I’m trying to figure this out, I’ve tried to look online but everything is the top number is bigger than the small number. I understand what regrouping means and you have to borrow. But I don’t understand
13 - 79
I dont understand. Like do I change the whole number at top? Or do I change the the number. Please help, I never went to school and I’ve never been taught this.
Consider this:
How might we do $536 - 254$.
We might think "let's get those close together by stripping of $4$ from each:
$536 - 254 = (536-4) - (254-4) = 532-250$
And then we might thing. "let's keep getting those closer together by stripping off $30$".
$532 - 250 = (532-30) -(250-30) = 502 - 220$
"let keep getting thos closer together by stripping off $20$"
$502 - 220 = (502-20) - (220 -20) = 482 - 200$.
"let get those closer together by stripping off $200$.
$482-200 = (482-200)-(200-200) = 282 - 0 = 282$.
And that's it.
What if we thought the same way.
$13 - 79$. "Let's get them closer together by stripping off $13$.
$13 - 79 = (13-13) - (79-13) = 0 - 66$.
So how do we subtract $66$ from $0$?
Well, we lie awake at night wondering how we can ever have less than $0$ and figure. Well, going into debt and owing money. Having many years after Christ and using the years A.D. but what about the people born before Christ using B.C. and what about mountains above sea level, and those who live below ground. And we figure...
Okay, negative numbers... we can live with them.
So
$13 - 79$. We must subtract $79$ from $13$. ANd $79 = 13 + 66$. So first we subtract $13$ to get us down to $0$. And then we subtract the remaining $66$ to get us below $0$ to $-66$.
That is.
$13 - 79 = $
$(13-13) - (79-13)=$
$0 - 66 =$
$-66$.
=====
Now.... the is a shortcut....
Once this stops being so new and strange and you realize:
That if $M > N$ then if you have to do
$N - M$ you realize you have to strip the smaller $N$ first
$(N-N) - (M-N) =$
$0 - (M-N)$ we get that
we will always "drop down to $0$ and then subtract whatever the difference between the bigger number to the smaller number.
So if $M > N$ then
$N - M = -(M-N)$.
SO.... shortcut....
When subtracting a bigger number from a smaller number and you know you will end up with less than $0$. Just subtract the smaller number from the bigger number and make that negative.
So $13 - 79$ .... well $79 -13 = 66$ so $13-79 = -66$. That's it.
But the first part of the answer was to explain why that works and why it will make sense once you start to think about it.
I'm guessing you're probably new to the concept of negative numbers. I'll give two different ways to intuit what's going on here, both have the same underlying math:
One way to intuit it is as debt: $13-79$ is the amount of money you would have if you had \$13 in your bank account, but spent \$79 on your credit. You'd be in debt since $79>13$, so the question is, how much in debt are you? Of that \$79, if you first spent \$13, you wouldn't be in debt; that would put you at a \$0 balance, but you spent an additional $79-13=66$ dollars, so you're \$66 dollars in debt. That means the answer is $-66$.
Another way is to think about elevation: Let's imagine a duck and a lake; the surface of the lake has elevation $0$ feet. If the duck is flying 13 feet in the air, and then descends 79 feet, it's diving beneath the surface of the lake, so the elevation is negative. How much negative? Well, it flew 13ft down to get to the surface of the lake. Then it swam down an additional 66ft under the lake's surface, so the elevation is $-66$ feet.
Mathematically, the principle I'm using is this:$$ 13-79 = 13-(13 + 66) = 13-13 - 66 = 0-66 = -66 $$
13-79=-(79-13)=-(66). these are negative numbers, which mean 66 to left of 0 in numberline.
