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### Course: MAP Recommended Practice>Unit 14

Lesson 22: Letters and symbols in multiplication and division equations

# Unknowns with multiplication and division

Sal finds the missing number in multiplication and division equations. Created by Sal Khan.

## Want to join the conversation?

• What is an equation?
• In case you or anyone else on KA needs to know this, the word "equation" comes from the root "equal," so an "equation" is a math sentence, but it is a particular kind where the information on each side of the "equal" sign are equal to each other.
There are other kinds of math sentences called "inequalities" which you will learn more about later, where the information on either side of the inequality symbol (greater than, less than, etc.) are related to each other but are not equal.
• How do you now to find the missing number?
• All you have to do is move the variables to one place and the numbers to the other place. Like for an example.
5*_=25
Then, do this _
=25/5
__=5
It is division on the other side because once you move something to the opposite side, the sign changes. Did you get. I am sorry if you didn't
(1 vote)
• WAIT at why use the all those symbols and say like u and a and c instead of all that?
• The A,U,and C symbols are there to have you figure out the problom like. 1/c * 4/1 then you would have to figure out the problem. Hope that helps!
• how can you do negative numbers?Is it the same as regular numbers?\
• Kind of, but negative numbers are like so:-1 -2 -3.
Like regular but -50 is less than -1 I forgot how but it is. Hope this helps!:)
• Does all types division use decimals?
• No. But it depends what the question is asking you.
• this is so confusing it was teaching me aljibra
• It is okay, everybody has their challenges.
P.S. It is spelled Algebra... I think
• does that mean that this entire video is pre-algebra/algebra for 3rd graders?
• Algebra involves solving for unknowns using placeholders for those unknowns (we call those unknowns "variables"). In this video, he introduces the idea of these place holders with a blank (__), a ?, a smiley face, a star, an A, and B. This enables 3rd Graders to become familiar with these placeholders long before Algebra introduces them in more complicated calculations.
(1 vote)
• Is it possible to solve an equation with two unknowns and only one known?
• Yes, you'll learn how to do this when you get into more difficult algebra.
• Sometimes things can get hard but try your best because we all get something wrong. -K.P.
• why use sybles like a,b,and c?
(1 vote)
• The letters and symbols that represent unknown numbers are called variables. We can represent a variable with anything we want! Letters, punctuation marks, emojis, etc. Letters are most common, and we typically use x when there's only one variable in an equation.

## Video transcript

- 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.