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## Integrated math 3

### Course: Integrated math 3>Unit 9

Lesson 3: Manipulating formulas

# Manipulating formulas: perimeter

Sal rewrites the formula for the perimeter of a rectangle so it is solved for width. Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

• This is not a question but hopefully some useful info for people who get stuck on the set of questions afterwards.
I have spent the last few months brushing up on algebra and I read these posts and understand your frustrations so I will sum up what I think the key things to remember are which may help some of you (someone correct me if I am wrong because there is a reason why I am relearning algebra!)

1) Change sides, change signs means if you have a negative on one side of the equals sign, when you move it to the other side, it becomes positive i.e. x +2 = y becomes x = y -2. Similarly x-2=y +2
Usually you don't write out what Sal shows in the video of him adding the same thing to both sides of the equation as it is a given that if you add -2 to +2 it will cancel out (because it adds to zero)

2) You don't change signs for the variable when the number is a coefficient and is moving into the denominator.
eg -4y =12 becomes y = 12/-4 (you divide by -4 rather than subtract -4 because you need to break the 'bond' between -4 and y (i.e. -4 times y which = -4y)
However the general rule seems to be multiply by -1 so you don't have a negative sign in the denominator so you could choose to make it y= -12/4 (both would give you a result of -3)

3) Learn how to factorise - this is how you end up isolating the unknown. I can't summarise this succinctly but do a search on this and get your head around what factorisation is. As algebra increases in complexity this gets more important.

4) When you are presented with a problem with denominators first priority is to get rid of the denominator by multiplying both sides of the equation by the denominator. From the exercises it appears preference is given to dealing with the negative denominaotr first. You won't end up actually multiplying the part of the equation which has the denominator you are dealing with as it will be cancelled out
so
x + y / 10 + 30 = 50
you would do 10 (x +y) / 10 + (10) 30 = (10) 50
but you cancel the first 10 in the numerator because it is cancelled by the denominator so
(x + y) + 300 = 500
x+ y = 500 - 300
x + y = 200

I hope this helps someone in some small fashion. Do the exercises, and click 'show me a hint' and it will step you through so you can uncover what mistakes you tend to make.
• This is GREAT! Thank you so much jacinta!
(1 vote)
• Why or when do you have to multiple the answer of an equation that is in fraction form by -1??? I know that isn't in this video, but it is in some of the problems in "practice this concept" for this video. And I don't see it explained in either video and it's driving me nuts!

For example,
-g-4h-4i+2 = -h+10i+4

The last step you have -1 as the denominator, and it say you have to make the denominator positive. Well, I swear I've seen answers with negatives in the denominator. ???

I found one!

8uv-6uw-9u+1 = 2v-7

The last step says to multiple top and bottom by -1. WHY!? You still are left with a negative in the denominator. The denominator goes from 8v-6w-9 to -8v+6w+9

Then ya got this!

4np+3nq-n-8 = 5p-6

Denominator is 4p+3q-1 but it doesn't say to change the denominator even though there is a negative number?? The only thing I can think is that the largest number in the denominator must be positive??

AND THIS!?!? What's going on?

5pq-5pr+p+6 = -q-5

You end up with the denominator being 5q-5r+1 but it say to change that to -5q+5r-1 WHY?
• In the denominator and the numerator, they want to have the least amount of negative numbers.
Here is my work on the last problem:
5pq-5pr+p+6=-q-5
-6 -6 =
5pq-5pr+p=-q-11 =
p(5q-5r+1)=-q-11 =
p(5q-5r+1)/(5q-5r+1)=-q-11/(5q-5r+1) =
p=-q-11/5q-5r+1* =
p=-q-11/-1/5q-5r+1/-1
p=q+11/5r-5q-1
*(Right now, they're 3 negatives. But if we multiply both sides by -1, they are now 2 negatives in the entire fraction(as opposed to the alternative of not dividing by -1 and having 3 negatives in the entire fraction))
Hope this helps.
• I don't get the part where Sal made 2l -2l
• It would seem to be confusing unless you realize that half of the work he is doing is off the left side of the screen. He is subtracting 2l from both sides of the equation. Alas, we can only see the right side of the equation. This video should be re-shot.
• Why are they called "variables"?
• Because they can vary; it is in the name: VARIable. That is an over-simplification, but I think it gets to the root of what you are after. Take x = y + 5. Each time you are given a different y it will change the value of x.
• The "Practice this concept" for this topic is way too hard compared to this video.
• A lot of people have this problem including me...
Someone needs to ask him for more videos!
(1 vote)
• So is factoring basically "un-distributing" a number??
• Yep! factoring and simplifying using the distributive property are basically the opposites..
Example:
Distributive property
3*(2x+3y) => 6x+9y
Factoring
6x+9y => 3*(x+y)
It works almost like multiplication and division, when they work together..
as in.. when you multiply 1*2.. the answer is 2..
If you divide the answer by the same number you multiplied by.. 2/2 makes 1... In simpler terms they reverse each other.
Hope this helps!
• When solving for w in P=2w+2l, the final product is P-2l/2. My question is: can you divide the 2s somehow to further simplify it or can it not even be simplified? Thanks!
• You can divide both terms in the numerator by 2, but it's not any more correct (or incorrect) than the current form.
W = (P-2L)/2 = P/2 - L