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Sometimes you Need to BorrowDo you remember the idea of carrying in addition? You took an extra value from one column and moved it to the next column. Borrowing flips that idea around and you borrow a value from a column to do your subtraction.
In subtraction, you borrow when you are subtracting one number that is greater than another is.
35 - 2 would not use borrowing.
32 - 5 would use borrowing because you can't easily subtract 5 from 2.
When your problem is set up, you borrow from the column on the left. If you are subtracting in the ones column and you need to borrow, look to the tens column. If you are working the tens, borrow from the hundreds. It goes on like that. Look to the left when you need to borrow.
When you borrow, you only borrow a "1" and then you subtract one from the number you borrowed from. You are really borrowing an extra ten (10) for your subtraction problem. Here's the breakdown.
32 - 5 = ?
(1) Subtract the ones column. Since you can't subtract 5 from 2, you need to borrow.
(2) Borrow "1" from the tens column. The "3" becomes a "2" because you took one away.
(3) Increase the "2" to "12" and try subtracting again. 12 - 5 = 7
(4) Complete subtraction in the tens column. 2 - 0 = 2
Answer: 32 - 5 = 27
Borrowing From ZeroSometimes you're going to need to borrow and you'll see a zero (0) in the column to the left. While a small problem, you will easily fix it. Let's look at an overview first.
105 - 9 = ?
(1) Subtract the ones column. Since you can't subtract 9 from 5, you need to borrow.
(2) Borrow "1" from the tens column. The problem is that you can't borrow "1" from "0". Look to the hundreds column.
(3) Since the value in the hundreds column is greater than "0", you can borrow.
(4) Take "1" away from the hundreds column. That number becomes a "0."
(5) In reality, the tens column would then become "10", but since you still need help in the ones, you will borrow again. The tens column changes from "10" to "9."
(6) Your "5" in the ones column becomes "15" because of the borrowing.
(7) Subtract the ones column. 15 - 9 = 6
(8) Subtract the tens column. 9 - 0 = 9
(9) There is no subtraction in the hundreds column because the number is now "0."
Answer: 105 - 9 = 96
The thing you need to remember is that if you need to borrow and the number to the left is zero, continue to the next column to the left. Keep going until you find a number that you can borrow from. Once that happens, bring your "1" to the original column and change all of the "0" values to "9." There are bigger ideas and theories involved in the process, but that's how to do it. If a computer were doing the above example it would be like this.
Problem: 105 - 9
- Subtract ones column.
- Since you cannot subtract 9 from 5, you must borrow.
- Look to tens column for borrowing.
- Since tens column value is zero, look to hundreds column.
- Hundreds column value is greater than zero. Borrow "1" and decrease hundreds value by "1."
- Skip tens column and change value from "0" to "9."
- Increase value in ones column from "5" to "15" and complete subtraction.
- Complete subtraction in tens column.
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