Borrowing From Zero
Sometimes you're going to need to borrow and you'll see a zero (0) in the column to the left. Don't worry. It's a little challenge that you can easily overcome. In all of these examples, we are working with whole numbers. You can get negative numbers when you subtract integers, but we are not there yet. Let's look at an overview first.Example:
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". When this happens, you need to look at the next column to the left (hundreds).
(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 column, 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 value is now "0."
Answer: 105 - 9 = 96
105 - 9 ? |
09 - 9 6 |
9 - 9 96 |
The idea you should 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 those are the basics. If a computer were doing the above example it would be like this:
Example:
105 - 9 = ?
Answer:
• 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.
Example:
432 - 61 = ?
- or -
432 - 61 ??? |
Steps to Solve:
(1) Subtract the ones column. 2-1=1
(2) Borrow so that the tens column problem is 13-6=7.
(3) Because you borrowed from the hundreds column, the problem is 3-0=3.
Answer:
432 - 61 = 371
- or -
432 - 61 371 |
Here are the steps...
432 - 61 ? |
432 - 61 1 |
3 - 61 71 |
3 - 61 371 |
- Overview
- Operations
- Addition
- Subtraction
- 1 to 10
- 1 to 20
- Borrowing
- Borrowing-2
- 2-Digit Numbers
- 3-Digit Numbers
- Multiple Values
- Integers
- Integers-2
- Workbooks
- Multiplication
- Division
- Activities
Useful Reference Materials
Wikipedia:https://en.wikipedia.org/wiki/Arithmetic
Encyclopædia Britannica:
http://www.britannica.com/topic/arithmetic
Encyclopedia.com:
http://www.encyclopedia.com/topic/arithmetic.aspx