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

Section overview

  • Definition of Subtraction
  • The Process of Subtraction
  • Calculators

Definition of subtraction

We know from experience with arithmetic that the subtraction 5 - 2 size 12{"5 – 2"} {} produces 3, that is 5 - 2 = 3 size 12{"5 – 2 "=" 3"} {} . We can suggest a rule for subtracting signed numbers by illus­trating this process on the number line.

A number line with hash marks from -1 to 7. There is an arrow from 0 to 5 and from 5 to 3.

Begin at 0, the origin.

Since 5 is positive, move 5 units to the right.

Then, move 2 units to the left to get to 6. (This reminds us of addition with a negative number.)

From this illustration we can see that 5 - 2 size 12{"5 – 2"} {} is the same as 5 + ( - 2 ) size 12{"5 "+ \( "–2" \) } {} . This leads us directly to the definition of subtraction.

Definition of subtraction

If a size 12{a} {} and b size 12{b} {} are real numbers, a - b size 12{"a–b"} {} is the same as a + ( - b ) size 12{"a "+ \( "–b" \) } {} , where - b size 12{ –b} {} is the opposite of b size 12{b} {} .

The process of subtraction

From this definition, we suggest the following rule for subtracting signed numbers.

Subtraction of signed numbers

To perform the subtraction a - b size 12{"a–b"} {} , add the opposite of b size 12{b} {} to a size 12{a} {} , that is, change the sign of b size 12{b} {} and add.

Sample set a

Perform the indicated subtractions.

5 3 = 5 + ( 3 ) = 2 size 12{5 - 3=5+ \( - 3 \) =2} {}

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4 - 9 = 4 + ( - 9 ) = - 5 size 12{"4–9 "=" 4 "+ \( "–9" \) =" –5"} {}

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4 6 = 4 + ( 6 ) = 10 size 12{ - 4 - 6= - 4+ \( - 6 \) = - "10"} {}

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3 ( 12 ) = 3 + 12 = 9 size 12{ - 3 - \( - "12" \) = - 3+"12"=9} {}

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0 - ( - 15 ) = 0 + 15 = 15 size 12{"0 – " \( "–15" \) =" 0 "+" 15 "=" 15"} {}

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The high temperature today in Lake Tahoe was 26°F. The low temperature tonight is expected to be -7°F. How many degrees is the temperature expected to drop?

We need to find the difference between 26 and -7.

26 - ( - 7 ) = 26 + 7 = 33 size 12{"26 – " \( "–7" \) =" 26 "+" 7 "=" 33"} {}

Thus, the expected temperature drop is 33°F.

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- 6 - ( - 5 ) - 10 = - 6 + 5 + ( - 10 ) = ( - 6 + 5 ) + ( - 10 ) = - 1 + ( - 10 ) = - 11

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Practice set a

Perform the indicated subtractions.

9 6 size 12{9 - 6} {}

3

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6 9 size 12{6 - 9} {}

-3

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0 7 size 12{0 - 7} {}

-7

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1 14 size 12{1 - "14"} {}

-13

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8 12 size 12{ - 8 - "12"} {}

-20

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21 6 size 12{ - "21" - 6} {}

-27

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6 ( 4 ) size 12{ - 6 - \( - 4 \) } {}

-2

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8 ( 10 ) size 12{8 - \( - "10" \) } {}

18

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1 ( 12 ) size 12{1 - \( - "12" \) } {}

13

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86 ( 32 ) size 12{"86" - \( - "32" \) } {}

118

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0 16 size 12{0 - "16"} {}

-16

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0 ( 16 ) size 12{0 - \( - "16" \) } {}

16

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0 ( 8 ) size 12{0 - \( 8 \) } {}

-8

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5 ( 5 ) size 12{5 - \( - 5 \) } {}

10

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24 [ ( 24 ) ] size 12{"24" - \[ - \( - "24" \) \] } {}

0

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Calculators

Calculators can be used for subtraction of signed numbers. The most efficient calculators are those with a A box with a plus and minus sign. key.

