Forgotten correct method of basic arithmetic (subtraction)

[Logical Dog]

What happens when you have to subtract:

30
-9

Basically 30 - 9 but the 3 must be made 13, so what happens to the zero? I know if it was any other number we would reduce its value by one.

Also, if possible, can anyone please show me how 30 in base 5 is 110?

I understand that its 1*5*5 + 1*5 + 0*1. But can anyone divide and show me how they arrive to it? I need to do the exercise in the book and I had the same situation as above! Took it to a friend in uni and he couldn't do it either.

 

[jedishrfu]

You could look at it as an expression:

30 = 30

30 - 9 = 20 + 10 - 9

30 -9 = 20 + 1 = 21

Here's a reference to look at for base conversion first:

 

[fresh_42]

What happens when you have to subtract:

30
-9

Basically 30 - 9 but the 3 must be made 13, so what happens to the zero? I know if it was any other number we would reduce its value by one.

What do you mean? I don't see a $13$.

Also, if possible, can anyone please show me how 30 in base 5 is 110?

I understand that its 1*5*5 + 1*5 + 0*1. But can anyone divide and show me how they arrive to it? I need to do the exercise in the book and I had the same situation as above! Took it to a friend in uni and he couldn't do it either.

How do you write $30$ in the base of $10$? It's the same procedure.
How often is $1000$ in included in $30$? Say $r$.
How often is $100$ in included in $30-1000r$? Say $s$.
How often is $10$ in included in $30-1000r-100s$? Say $t$.
How often is $1$ in included in $30-1000r-100s-10t$? Say $u$.
So $30 = 1000r + 100s + 10t + 1u$.

 

[jedishrfu]

How not to do the math:

 

[Mark44]

What happens when you have to subtract:

30
-9

Basically 30 - 9 but the 3 must be made 13, so what happens to the zero? I know if it was any other number we would reduce its value by one.

There's no 13 in the problem or the work.

To subtract 9 from 0, you need to "borrow" 10 from the 30, so that you have in effect 20 + 10 - 9, or 21.

 

[Logical Dog]

I got it. Me and a couple of freinds worked it out, you have to keep dividing until the remainder is less than the base!

Sorry!

 

[symbolipoint]

No dividing necessary and none indicated for the example. Mark44's post #5 should be clear.

 

[Logical Dog]

Honestly I am not sure what I was thinking when I asked this, very sorry. :(

 

[Fervent Freyja]

Honestly I am not sure what I was thinking when I asked this, very sorry. :(

That's alright, everyone slips up every now-and-then, especially when stressed! I'm notorious for overthinking and overlooking things. When you get older it will worsen. I found my cell phone in the refrigerator the other day. I know I had to have done it because things have ended up in there in the past. You are just fine!

 

[OCR]

When you get older it will worsen.

Best definition of reassurance I've ever seen....

 

[symbolipoint]

One gets comfortable with the simpler things as one gets older and more experienced and reexamines them, even the "easy" things. One recognizes these ideas about Subtraction and borrowing, whether whole numbers, mixed numbers (fractions) , decimal numbers, or bags of objects. The miner mental slips should be only temporary, or occasional.