Negative Numbers 

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)

Thanks!

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.

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

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

You just explained debt in a basic selling way

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

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

Thank you very much really helpful video!!

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

Awesome vid professor!

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

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

thanks for the video

very helpful thank you :)

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

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".

thx very helpful

This is gold

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

studying math at 3 am XD

I wish the ATM had that mistake xD

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

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

Sir I like your teaching

Ty

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

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

3:58 how -1.15/-1.3 = 5 😅

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.

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

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

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

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

Yes they should

Genius!!!!

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?

Hello from Sean, SGS

What is 425×12= to u guys?

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

hieeee hieee niceee explanationn

7 5 72 -17

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

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

7 5 72 -25

❤❤❤

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

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

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...

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

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

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. 👎🏼👎🏼