Unit 3.5: Fractions, Decimals and Percent Lesson: Dividing Decimals Objectives: Students will learn to divide decimals with both paper and pencil as well as with the use of a calculator. Procedure: Dividing decimals is like dividing normal whole numbers, except that we do not stop at a remainder anymore. Lets review dividing whole numbers first. Lets review the names of the parts first: Dividing Whole Numbers: What is the result of dividing 648 by 6? 18 6 648 4 48 48 Divide 6 by 6, subtract to get 6 does not go into 4, so bring down the 8 divide 48 by 6, goes in 8 times, subtract get zero 1
Dividing Decimals Decimal in the Dividend The next step is to divide when there is a decimal in the dividend. (in the box). When this happens it is very important to make sure that you keep the place values in the proper locations. What is the quotient of 66.46 divided by 6? This problem sets up in the same way as a whole number division, with the exception that you move the decimal up to where the answer is. 6 66.48. move the decimal up first Now divide normally, make sure that you place the quotient in the proper location. 1. 6 66.48 6 divides into 6 one time, so place a 1 above the 6, subtract to get. 1. 6 66.48 Bring down the 6, now how many times does 6 go into 6? 6 1 1. 6 4 6.48 6 6 It goes in 1 time, place the 1 above the 6, and subtract 6 from 6 to get. 2
11. 6 46.48 6 6 4 Bring down the 4. How many times does 6 go into 4? It goes in times, place a above the 4, and bring down the 8. 11.8 6 66.48 6 6 4 48 48 Bring down the 8. How many times does 6 go into 48? 8 times, so subtract 48 from 48 to get. Place a 8 above the 8. The quotient is 11.8 Complete several other examples dividing by a non-decimal divisor, and decimal dividend. 3
Example: What is 1.26 divided by 5? Example: What is 15.92 divided by 8 gives 13.24 4
Dividing by a Decimal Divisor. To divide a decimal with a decimal divisor all you have to do is change the set up at the beginning. Lets work with that first. 1.44.8 Normally we would just set up the division with the second number in outside the box and the first number in the box..8 1.44 But this leads to a problem. The first question is how many times does.8 divide into 1? This is not an easy question, so we are going to use equivalent decimal facts to change the question so that we can answer it without a decimal in the divisor. 1.44.8 Multiply both numbers by 1 This gives : 14.4 8 To see why this works, look at the following questions. What is 6 3? Multiply both the divisor and the dividend by 1. What is the answer after your divide. 6 3 6 3 This also gives us an answer of. We can use this fact to get the decimal divisor to a whole number when we divide by decimals everytime. It makes our dividing much easier. So we can modify the question to a equivalent question to get the answer..8 1.44 can become 8 14.4 and will give the. 5
So now divide like we did earlier. 1.8 8 1 4.4 8 64 64 Example What is the quotient of 59.4 2.4? Setup: 2.4 59.4 Change the setup to eliminate the decimal in the divisor: 2 4 5 9 4 Now divide : 24 5 9 4 6
Repeating Decimals Up until now all the answer have not had repeating decimals. When you have repeating decimals in the quotient you follow the following rules. 1. If you are not told what to divide to, divide to the first three non-zero digits and round back to the nearest 2 non-zero digits. (two non zero decimal places rounded correctly) 2. If you are told to round to a specific decimal place, remember to calculate one extra place value so you can round correctly. Example: 3. If you can, you may place the repeating sign on as we did earlier with the calculator. What is the quotient of.2 divided by.3? Setup:.3.2 Change the setup to eliminate the decimal divisor: Now divide: answer is 7
Complete the following questions: Page 16#1-13. Note only use calculators on questions marked with a calculator. 8