12 or right over here this 25 notice this is the same row as this five and the same column as that five so it's saying that five times five is 25 and so you notice that if you're going to any row you're counting by that number and if you go into any number if you go into any column you're also counting by that number so for example in this twos column right over here you go you're counting by two is two four six eight in this five column you're counting by fives five 10 15 20 and that makes sense because 5 times 1 is 5 5 times 2 is 10 5 times 3 is 15 5 times 4 is 20 and the same thing is happening as you go up a row 2 4 6 8 because 2 times 1 is 2 2 times 4 is 4 on and on and on you're counting by twos here you're counting by 6 is 6 times 1 is 6 6 times 2 is 12 6 times 3 is 18 6 times 4 is 24 so hopefully now we understand the multiplication table and it is actually pretty pretty cool to just keep looking at it and thinking about how it works but let's answer their question what would a and B be well we have this a right over here so one way to think about it it needs to be whatever 4 times 4 is and you might know that 4 times 4 is 16 4 times 4 is 16 or another way is you could just go down this column and count by fours 4 8 12 and then you add 4 again 12 four is sixteen now let's figure out what B is and actually let's do it that way if you were to B is in this column so we can count by threes three six nine add 3 to that you get to 12 so B could be 12 or you could go it from the row you go for 8 add 4 to that you get 12 and that makes sense because this where B is that should be whatever 4 times 3 is because 4 times 3 is 12 then they say complete the inner complete the inequalities with the greater than less than or equal symbol so a is greater than B greater than and I always remember the greater than symbol because it is opened to the number on the left the number on the left is greater then it's open to the larger number a is greater than B because 4 times 4 is going to be greater than 4 times 3 is greater than 4 times 3 all right 4 times 4 is greater than 4 times 3 it makes sense you have I guess if you view 4 times 4 is 4 4 is in few 4 times 3 is 3 4 is you have more fours here so hopefully that makes sense let's do let's do a couple more of these so now what number should replace a and B in the multiplication table so same idea so a should be whatever 4 times 5 is so it should be 20 or you could look at whatever row or column it's in if you look at its column 5 10 15 20 now let's do the same thing for B B should be whatever 5 times 4 is well that's going to be 20 as well that's going to be 20 and you could say well like a is going to be 4 times 5 which is 20 and B is going to be 5 times 4 which is 20 so either way you look at they're the same so complete the inequalities well a is equal to B because 4 times 5 is the same thing as 5 times 4 doesn't matter what order you multiply them in let's do one more of these I think you're getting the sense of it so what is a so we see it's in it's it's where it's located it's in this row for this 2 and the column for the 6 so it needs to be whatever 2 times six is which is twelve and you could count by sixes six twelve or you can count by two is two four six eight ten twelve to get to a now B this is going to be whatever six times two is well that's going to be twelve again be twelve again and so it's just like the last one we sell a is going to be equal to B because two times six is equal to six times two let's do one more this is this is actually a lot of fun all right so a could is whatever four times one is which we know is going to be four B is going to be whatever one times four is which is also going to be 4 and I think you see a pattern here AE equals B because 4 times 1 is the same thing as 1 times 4