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Chapter 4—Decimals 4-6 Dividing Decimals
When you complete the work for this section, you should be able to: - Demonstrate an ability to divide decimal numbers without making errors.
| | Say 'Good-Bye' to Remainders. Recall that you work with dividing whole numbers turned up remainder terms. You would say, for example, that 17 ÷ 5 = 3 R 2, or "seventeen divided by five equals three with a remainder of two." In this section, you are going to find that the remainders can be converted into decimal fractions. This way, the result of such division operation is a far more useful number value than a whole number with a remainder. You will find, for example, that 17 ÷ 5 = 3.4, or "seventeen divided by five equals three point four." | 
Review the names of the parts of a division operation.
| | Here are a few examples of decimal division: | Problem | Notes | | 5 ) 17 | There are no decimal places in the problem, but there will be a decimal point in the quotient. | | 21 ) 34.6 | There is no decimal point in the divisor; but there is a decimal point in the divident, and there will be a decimal point in the quotient. | | 56 ) 0.0034 | This is an example of divding into a number that is much smaller than 1. | | 56.8 ) 124.89 | This problem will have decimal points all around. | The procedures for dividing decimal fractions is almost the same as dividing whole numbers. The only difference is that we have to deal with the decimal points in the decimal-fraction versions. Procedure - Step 1: Multiply both the divisor and dividend by 10 until the divisor is a whole-number value.
- Step 2: Perform the division operations without paying any attention to the decimal points.
- Step 3: Place the decimal point for the quotient directly above the decimal point in the dividend.
| Preparing the Problem for Division When the divisor does not have a fraction part, you do not have to make any special preparation for doing the division. Problem such as 12 )1.28 and 245 )356.75 do not require any preparation. But the next example do require special preparation because the divisors all include a decimal fraction: 1.23 ) 448 and 0.045 ) 34.78. When preparing a decimal-division problem, you multiply the divisor and dividend by 10—over and over again—until the divisor becomes a whole number. Example | Prepare 1.256 ) 6.28 for division. The objective is to change the the divisor, 1.256, into a whole-number value. Multiply 1.256 by 10, and then do the same to the dividend.
The result is 12.56 ) 62.8
The divisor is not yet a whole-number value. Multiply 12.56 by 10, and then do the same to the dividend.
The result is 125.6 ) 628.0
The divisor is not yet a whole-number value. Multiply 125.6 by 10, and then do the same to the dividend.
The result is 1256 ) 6280.0 Now the divisor is a whole-number value and the actual division operation can begin. |  | Examples and Exercises Dividing Decimals Use these interactive examples and exercises to strengthen your understanding and build your skills: Prepare these problems for division by converting the divisor to a whole-number value. | | Completing the Division
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