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Chapter 1 Whole Numbers 1-5 Subtracting Whole Numbers Subtraction is the reverse of addition. - When you add 3 and 4 you get 7
- When you subtract 3 from 7 you get back to 4
- Or when you subtract 4 from 7 you get back to 3
| | | Subtraction facts | Definitions - The top number is the minuend
- The number being subtracted is the subtrahend.
- The result of the subtraction operation is called the difference.
|  | The minus sign (–) indicates the subtraction operation. | Examples 1. 9
– 6
3 | 2. 10
– 4
6 | 3. 7
– 1
6 | 4. 10
– 0
10 | 5. 120
– 120
0 | The whole number system does not allow us to subtract a larger number from a smaller value. For example, subtracting 5 from 3 is "illegal " because a value that is "less than nothing" doesn't make sense for whole numbers. This means that the minuend will always be larger then the subtrahend or equal to the subtrahend, but never smaller than the subtrahend. Subtraction problems are sometimes written in a horizontal form such as: 5 – 3 = 2 This form is also known as a number sentence. It is read as, "Five minus three equals two." - The minus sign (–) indicates the subtraction operation.
- The equal sign (=) expresses the equality of the two parts of the sentence.
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| Examples | 1. 3 – 1 = 2 | 2. 5 – 2 = 3 | 3. 4 – 0 = 4 | 4. 9 – 3 = 6 | 5. 9 – 9 = 0 | Notes | Zero subtracted from any value is equal to the original value. | Example: 2 – 0 = 2 | | Any number subtracted from itself equals zero. | Example: 6 – 6 = 0 | | 1-5.2 "Borrowing" in Subtraction Problems "Borrowing" is necessary whenever you face a situation where you are trying to subtract a larger number from a smaller one. 27
– 4
| This example does not require borrowing,
because 4 can be subtracted from 7 with no trouble at all. | 72
– 4
| But this example requires "borrowing,"
because 4 cannot be subtracted from 2 in the whole-number system. | | The idea behind borrowing is to add 10 to the top value. In our example here, you can add 10 to the 2. Now you can subract 4 from 12. That works. But it is not a good idea to simply pull the number 10 out of thin air. That's illegal. The 10 has to come from somewhere, and that "somewhere" is the next-higher place value. In this example, subtracting 1 from the 7 makes that extra 10 available for changing 2 to 12. Procedure When you are working a subtraction problem, and you find you are trying to subtract a larger value from a smaller one, add 10 to the top value by subracting 1 from the next-higher place value. | | 
Borrowing is often necessary for completing subtraction problems. | Examples | 1. | 1
2 14
– 8
1 6 | 2. | 1 10
2 1 14
– 1 8 6
2 8 | 3. | | 4. | | 5. | |
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