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This module is from Fundamentals of Mathematics by Denny Burzynski and Wade Ellis, Jr. This module discusses how to add and subtract decimals. By the end of the module students should understand the method used for adding and subtracting decimals, be able to add and subtract decimals and be able to use the calculator to add and subtract decimals.

Section overview

  • The Logic Behind the Method
  • The Method of Adding and Subtracting Decimals
  • Calculators

The logic behind the method

Consider the sum of 4.37 and 3.22. Changing each decimal to a fraction, we have

4 37 100 + 3 22 100 size 12{4 { {"37"} over {"100"} } +3 { {"22"} over {"100"} } " Performing the addition, we get"} {} Performing the addition, we get

4 . 37 + 3 . 22 = 4 37 100 + 3 22 100 = 4 100 + 37 100 + 3 100 + 22 100 = 437 100 + 322 100 = 437 + 322 100 = 759 100 = 7 59 100 = seven and fifty-nine hundredths = 7.59

Thus, 4 . 37 + 3 . 22 = 7 . 59 size 12{4 "." "37 "+" 3" "." "22 "=" 7" "." "59"} {} .

The method of adding and subtracting decimals

When writing the previous addition, we could have written the numbers in col­umns.

4.37 + 3.22 ̲ 7.59

This agrees with our previous result. From this observation, we can suggest a method for adding and subtracting decimal numbers.

Method of adding and subtracting decimals

To add or subtract decimals:
  1. Align the numbers vertically so that the decimal points line up under each other and the corresponding decimal positions are in the same column.
  2. Add or subtract the numbers as if they were whole numbers.
  3. Place a decimal point in the resulting sum or difference directly under the other decimal points.

Sample set a

Find the following sums and differences.

9 . 813 + 2 . 140 size 12{9 "." "813"+2 "." "140"} {}

9.813 The decimal points are aligned in the same column. + 2.140 ̲ 11.953

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841 . 0056 + 47 . 016 + 19 . 058 size 12{"841" "." "0056"+"47" "." "016"+"19" "." "058"} {}

841.0056 47.016   + 19.058   ̲

To insure that the columns align properly, we can write a 0 in the position at the end of the numbers 47.016 and 19.058 without changing their values.

Vertical addition. 841.0056 plus 47.0160 plus 19.0580 equals 907.0796. A 1 needed to be carried in the hundredths, the tens, and the hundreds columns.

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1.314 - 0.58

1.314 - 0.58   ̲ Write a 0 in the thousandths position.

Vertical subtraction. 1.314 minus 0.580 equals 0.734. The ones, and hundredths digits need to be borrowed from once, and the tenths needs to be borrowed from twice to perform the subtraction.

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16.01 - 7.053

16.01   - 7.053 ̲ Write a 0 in the thousandths position.

Vertical subtraction. 16.101 minus 7.053 equals 8.957. The ones, tenths, hundredths, and thousandths digits need to be borrowed from once to perform the subtraction.

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Find the sum of 6.88106 and 3.5219 and round it to three decimal places.

6.88106 + 3.5219   ̲ Write a 0 in the ten thousandths position.

Vertical addition. 6.88106 plus 3.52190 equals 10.40296. A 1 needs to be carried over the tenths and ones digits to perform the addition.

We need to round the sum to the thousandths position. Since the digit in the position immediately to the right is 9, and 9>5, we get

10.403

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Wendy has $643.12 in her checking account. She writes a check for $16.92. How much is her new account balance?

To find the new account balance, we need to find the difference between 643.12 and 16.92. We will subtract 16.92 from 643.12.

Vertical subtraction. 643.12 minus 16.92 equals 626.20.

After writing a check for $16.92, Wendy now has a balance of $626.20 in her checking account.

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Practice set a

Find the following sums and differences.

3 . 187 + 2 . 992 size 12{3 "." "187 "+" 2" "." "992"} {}

6.179

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14 . 987 - 5 . 341 size 12{"14" "." "987 - 5" "." "341"} {}

9.646

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0 . 5261 + 1 . 0783 size 12{0 "." "5261 "+" 1" "." "0783"} {}

1.6044

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1.06 - 1.0535 size 12{1 "." "06 - 1" "." "0535"} {}

0.0065

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16,521 . 07 + 9,256 . 15 size 12{"16,521" "." "07 "+" 9,256" "." "15"} {}

25,777.22

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Find the sum of 11.6128 and 14.07353, and round it to two decimal places.

25.69

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Calculators

The calculator can be useful for finding sums and differences of decimal numbers. However, calculators with an eight-digit display cannot be used when working with decimal numbers that contain more than eight digits, or when the sum results in more than eight digits. In practice, an eight-place decimal will seldom be encoun­tered. There are some inexpensive calculators that can handle 13 decimal places.

Sample set b

Use a calculator to find each sum or difference.

