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Chapter 1—Whole Numbers

1-5 Subtracting Whole Numbers

 When you complete the work for this section, you should be able to: Subtract small whole numbers without making any errors. Explain how to use a standard subtraction table. Explain when and how to use the borrowing principle in subtraction.

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

Introduction to Subtracting Whole Numbers

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.

Here is a basic subtraction  table. It shows the results of subtracting all possible combinations of two digits, from 0 – 0 = 0 through 9 – 9 = 0. Study the table carefully, and see if you can figure out how it works.

Subtraction Table

 Subtraction facts
 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.

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

Important

When you are subtracting whole numbers, the subtrahend must be less than the minuend. Or in other words, you should not try to subtract a larger whole number from a smaller whole number.

Example

• You can subtract 5 from 7:  7 – 5 = 2     The subtrahend is smaller than the minuend.
• You cannot subtract 7 from 5 in the whole number system:  5 - 7 = invalid

Examples and Exercises

 Basic Subtraction Use these interactive examples and exercises to strengthen your understanding and build your skills:

Subtracting Larger Whole Numbers

When subtracting pairs of whole numbers that are larger than 9, you must subtract digits that have the same place values—subtract the ones digit in the subtrahend from the ones digit in the minuend, the tens digit from the tens digit, the hundreds digit from the hundreds digit, and so on. So when you are setting up subtraction operations in the vertical form, always begin by aligning the place values.

 For example: Then subtract each of the columns from right to left. Write the difference digits under their corresponding place columns.

Procedure

When subtracting a pair of whole numbers larger than 9:

 Step 1: Align the numbers vertically — minuend on top — so that the places values line up vertically. Step 2: Subtract the digits in each column, beginning from the right (ones place) column. Step 3: When the top number in a column happens to be smaller than the bottom number, borrow 1 from the next column to the left.

Example 1

"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 subtract 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. Borrowing is often necessary for completing subtraction problems.
 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 subtracting 1 from the next-higher place value.

Example 2

Examples and Exercises

 Subtraction With Borrowing Use these interactive examples and exercises to strengthen your understanding and build your skills:

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