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)

[npcx-mqcr]

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

[jnmc]

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.

[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

[rushikeshkadam]

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

[_Jake]

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

[kev]

I thought we were dealing in facts, until the bank forgave my $10 dept

[catfinity]

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

[Oliver-wxsf]

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

[PranayZVlogs]

Thank you very much
really helpful video!!

[yuinurahilyon]

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

[alyxkrieger]

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

[hareecionelson]

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

[An_ony_mous]

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

[thewatchmansson]

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".

[peta]

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?

[lucifermaestro]

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

[menacingskull]

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

[kripashankarshukla]

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