Borrowing and Regrouping Values in Subtraction
Do you remember the idea of carrying in addition? You took an extra value from one column and moved it to the next column. Borrowing or regrouping in subtraction flips that idea around so that you borrow a value from the next column to the left. Some of you will hear the word regrouping. Borrowing and regrouping are the same ideas when you subtract. Sometimes you need a little bit extra in order to do your subtraction, so you use an amount from the column to the left.In subtraction, you borrow when you are subtracting one number that is greater than another (the subtrahend is greater than the minuend).
35 - 2 would not need borrowing/regrouping.
32 - 5 would use borrowing/regrouping because you can't subtract 5 from 2 in this example.
To be honest, we like the term borrow, but you need to say the word your teacher wants to hear.
Examples:
4 - 2 = 2 (no borrowing/regrouping)
39 - 6 = 33 (no borrowing/regrouping)
32 - 5 = 27 (borrowing/regrouping needed)
- or -
2 - 5 27 |
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. Also, you only borrow a "1" and then you decrease the value of the number by one. In the above example, you are borrowing an extra ten (10) for your subtraction problem. Here's the breakdown.
Example:
32 - 5 = ?
(1) Subtract the ones column. Since you can't subtract 5 from 2, you need to borrow/regroup.
(2) Borrow "1" from the tens column. The "3" becomes a "2" because you took away one group of ten.
(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
Always Moving to the Left
Let's start with a little reminder. When you are subtracting, you will always move to the left. Always start with the smallest values. If you have a five-digit number such as 12,345 you will start subtracting values from the ones column first. Then you will move to the tens, hundreds, thousands, and ten thousands columns. If borrowing/regrouping was involved, you would take the borrowed value and place it in the column to the right. So, if you were subtracting numbers in the tens column and you needed to borrow a "1", you would remove "1" from the hundreds column.Problem:
922 - 599 ??? |
Steps to Solve:
• Start with the ones column: 2-9 requires regrouping. Borrow one from the tens column.
• Now 12-9=3. Write the three in the ones column of your answer.
• Move to the tens column and you have the problem 1-9 (it's a 1 because you borrowed before). You need grouping again, so borrow from the hundreds column.
• Now 11-9=2. Write the 2 in the tens column of your answer.
• Finally the hundreds column. 8-5=3
Answer:
323
We built our difference like this... --3, then -23, then 323
922 - 599 ? |
1 9 - 599 3 |
81 - 599 23 |
81 - 599 323 |
- 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