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This module is from Fundamentals of Mathematics by Denny Burzynski and Wade Ellis, Jr. This module discusses how to subtract whole numbers. By the end of this module, students should be able to understand the subtraction process, subtract whole numbers, and use a calculator to subtract one whole number from another whole number.

Section overview

  • Subtraction
  • Subtraction as the Opposite of Addition
  • The Subtraction Process
  • Subtraction Involving Borrowing
  • Borrowing From Zero
  • Calculators

Subtraction

Subtraction

Subtraction is the process of determining the remainder when part of the total is removed.

Suppose the sum of two whole numbers is 11, and from 11 we remove 4. Using the number line to help our visualization, we see that if we are located at 11 and move 4 units to the left, and thus remove 4 units, we will be located at 7. Thus, 7 units remain when we remove 4 units from 11 units.

A number line, with an arrow, labeled -4, drawn from the mark for 11 to the mark for 7.

The minus symbol

The minus symbol (-) is used to indicate subtraction. For example, 11 4 size 12{"11" - 4} {} indicates that 4 is to be subtracted from 11.

Minuend

The number immediately in front of or the minus symbol is called the minuend , and it represents the original number of units.

Subtrahend

The number immediately following or below the minus symbol is called the subtrahend , and it represents the number of units to be removed .

Difference

The result of the subtraction is called the difference of the two numbers. For example, in 11 4 = 7 size 12{"11" - 4=7} {} , 11 is the minuend, 4 is the subtrahend, and 7 is the difference.

Subtraction as the opposite of addition

Subtraction can be thought of as the opposite of addition. We show this in the problems in Sample Set A.

Sample set a

8 5 = 3 size 12{8 - 5=3} {} since 3 + 5 = 8 size 12{3+5=8} {} .

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9 3 = 6 size 12{9 - 3=6} {} since 6 + 3 = 9 size 12{6+3=9} {} .

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Practice set a

Complete the following statements.

7 5 = size 12{7 - 5={}} {} since + 5 = 7 size 12{+5=7} {} .

7 - 5 = 2 since 2 + 5 = 7

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9 1 = size 12{9 - 1={}} {} since + 1 = 9 size 12{+1=9} {} .

9 - 1 = 8 since 8 + 1 = 9

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17 8 = size 12{"17" - 8={}} {} since + 8 = 17 size 12{+8="17"} {} .

17 - 8 = 9 since 9 + 8 = 17

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The subtraction process

We'll study the process of the subtraction of two whole numbers by considering the difference between 48 and 35.

Vertical subtraction. 48 - 35 means, 4 tens + 8 ones, minus 3 tens - 5 ones = 1 ten + 3 ones.

which we write as 13.

The process of subtracting whole numbers

To subtract two whole numbers,

The process

  1. Write the numbers vertically, placing corresponding positions in the same column.

    48 - 35 ̲

  2. Subtract the digits in each column. Start at the right, in the ones position, and move to the left, placing the difference at the bottom.

    48 - 35 ̲ 13

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Sample set b

Perform the following subtractions.

275 - 142 ̲ 133

5 2 = 3 . 7 4 = 3 . 2 1 = 1 . alignr { stack { size 12{5 - 2=3 "." } {} #size 12{7 - 4=3 "." } {} # size 12{2 - 1=1 "." } {}} } {}

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46,042 -   1,031 ̲ 45,011

2 1 = 1 . 4 3 = 1 . 0 0 = 0 . 6 1 = 5 . 4 0 = 4 . alignr { stack { size 12{2 - 1=1 "." } {} #size 12{4 - 3=1 "." } {} # size 12{0 - 0=0 "." } {} #size 12{6 - 1=5 "." } {} # size 12{4 - 0=4 "." } {}} } {}

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Find the difference between 977 and 235.

Write the numbers vertically, placing the larger number on top. Line up the columns properly.

977 - 235 ̲ 742

The difference between 977 and 235 is 742.

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In Keys County in 1987, there were 809 cable television installations. In Flags County in 1987, there were 1,159 cable television installations. How many more cable television installations were there in Flags County than in Keys County in 1987?

We need to determine the difference between 1,159 and 809.

1,159 - 809 = 350, with a 1 above the thousands and hundreds columns.

There were 350 more cable television installations in Flags County than in Keys County in 1987.

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Practice set b

Perform the following subtractions.

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Source:  OpenStax, Fundamentals of mathematics. OpenStax CNX. Aug 18, 2010 Download for free at http://cnx.org/content/col10615/1.4
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