DIVISION OF DECIMALS We then we multiply by the

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1 Tallahassee Community College 0 DIVISION OF DECIMALS To divide 9, we write these fractions: reciprocal of the divisor 0 9. We then we multiply by the = = The decimal equivalent of is. 67. Think how you read, then write that number with a decimal point. NOTICE 67 =. 67. The decimal point of 67 simply moved 2 places to the left. To find 9 by dividing with the decimals we would write: RULE: When the divisor is a whole number, simply place the decimal point for the quotient directly above the decimal point in the dividend and divide as you did with whole numbers. Instead of having a remainder, you will be told to round the answer to a given place. There is more than one way to write a division problem. 9 in decimal form is.0 9. This is the way you would do this with a calculator. To use long division, you must write 9. 0 REMEMBER to round correctly, you must divide to one place beyond the place to be rounded.

2 EXAMPLE: Divide and round to the nearest hundredth To round to hundredths we ll need to get the answer to thousandths first. Use.870 in the dividend It has the same value as With a calculator, your answer is You still round as you did above. When you divide, be sure to keep each zero unless the value of the number is the same without that zero. EXAMPLE: = Only these zeros can be left off without changing the value! 4. DIVIDE. Practice these problems by using long division. Then check yourself with your calculator. The order of the numbers must be correct! dividend divisor Round to the nearest hundredth. Round to the nearest tenth. HINT: where is the decimal understood to be in 2? To divide by a decimal, we can use a short cut to write an equivalent division problem which has a whole number divisor We will change. to the whole number. We moved the decimal point place to the right a short way of multiplying. 0. We will change the decimal point of the dividend the same way that we changed the divisor move it one place to the right. 2

3 This problem will have the same value as the original because is We then multiply by, a name for. Remember, 0 a number is the same number = We know how to divide by a whole number.. 0. Let's round to the nearest tenth, so we'll divide to the hundredths place Doesn't this answer seem reasonable? is close to 4 6 or to ROUND to the nearest hundredth Learning to divide by powers of 0 will make your work go much faster and it will probably be more accurate! Compare division by powers of 0 with multiplication by powers of 0. Carefully work these problems but do them mentally! 9 4. DIVIDE or MULTIPLY mentally! Use the rules for multiplying and dividing by powers of ten

4 Compare problems and 4. Think why these answers are the same. In an earlier chapter, we saw that dividing by a number is the same as multiplying by the reciprocal of that divisor. In #, the divisor is. The reciprocal of is. In #4, we multiplied by 0.0, the decimal form of. Those who study to understand things like this will become much stronger students than those who just try to get the answers!. Write a decimal multiplication problem equivalent to.9, Write a decimal division problem equivalent to APPLICATIONS: An understanding of the relationship between multiplication and division is helpful. 6 2 is because 2 = 6 If a problem describes a situation where multiplication is implied, but only one factor and the product are known, you will divide the factor into the product to find the missing factor. EXAMPLES: factor? = Product factor Product or: product factor or if your instructor prefers, you may use a little algegra here! a) I bought notebooks for $.29 each. Find the total cost. We know.29 = the total cost. Here both factors are known, so multiply. $6.4 is the total cost! b) I paid $6.4 for identical notebooks. What was the price of each notebook? I know price = $6.4 4

5 Here I am missing a factor, so I divided by the known factor is the cost of one notebook or with algebra, let n = the cost of notebook. n = 6.4 n = 6.4 n = $.29 c) How many notebooks costing $.29 each can be bought for $6.4? I know the number of notebooks $.29 = $6.4. Again, I am missing one factor, so I divide by the other factor.. notebooks or let n = the number of notebooks n.29 = 6.4 n = n = Work these problems. REMEMBER to use common sense to plan your strategy! Answers should seem reasonable. 7. John receives an annual salary of $7,40.84 in 2 equal monthly payments. Find his monthly income. 8. The tax on one sofa is $4.80. A store collected $9.60 in taxes from sales of these sofas. How many sofas were sold?

6 9. The total cost of a TV including interest is $ Find the monthly payments if a $240 down payment is made followed by six monthly payments. 20. Seven people will share a prize of one million six hundred fifty-nine thousand dollars after taxes. Each person will receive 20 equal yearly payments. Find how much each person will get each year. (HINT: How much will one person's total share be? How much will one year of that part be?) ANSWERS: compare these two examples and their answers! (the zero is kept because it's in the rounded place) ,004.6 (How is #2 different from #0?) compare these two problems. Why are the answers the same? is the reciprocal of This is , the same as $,40.2 each month 8. 7 sofas 9. $66.40 per month (A calculator would give 66.4; you write with 2 decimal places, since it is money.) 20. Each person will receive $,80 a year for 20 years. 6

2. Perform the division as if the numbers were whole numbers. You may need to add zeros to the back of the dividend to complete the division

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