Forgotten correct method of basic arithmetic (subtraction)

In summary: They're opportunities for learning some new things, again or anew. (Sigh! I have to learn this again. Or, I have to learn this again. Or, I have to learn this again.)"In summary, when subtracting 9 from 30, one must "borrow" 10 from the 30 to create 20 + 10 - 9, which equals 21. When converting 30 into base 5, one can use the same procedure as converting to base 10, dividing until the remainder is less than the base."
  • #1
Logical Dog
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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.
 
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  • #2
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:

 
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  • #3
Bipolar Demon said:
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##.
 
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  • #5
Bipolar Demon said:
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.
 
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  • #6
o_O 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! :DD
 
  • #7
No dividing necessary and none indicated for the example. Mark44's post #5 should be clear.
 
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  • #8
Honestly I am not sure what I was thinking when I asked this, very sorry. :(
 
  • #9
Bipolar Demon said:
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!
 
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  • #10
Fervent Freyja said:
When you get older it will worsen.
Best definition of reassurance I've ever seen...[COLOR=#black].[/COLOR] :oldlaugh:
 
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  • #11
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.
 
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1. What is the forgotten correct method of basic arithmetic (subtraction)?

The forgotten correct method of basic arithmetic (subtraction) is known as the borrowing method or the traditional method. It involves borrowing from the next column when the minuend (top number) is smaller than the subtrahend (bottom number).

2. Why is the traditional method of subtraction considered forgotten?

The traditional method of subtraction is considered forgotten because it has been replaced by the more modern and efficient method of subtraction called the regrouping method or the column method. This method involves breaking down numbers into place values and regrouping them to solve the subtraction problem.

3. What are the benefits of using the traditional method of subtraction?

The traditional method of subtraction helps students develop a better understanding of place value and the concept of borrowing. It also allows for a step-by-step approach to solving subtraction problems, making it easier for students to follow and understand the process.

4. Is the traditional method of subtraction still relevant in today's education system?

Yes, the traditional method of subtraction is still relevant in today's education system. While the regrouping method is used more commonly, the traditional method can still be useful for students who are struggling with understanding place value and borrowing.

5. Are there any drawbacks to using the traditional method of subtraction?

One potential drawback of using the traditional method of subtraction is that it can be time-consuming compared to the regrouping method. It also requires a good understanding of place value and can be more challenging for some students to grasp. However, with practice and patience, students can become proficient in using this method.

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