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### Course: 3rd grade > Unit 4

Lesson 3: Relating multiplication and division- Relating division to multiplication
- Relate division to multiplication
- Relate multiplication and division equations
- Fact families
- Multiplication word problem: parking lot
- Division word problem: school building
- Relate division to multiplication word problems

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# Relating division to multiplication

Sal talks about the relationship between multiplication and division problems.

## Want to join the conversation?

- What does division have to do with multiplication?(40 votes)
- They are directly related to each other. Say you have 12 / 3 = 4. With this, you know that 3 x 4 = 12.(35 votes)

- Is this sort of the start of algebraic thinking?

( doing ( _ / 2 = 9 ) other than ( 9 * 2 = _ ) ? )(21 votes)- one of the cool new things I see in this algebra stuff (which coincidentally I'm relearning right now) is that in algebra we begin to tolerate unknowns, working WITH the unknowns to arrive at the solution we're looking for. at first you usually are solving for x but gradually you learn to solve for y or z and allow x to just be x....the system still works and the rules remain the same.

eventually we come to f(x) which has a shape, identity, behavior we know (like a fractal or a sine wave) without ever having to wring any specific number out of little x

if it's all in the same system you don't always have to answer EVERY question or every portion of every question, look for what you need. work with the system to derive it

especially if your testing/contest system is using multiple choice, eliminate the wrong answers and see what's left to pick

but I digress

yes! _/2=9 and instead of "blank" you can say/write x

this is the beginning of algebra

good catch Zhang(31 votes)

- Can we use Mutiplecation to check our work from division(13 votes)
- Yes, if you answer is correct you can multiply it by what you divided by to get the starting number. :)(9 votes)

- is it reverse? than multipalcation?(8 votes)
- It is like reverse multiplication. Multiplication is a faster way instead of doing repeated addition, and division is a faster way instead of doing repeated subtraction.(8 votes)

- How can I relate division to multiplication when I'm working on Division?(7 votes)
- Think of it like this: When you divide 8 by 2 you are basically saying "What would I have to multiply 2 by to get 8." So instead of writing 8 / 2 = X you could write 2 * X = 8. Does this help?(4 votes)

- Okay, just putting this out there, when I'm doing math, sometimes I get confused with all of the symbols: ×,+,-,÷ etc. And I end up dong the wrong thing, like subtacting instead of adding. Does anyone have a trick they use to remember what means what? Or is it just that I have to pay more attention to the symbols when doing problems? ;P(6 votes)
- Both of the ones that make the number go up are a X shape and the ones smaller have a -- in them(5 votes)

- Is this the start of algebra with blanks and question marks?(4 votes)
- Yes, blanks and question marks are the start of algebra.(8 votes)

- what is?÷4=7question mark, divided by, 4, equals 7.(4 votes)
- ?÷4=7 is in the same fact family as 4x7=?. So the ? is 28.

Have a blessed, wonderful day!(5 votes)

- Can someone give me an example of P.E.M.D.A.S

(It's 5th grade math my sis know it)(4 votes)- Yup. Order of operations, acronym PEMDAS, says the main two things:

- Multiplication/division are performed before addition/subtraction.

- Things inside brackets/parentheses () {} [] are solved first, same with the numerator and denominator in fractions (don't worry if you haven't learned fractions yet).

There are other things, but that's basically most of it. It tells us how math expressions are to be formatted and read.*What operations do we do first?*That's why it's the**Order of Operations**.

For example, evaluating`8/2 + 5*7 - (2 + 3)`

, first look out for brackets. Well there is the`(2 + 3)`

. We do that first which is just`(5)`

, then we can remove the brackets around it.

The expression turns into`8/2 + 5*7 - 5`

. Now see that division of`8/2`

which is`4`

, and multiplication of`5*7`

which is`35`

. This becomes`4 + 35 - 5`

. At this point, there are only additions and subtractions, so these are done left-to-right like so:`4 + 35 - 5 = 39 - 5 = 34`

If you want a*summary*of this:`8/2 + 5*7 - <(2 + 3)>`

(brackets first)`= 8/2 + 5*7 - (5)`

(you can then eliminate the brackets)`= <8/2> + <5*7> - 5`

(now, do multiplications and divisions left-to-right)`= <4 + 35> - 5`

(now, do additions and subtractions left-to-right)`= <39 - 5>`

`= 34`

I hope you learned something from this :D(3 votes)

- what does division have to do with multplying(3 votes)
- Division could in theory be considered like the opposite of multiplying (i.e. if subtraction is the parallel for addition, then division is the parallel multiplication)(3 votes)

## Video transcript

- [Voiceover] Let's say
someone walks up to you on the street and says to you, 50 divided by five, 50 divided by five is equal to blank, is equal to blank. How can you think about this as a multiplication problem? Well, whatever blank
is, whatever blank is, if you multiply it by five, if you multiply by five, you should get 50. You should get 50. You should get 50. So one way of thinking
about it, you could say "what times five is 50?" Well, 10 times five is 50. 10 times five is 50, so 50 divided by five is going to be 10. Hopefully you see the relationship here. If 50 divided by five is 10,
then 10 times five is 50. 10 times five is 50. And you could do it the other way around. What is 50 divided by 10 going to be? 50 divided by 10, well that's
going to be equal to five. 50 divided by 10 is going
to be equal to five. How do I know that? Well, five times 10, five times 10, five times 10, is equal to 50. Is equal to 50. So let's keep thinking about this. If someone walked up to
you in the street again, and said blank, blank, divided by, divided by two, blank divided by two is equal to, is equal to nine. How would you figure out what blank is? Something divided by two is equal to nine. Well, one way to think about
it, and if we just follow here, if you said 50 divided by five is 10, you could say 10 times five is 50, so right over here we could say well, nine times two, nine times two, must be equal to blank. Must be equal to our blank. Well we know what nine times two is, that is 18, so this must be 18. 18 divided by two is nine. And that's really describing how 18, two, and nine relate to each other. Two nines is 18, or nine twos is 18, or if I were to divide 18 into two groups, each group would have nine. Or if I were to divide into groups of two, you would have nine groups. Any way you look at it, 18 divided by two is nine,
nine times two is 18. Let's do one more of these. So, someone walks up to you on the street, and tells you, and tells you that 12 divided by, divided by blank, 12 divided by blank is equal to three. Is equal to three. What is blank going to be? Well one way to think about this is three times blank is
going to be equal to 12. Three times blank, three times this unknown number, is going to be equal to 12. And three times what is equal to 12? Well three times four is equal to 12, so 12 divided by four is equal to three.