42.0638 + 126.551

Display Reads
Type 42.0638 42.0638
Press + 42.0638
Type 126.551 126.551
Press = 168.6148

The sum is 168.6148.

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Find the difference between 305.0627 and 14.29667.

Display Reads
Type 305.0627 305.0627
Press 305.0627
Type 14.29667 14.29667
Press = 290.76603

The difference is 290.76603

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51.07 + 3,891.001786

Since 3,891.001786 contains more than eight digits, we will be unable to use an eight-digit display calculator to perform this addition. We can, however, find the sum by hand.

51.070000 3891.001786 ̲ 3942.071786

The sum is 3,942.071786.

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Practice set b

Use a calculator to perform each operation.

4 . 286 + 8 . 97 size 12{4 "." "286 "+" 8" "." "97"} {}

13.256

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452.0092 - 392.558 size 12{"452" "." "0092 - 392" "." "558"} {}

59.4512

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Find the sum of 0.095 and 0.001862

0.096862

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Find the difference between 0.5 and 0.025

0.475

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Find the sum of 2,776.00019 and 2,009.00012.

Since each number contains more than eight digits, using some calculators may not be helpful. Adding these by “hand technology,” we get 4,785.00031

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Exercises

For the following 15 problems, perform each addition or subtraction. Use a calculator to check each result.

1 . 84 + 7 . 11 size 12{1 "." "84"+7 "." "11"} {}

8.95

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15 . 015 6 . 527 size 12{"15" "." "015"-6 "." "527"} {}

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11 . 842 + 28 . 004 size 12{"11" "." "842"+"28" "." "004"} {}

39.846

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3 . 16 2 . 52 size 12{3 "." "16"-2 "." "52"} {}

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3 . 55267 + 8 . 19664 size 12{3 "." "55267"+8 "." "19664"} {}

11.74931

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0 . 9162 0 . 0872 size 12{0 "." "9162"-0 "." "0872"} {}

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65 . 512 8 . 3005 size 12{"65" "." "512"-8 "." "3005"} {}

57.2115

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761 . 0808 53 . 198 size 12{"761" "." "0808"-"53" "." "198"} {}

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4 . 305 + 2 . 119 3 . 817 size 12{4 "." "305"+2 "." "119"-3 "." "817"} {}

2.607

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19 . 1161 + 27 . 8014 + 39 . 3161 size 12{"19" "." "1161"+"27" "." "8014"+"39" "." "3161"} {}

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0 . 41276 0 . 0018 0 . 00011 size 12{0 "." "41276"-0 "." "0018"-0 "." "00011"} {}

0.41085

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2 . 181 + 6 . 05 + 1 . 167 + 8 . 101 size 12{2 "." "181"+6 "." "05"+1 "." "167"+8 "." "101"} {}

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1.0031+6.013106+0.00018+0.0092+2.11

9.135586

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27 + 42 + 9 . 16 0 . 1761 + 81 . 6 size 12{"27"+"42"+9 "." "16"-0 "." "1761"+"81" "." 6} {}

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10 . 28 + 11 . 111 + 0 . 86 + 5 . 1 size 12{"10" "." "28"+"11" "." "111"+0 "." "86"+5 "." 1} {}

27.351

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For the following 10 problems, solve as directed. A calculator may be useful.

Add 6.1121 and 4.916 and round to 2 decimal places.

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Add 21.66418 and 18.00184 and round to 4 decimal places.

39.6660

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Subtract 5.2121 from 9.6341 and round to 1 decimal place.

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Subtract 0.918 from 12.006 and round to 2 decimal places.

11.09

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Subtract 7.01884 from the sum of 13.11848 and 2.108 and round to 4 decimal places.

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A checking account has a balance of $42.51. A check is written for $19.28. What is the new balance?

$23.23

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A checking account has a balance of $82.97. One check is written for $6.49 and another for $39.95. What is the new balance?

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A person buys $4.29 worth of hamburger and pays for it with a $10 bill. How much change does this person get?

$5.71

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A man buys $6.43 worth of stationary and pays for it with a $20 bill. After receiving his change, he realizes he forgot to buy a pen. If the total price of the pen is $2.12, and he buys it, how much of the $20 bill is left?

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A woman starts recording a movie on her video cassette recorder with the tape counter set at 21.93. The movie runs 847.44 tape counter units. What is the final tape counter reading?

869.37

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Exercises for review

( [link] ) Find the difference between 11,206 and 10,884.

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( [link] ) Find the product, 820 10,000 size 12{"820 " cdot " 10,000"} {} .

8,200,000

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( [link] ) Find the value of 121 25 + 8 2 + 16 ÷ 2 2 size 12{ sqrt {"121"} - sqrt {"25"} +8 rSup { size 8{2} } +"16" div 2 rSup { size 8{2} } } {} .

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( [link] ) Find the value of 8 1 3 36 75 ÷ 2 2 5 size 12{8 { {1} over {3} } cdot { {"36"} over {"75"} } div 2 { {2} over {5} } } {} .

