Negative Numbers

We figured out how to use numbers a long time ago, but then the concept of negative numbers came about. This is a much more abstract concept, because you can't have a negative amount of apples, or something like that. Nevertheless, negative numbers are ubiquitous in math, so we had better learn all about them!
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[@FlawedFabrications]

Some tips/rationales that helped me solidify my understanding: - Adding is moving away from 0, subtracting is moving closer to 0. If you're as a positive number on a number line and you take away, you move LEFT towards 0. If you're at a negative number on a number line and you take away, you move RIGHT towards 0. Similarly, if you're at a positive number and you're adding, you move RIGHT away from 0. If you're at a negative number and you're adding, you move LEFT away from 0. - For additions/subtractions, think of the first number as where you ARE, and the second as the DIRECTION and how FAR you are going. If I'm at -10 and I'm adding 5, I'm moving 5 further away from 0 than -10, so I get to -15. If I'm at -10 and I'm adding -15, then I'm moving 15 CLOSER to 0 than -10, which takes me PAST 0 and all the way to POSITIVE 5. - For multiplication and division, remember the direction/distance metaphor for add/subbing, but remember that you ALWAYS start at 0. 5x5 is 0 + 5 + 5 + 5 + 5 + 5, we usually just omit the 0, and it's the same for all other multiplications. As such, instead of the first number being where you ARE like with addition/subtraction, think of it as one number is how far you go each step, and the second as how many steps you're taking. The direction still stays the same. For instance, (-15) * 5 is starting at 0, then moving left into the negative numbers AWAY from 0, 5 times in increments of 15, or 0 - 15 - 15 - 15 - 15 - 15, which is -75. - For division, I find it much easier to flip it around into a multiplication. For instance, -75/5. Rather than thinking -75/5, I figure out what I need to multiply by 5 to get to -75. Since we're starting at 0, but 5 is going into positive numbers, we need to flip it around so it goes in the opposite direction - so the answer is going to be a negative number. So -75 would be 5 * (-15)

[@jnmc2498]

In Europe a way to explain negative numbers is by using the surrounding temperatures. Since Celsius is used, zero (degrees) is where water freezes to ice. And this makes it easy for children to understand. Since when it’s ”freezing cold” 🥶 that means the temperature shows a negative number. When I explained this to my 6 year old daughter she immediately understood the concept of negative numbers, as opposed to having a negative number of apples, which I initially tried with but confused her. Now she’s 8 and can do multiplication and division with negative numbers in her head.

[@npcx-mq6cr]

if the bank forgiving your overdraft isn't magic than i don't know what is

[@stephend.4342]

Thanks!

[@eCouchPotatoe]

Me: Thinking this video is for kids. Prof Dave: shows my account balance 😱🤔😆😭

[@Carlos_Beans]

You just explained debt in a basic selling way

[@rushikeshkadam8773]

this is the best series for mathematics on youtube thanks professor dave to help me to feel mathematics

[@PranayZVlogs]

Thank you very much really helpful video!!

[@_Jake5642]

This is helping me study for the asvab!! Thank you Dave‼️‼️❤️

[@Oliver-wx8sf]

Thanks you a lot the whole time i always wondered why teachers told us two negatives is positive but makes sense since -10-(-10)=0 by saying -10 taking out or less than -10=0

[@Jasmita-8]

Awesome vid professor!

[@yuinurahilyon5711]

1:43 Yup... my bank account is already at -$738.

[@thepeoplewholovedeeply7675]

Send me 8 dolars😂

[@animeoo7]

@@thepeoplewholovedeeply7675 lol

[@catfinity]

I finally get it after years of confusion😭😭😭 Feel like I leveled up thank you sm

[@renuelcruz9065]

thanks for the video

[@thewatchmansson6472]

The positive number is like a number on a thermometer that's in the warm range, if its "subtracting" a negative number it's going in the opposite way of the negative, or the "cold" into the "warmer".

[@yuinurahilyon5711]

Makes sense since cold is a low temperature, warm is at the mid temperature, while hot is the highest temperature.

[@Austin-jj8fs]

very helpful thank you :)

[@alyxkrieger6764]

I use to be confused dealing with negative numbers. I'm finally finding it easier to understand, now that I have a developed brain.

[@Stoirelius]

Learning things when you're older is amazing. I wish I had this passion when I was a student.

[@bean7225]

studying math at 3 am XD

[@rebeccafreehill369]

thx very helpful

[@An_ony_mous]

Was never taught the application of negative numbers in real life. Thanks a lot.

[@lucifermaestro8332]

Please never stop making videos.... And yes, if my math teacher is watching this, please resign.

[@mxoeneod90]

Ok

[@emanandchill]

Ironic. Considering your name means "devil teacher". You resign!

[@itsallaboutfeeling]

I wish the ATM had that mistake xD

[@amarnathguptavlogs]

It’s a good idea you should start it doing first 😂

[@Ocean_Man_]

This is gold

[@hareecionelson5875]

Until I had to explain negative numbers, I never realised how counter intuitive they were. Now it feels like negative numbers are the shadow of imaginary numbers

[@chourouk-gr9qg]

Ty

[@Uncertainarmy074]

Sir I like your teaching

[@malihealizadeh2720]

it seems strange but in my opinion, we have only add and also multiply, which is a creating abstract efficient way for adding. minus and dividing are not very useful. they only create some sort of complexity which could be confusing in many cases.

