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### Course: Arithmetic (all content)>Unit 3

Lesson 8: Relating multiplication and division

# 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?
• They are directly related to each other. Say you have 12 / 3 = 4. With this, you know that 3 x 4 = 12.
• Is this sort of the start of algebraic thinking?
( doing ( _ / 2 = 9 ) other than ( 9 * 2 = _ ) ? )
• 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
• Can we use Mutiplecation to check our work from division
• Yes, if you answer is correct you can multiply it by what you divided by to get the starting number. :)
• is it reverse? than multipalcation?
• 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.
• How can I relate division to multiplication when I'm working on Division?
• 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?
• 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
• Both of the ones that make the number go up are a X shape and the ones smaller have a -- in them
• Is this the start of algebra with blanks and question marks?
• Yes, blanks and question marks are the start of algebra.
• what is?÷4=7question mark, divided by, 4, equals 7.
• ?÷4=7 is in the same fact family as 4x7=?. So the ? is 28.

Have a blessed, wonderful day!
• what does division have to do with multplying
• 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)
• Can someone give me an example of P.E.M.D.A.S
(It's 5th grade math my sis know it)
• 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