20 9 = 5 3  or  2 2 9 size 12{ { {"20"} over {9} } = { {5} over {3} } " or " { {2} over {9} } } {}

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( [link] ) Round 1.08196 to the nearest hundredth.

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Questions & Answers

how did you get 1640
Noor Reply
If auger is pair are the roots of equation x2+5x-3=0
Peter Reply
Wayne and Dennis like to ride the bike path from Riverside Park to the beach. Dennis’s speed is seven miles per hour faster than Wayne’s speed, so it takes Wayne 2 hours to ride to the beach while it takes Dennis 1.5 hours for the ride. Find the speed of both bikers.
MATTHEW Reply
420
Sharon
from theory: distance [miles] = speed [mph] × time [hours] info #1 speed_Dennis × 1.5 = speed_Wayne × 2 => speed_Wayne = 0.75 × speed_Dennis (i) info #2 speed_Dennis = speed_Wayne + 7 [mph] (ii) use (i) in (ii) => [...] speed_Dennis = 28 mph speed_Wayne = 21 mph
George
Let W be Wayne's speed in miles per hour and D be Dennis's speed in miles per hour. We know that W + 7 = D and W * 2 = D * 1.5. Substituting the first equation into the second: W * 2 = (W + 7) * 1.5 W * 2 = W * 1.5 + 7 * 1.5 0.5 * W = 7 * 1.5 W = 7 * 3 or 21 W is 21 D = W + 7 D = 21 + 7 D = 28
Salma
Devon is 32 32​​ years older than his son, Milan. The sum of both their ages is 54 54​. Using the variables d d​ and m m​ to represent the ages of Devon and Milan, respectively, write a system of equations to describe this situation. Enter the equations below, separated by a comma.
Aaron Reply
find product (-6m+6) ( 3m²+4m-3)
SIMRAN Reply
-42m²+60m-18
Salma
what is the solution
bill
how did you arrive at this answer?
bill
-24m+3+3mÁ^2
Susan
i really want to learn
Amira
I only got 42 the rest i don't know how to solve it. Please i need help from anyone to help me improve my solving mathematics please
Amira
Hw did u arrive to this answer.
Aphelele
hi
Bajemah
-6m(3mA²+4m-3)+6(3mA²+4m-3) =-18m²A²-24m²+18m+18mA²+24m-18 Rearrange like items -18m²A²-24m²+42m+18A²-18
Salma
complete the table of valuesfor each given equatio then graph. 1.x+2y=3
Jovelyn Reply
x=3-2y
Salma
y=x+3/2
Salma
Hi
Enock
given that (7x-5):(2+4x)=8:7find the value of x
Nandala
3x-12y=18
Kelvin
please why isn't that the 0is in ten thousand place
Grace Reply
please why is it that the 0is in the place of ten thousand
Grace
Send the example to me here and let me see
Stephen
A meditation garden is in the shape of a right triangle, with one leg 7 feet. The length of the hypotenuse is one more than the length of one of the other legs. Find the lengths of the hypotenuse and the other leg
Marry Reply
how far
Abubakar
cool u
Enock
state in which quadrant or on which axis each of the following angles given measure. in standard position would lie 89°
Abegail Reply
hello
BenJay
hi
Method
I am eliacin, I need your help in maths
Rood
how can I help
Sir
hmm can we speak here?
Amoon
however, may I ask you some questions about Algarba?
Amoon
hi
Enock
what the last part of the problem mean?
Roger
The Jones family took a 15 mile canoe ride down the Indian River in three hours. After lunch, the return trip back up the river took five hours. Find the rate, in mph, of the canoe in still water and the rate of the current.
cameron Reply
Shakir works at a computer store. His weekly pay will be either a fixed amount, $925, or $500 plus 12% of his total sales. How much should his total sales be for his variable pay option to exceed the fixed amount of $925.
mahnoor Reply
I'm guessing, but it's somewhere around $4335.00 I think
Lewis
12% of sales will need to exceed 925 - 500, or 425 to exceed fixed amount option. What amount of sales does that equal? 425 ÷ (12÷100) = 3541.67. So the answer is sales greater than 3541.67. Check: Sales = 3542 Commission 12%=425.04 Pay = 500 + 425.04 = 925.04. 925.04 > 925.00
Munster
difference between rational and irrational numbers
Arundhati Reply
When traveling to Great Britain, Bethany exchanged $602 US dollars into £515 British pounds. How many pounds did she receive for each US dollar?
Jakoiya Reply
how to reduced echelon form
Solomon Reply
Jazmine trained for 3 hours on Saturday. She ran 8 miles and then biked 24 miles. Her biking speed is 4 mph faster than her running speed. What is her running speed?
Zack Reply
d=r×t the equation would be 8/r+24/r+4=3 worked out
Sheirtina
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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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