Sample set b

Use a calculator to find each difference.

3, 187 8, 719 size 12{3,"187" - 8,"719"} {}

Display Reads
Type 3187 3187
Press - 3187
Type 8719 8719
Press = -5532

Thus, 3, 187 8, 719 = 5, 532 size 12{3,"187" - 8,"719"= - 5,"532"} {} .

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156 ( 211 ) size 12{ - "156" - \( - "211" \) } {}

Method A:

Display Reads
Type 156 156
Press A box with a plus and minus sign. -156
Type - -156
Press 211 211
Type A box with a plus and minus sign. -211
Press = 55

Thus, 156 ( 211 ) = 55 size 12{ - "156" - \( - "211" \) ="55"} {} .

Method B:

We manually change the subtraction to an addition and change the sign of the number to be subtracted.

156 211 size 12{ - "156" - left ( - "211" right )} {} becomes 156 + 211 size 12{ - "156"+"211"} {}

Display Reads
Type 156 156
Press A box with a plus and minus sign. -156
Press + -156
Type 211 211
Press = 55
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Practice set b

Use a calculator to find each difference.

44 315 size 12{"44" - "315"} {}

-271

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12 . 756 15 . 003 size 12{"12" "." "756" - "15" "." "003"} {}

-2.247

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31 . 89 44 . 17 size 12{ - "31" "." "89" - "44" "." "17"} {}

-76.06

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0 . 797 ( 0 . 615 ) size 12{ - 0 "." "797" - \( - 0 "." "615" \) } {}

-0.182

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Exercises

For the following 18 problems, perform each subtraction. Use a calculator to check each result.

8 3 size 12{8-3} {}

5

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12 7 size 12{"12"-7} {}

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5 6 size 12{5-6} {}

-1

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14 30 size 12{"14"-"30"} {}

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6 8 size 12{-6-8} {}

-14

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1 12 size 12{-1-"12"} {}

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5 3 size 12{-5- left (-3 right )} {}

-2

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11 8 size 12{-"11"- left (-8 right )} {}

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0 6 size 12{0-6} {}

-6

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0 15 size 12{0-"15"} {}

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0 7 size 12{0- left (-7 right )} {}

7

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0 10 size 12{0- left (-"10" right )} {}

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67 38 size 12{"67"-"38"} {}

29

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142 85 size 12{"142"-"85"} {}

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816 1140 size 12{"816"-"1140"} {}

-324

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105 421 size 12{"105"-"421"} {}

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550 121 size 12{-"550"- left (-"121" right )} {}

-429

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15 . 016 4 . 001 size 12{-"15" "." "016"- left (4 "." "001" right )} {}

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For the following 4 problems, perform the indicated operations.

26 + 7 52 size 12{-"26"+7-"52"} {}

-71

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15 21 2 size 12{-"15"-"21"- left (-2 right )} {}

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104 216 52 size 12{-"104"- left (-"216" right )- left (-"52" right )} {}

164

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0 . 012 0 . 111 0 . 035 size 12{-0 "." "012"- left (-0 "." "111" right )- left (0 "." "035" right )} {}

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When a particular machine is operating properly, its meter will read 34. If a broken bearing in the machine causes the meter reading to drop by 45 units, what is the meter reading?

-11

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The low temperature today in Denver was 4 ° size 12{-4°} {} F and the high was 42 ° size 12{-"42"°} {} F. What is the temperature difference?

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Exercises for review

( [link] ) Convert 16 . 02 1 5 size 12{"16" "." "02" { {1} over {5} } } {} to a decimal.

16.022

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( [link] ) Convert 5 16 size 12{ { {5} over {"16"} } } {} to a percent.

31.25%

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( [link] ) Use the distributive property to compute the product: 15 82 size 12{"15" cdot "82"} {} .

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( [link] ) Find the sum: 16 + ( 21 ) size 12{"16"+ \( -"21" \) } {} .

-5

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Questions & Answers

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Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
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The nanotechnology is as new science, to scale nanometric
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nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
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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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