Letters and symbols in multiplication and division equations
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- I have six equations here, where there is an unknown. What I want you to do, is pause the video right now and try to figure out what that unknown is. So, in this first one, the unknown is a blank. What is this blank? What is this question mark? What is this smiley face? What does this letter A need to be in terms of a number? What is B? What is this star? So, pause the video now. So, let's think through each of them. This says three times something is equal to 12. So, let's think about what we have to multiply by three to get to 12. So, three times one is three, three times two is six. Three times three is nine, three times four is 12. Three times four is 12, so we could say that the blank needs to be equal to four. Three times four is 12. Now, let's work on this one. Something divided by, so question mark divided by four is equal to six. Well, this is the same thing as saying that question mark is equal to four times six, or you could say six times four, they're the same. It is equal to six times four, which is the same thing as four times six. So, what is six times four? Well six times one is six, six times two is twelve, six times three is eighteen, six time four is 24. So, question mark, so this is equal to 24, so question mark must be equal to 24. Write that down, question mark, in this case, is equal to 24. Now, here I have 54 is equal to nine times smiley face. So, nine times what is equal to 54? Well, let's just skip count with nine and try to figure that out. Nine times one is nine. Nine times two is 18. Nine times three is 27, notice I'm just adding nine each time, nine times four is 36. Nine times five is 45. Nine times six is 54. This is 54 is nine times six. Nine times six is equal to 54. So, we now know that the smiley face, so smiley face must be equal to six. If we replace the smiley face with a six, then this equation is true. 54 is equal to nine times six. Let's work on this one up here. Nine is equal to A divided by eight. Well, this is the same thing as saying that if A divided by eight is equal to nine, well that means that nine times eight must be equal to A. Nine times eight must be equal to A. If I divide A into eight groups and I have nine in each group, that means if I have nine in a group times eight groups, I must have the total number of things. So, what is nine times eight? Well, nine times one is nine, in fact we already did a lot of our nine times tables down here, we could just keep going. Nine times six was 54, nine times seven is 63. Nine times eight is 72, so nine times eight, nine times eight is equal to 72. So, we can say that A is equal to 72 and if A is equal to 72, then this equation becomes nine is equal to 72 divided by eight, which is absolutely true. 72 divided by eight is nine, nine times eight is 72. B is equal to 20 divided by five. Well, what's 20 divided by 5? Well, there's a couple of ways you could think about it. You could literally view this as the same thing as saying that five times B is equal to 20. So, five times what is equal to 20? Five times one is five, five times two is 10. Five times three is fifteen, five times four is 20. Five times four is equal to 20, so that tells us that B, B must be equal to four. B is equal to four, so we could write four is equal to 20 divided by five, which is absolutely true. If 20 divided by five is equal to four, four is equal to 20 divided by five. Now, we have one last one. We have star times two is equal to four, is equal to 14. So, what times two is equal to 14? Well, let's just look at our two, alright, our two, our multiples of two. So, let's see if two times one is two, four, six, eight, 10, 12, 14, so how did, how many times did we have to multiply two to get to 14? So, this is one, two, three, four, five, six, seven. Two times seven is 14, so if I wrote seven times two is equal to 14, this is absolutely true. So, star must be equal to seven. Star is equal to seven.