[@Mrutyunjaya_Kar.Official]

3:58 how -1.15/-1.3 = 5 😅

[@DrApathetic]

minus cancel out each other then... 1 x 15 = 15 / 1 x 3 = 3 then... 3 x '5' = 15 & 3 x '1' = 3 hence... 5 / 1

[@rohithrajstudies2136]

the second problem slightly confused me but i can able to understand after some time thanks dave

[@malihealizadeh2720]

this idea would be helpful to look at the world with a more abstract view.

[@kripashankarshukla4073]

I like your previous intro very much but why have you changed it?

[@ProfessorDaveExplains]

because math isn't science! i needed a new one for all non-science tutorials. don't worry, all future science tutorials will have the original intro.

[@bullpup1337]

Professor Dave Explains That's debatable. In Germany it's actually considered a science ("science of the mind").

[@FawadAli_SST]

@@bullpup1337 I think science of the mind is psychology.

[@menacingskull740]

the teachers should make this type of tricks in math more clear

[@peta1001]

I have also passed all the math exams required for university degree in electronic engineering. However, it basically proves that I can learn and follow the rules. There is this dilemma, however, that I carry forever. If multiplication is short addition, how come (-5) x (-2) = 10? How did we get 15 points away from -5 (or 12 points away from -2)? ==> points being steps on the integer number scale. Can anyone see my dilemma and what is the possible explanation?

[@TruthandReality_in2]

If you don't mind can you Plz explain question well bcz I couldn't able to understand so that i can also learn new things

[@DanielleDagg]

What is 425×12= to u guys?

[@Nishantmakadiya]

Now i know why my bank account increase as i buy things

[@preparationoftheelect2023]

Woohoooooooo! I got 3 1/2 right at the end 😆 Math is awesome haha

[@DanielleDagg]

Yes they should

[@wpsean_ts7131]

Hello from Sean, SGS

[@Wasoska]

Genius!!!!

[@nothing...5170]

hieeee hieee niceee explanationn

[@LC-yv9ey]

7 5 72 -17

[@timucintarakc2281]

What if it was -15/3 instead of 15/-3

[@ljr6490]

If anything over itself is one does that mean we have found what 0/0 is? But then anything under 0 should be zero? 🤔

[@airiksg817]

A bank is not a good example. They will never forgive. They will never forget😊

[@kommusaipraneeth1471]

7 5 72 -25

[@mamadwali4278]

❤❤❤

[@chrysabentouli6464]

Sorry but you did not explain why 15/-3 = -5

[@Alex-02]

(-5) fits in to 15 (-3) times -(-5)-(-5)-(-5)=5+5+5=15 Hope that makes some sense

[@girirajvardhan2722]

kzbin.info/www/bejne/qHyXpIujlLKDjdE

[@davidzubiria3783]

Sorry, but I don't see any practical example of (-x . -x) being "-". I can understand that -2.5 is -10 coz if I have -2 in my account and I multiply that I'll end up having -2 + (-2) + (-2) + (-2) + (-2). But I don´t find an equivalent example. Not the I´m an expert anyway...

[@girirajvardhan2722]

May be this will help you out

[@girirajvardhan2722]

kzbin.info/www/bejne/qHyXpIujlLKDjdE

[@carultch]

Suppose I'm driving my car backwards on an icy road at 10 mph. Because I'm backing up, we'll assign a negative sign to my initial velocity, so it is -10 mph. I then hit a tree, and rebound at half my speed but in the opposite direction. What is my new velocity? Backing up at 10 mph = -10 mph Rebounding at half my original speed = multiply by -1/2 New velocity = -10 mph * (-1/2) = +5 mph, with the positive indicating that I rebound in the forward direction of the car. This is a practical example of why a negative times a negative is a positive.

[@traviswhitten5695]

Lmao why is it that we do everything right to left except negative numbers someone needs to get hit with a text book considering when we do decimals the smaller numbers are to the right which arent exactly whole numbers if you look at them negative numbers should go the exact same way so why exactly is the negative number on the left and positive on the right thats always irked me and no one can explain it to me

[@user-lm7xr6iv3f]

Ok i cant be the only one thinking how cringe the entrance

[@shehransaibah2770]

Fr Bro I sent screenshots of it to ppl💀

[@wildtiger8963]

Sorry but you are just making this video more and more confusing

[@girirajvardhan2722]

kzbin.info/www/bejne/qHyXpIujlLKDjdE

[@Monty7473]

If you’re going to target young kids with your “educational videos”, cover up your frinkin forearm tattoo. It shows your lack of forethought and respect for students and their parents. 👎🏼👎🏼

[@ProfessorDaveExplains]

My tattoo is dope and anyone who freaks out about adults having tattoos in the 21st century is an enormous tool.

[@DrApathetic]

average twitter user