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Decimal Subtraction

Subtract decimals by lining up the decimal points.

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Subtraction of Decimals

Jeremy and his family are driving to visit his grandparents. On the first day they drove 234.8 miles and on the second day they drove 251.6 miles. How many more miles did they drive on the second day?

Subtracting Decimals

To subtract decimals, first write the decimals using the vertical alignment method. The decimal points must be kept directly under each other and the digits in the same place value must be kept in line with each other. If the decimal numbers are signed numbers, the rules for adding integers are applied to the problem. The number of greater magnitude should be placed above the number of smaller magnitude. Magnitude is simply the size of the number without respect to its sign. The number -42.8 has a magnitude of 42.8.

Subtract the decimals

Subtract: 57.626.18

Subtracting decimals is similar to subtracting whole numbers. Line up the decimal points so that you can subtract corresponding place value digits (e.g. tenths from tenths, hundredths from hundredths, and so on). As with whole numbers, start from the right and work toward the left remembering to borrow when it is necessary.

57.65 126.1851.4  4

Subtract the decimals

(98.04)(32.801)

Begin by writing the question using the vertical alignment method. To ensure that the digits are aligned correctly, add zero to 98.04.

98.04032.801

Subtract the numbers.

987.1043 1032.180 1165.123 19

Subtract the decimals

(67.65)(25.43)

The first step is to write the problem as an addition problem and to change the sign of the original number being subtracted. In other words, add the opposite.

(67.65)+(+25.43)

Now, write and solve the problem using the vertical alignment method.

67.65+25.43+93.08

Subtract the decimals

(137.4)(+259.687)

The first step is to write the problem as an addition problem and to change the sign of the original number being subtracted. In other words, add the opposite.

(137.4)+(259.687)

Now write the problem using the vertical alignment method. Remember to put 259.687 above 137.4 because 259.687 is the number of greater magnitude. The two numbers that are being added have opposite signs. Apply the same rule that you used when adding integers that had opposite signs – subtract the numbers and use the sign of the larger number in the answer.

259.687+137.400

To ensure that the digits are aligned correctly, add zeros to 137.4.

259.687+137.400

Subtract the numbers.

259.687+137.400122.287

The numbers being added have opposite signs. This means that the sign of the answer will be the same sign as that of the number of greater magnitude. In this problem the answer has a negative sign.

Examples

Example 1

Earlier, you were asked how many more miles did Jeremy and his family drive on the second day. 

Jeremy and his family are driving to visit his grandparents. On the first day they drove 234.8 miles and on the second day they drove 251.6 miles.

The decimal number 251.6 is of greater magnitude than 234.8. The numbers must be vertically aligned with the larger one above the smaller one. Now the numbers can be subtracted.

License: CC BY-NC 3.0

They drove 16.8 miles more on the second day.

Example 2

Subtract these decimal numbers: (243.67)(196.3579)

(243.67)(196.3579)=47.3121

Example 3

(32.47)(28.8)(19.645)

(32.47)(28.8)(19.645)=41.625

Write the question as an addition problem and change the sign of the original number being subtracted.

(32.47)+(+28.8)+(19.645)

Follow the rules for adding integers.

Example 4

Josie has $59.27 in her bank account. She went to the grocery store and wrote a check for $62.18 to pay for the groceries. Describe Josie’s balance in her bank account now.

$59.27-$62.18=$-2.91. The account will have a negative value. This means that her account is overdrawn.

Review

Subtract the following numbers:

  1. 42.3715.32
  2. 37.8917.2827
  3. 579.23745.68
  4. 4.29350.327
  5. 16.0747.58
  6. (17.39)(49.68)
  7. (92.75)+(106.682)
  8. (72.5)(77.57)(31.724)
  9. (82.456)(279.83)+(567.3)
  10. (57.76)(85.9)(33.84)

Determine the answer to the following problems.

  1. The diameter of No. 12 bare copper wire is 0.08081 in., and the diameter of No. 15 bare copper wire is 0.05707 in. How much larger is the diameter of the No.12 wire compared to the diameter of the No. 15 wire?
  2. The resistance of an armature while it is cold is 0.208 ohm. After running for several minutes, the resistance increases to 1.340 ohms. Find the increase in resistance of the armature.
  3. The highest temperature recorded in Canada this year was 114.8F. The lowest temperature of 62.9F was recorded in February this year. Find the difference between the highest and lowest temperatures recorded in Canada this year.
  4. The temperature in Alaska was recorded as 78.64F in January of 2010 and as 59.8F on the same date in 2011. What is the difference between the two recorded temperatures?
  5. Laurie has a balance of -$32.16 in her bank account. Write a problem that could represent this balance.

Answers for Review Problems

To see the Review answers, open this PDF file and look for section 1.6. 

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Vocabulary

Decimal point

A decimal point is a period that separates the complete units from the fractional parts in a decimal number.

Magnitude

The magnitude of a number is the size of a number without respect to its sign. The number -35.6 has a magnitude of 35.6.

Place Value

The value of given a digit in a multi-digit number that is indicated by the place or position of the digit.

Image Attributions

  1. [1]^ License: CC BY-NC 3.0

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