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Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. 4.5 Dividing Decimals and Order of Operations

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Martin-Gay, Basic Mathematics, 4e 22 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Dividing Decimals Dividing decimal numbers is similar to dividing whole numbers. The only difference is that we place a decimal point in the quotient. Dividing by a Whole Number Step 1: Place the decimal point in the quotient directly above the decimal point in the dividend. Step 2: Divide as with whole numbers.

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Martin-Gay, Basic Mathematics, 4e 33 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Dividing Decimals Dividing by a Whole NumberExample Step 1 : Place the decimal point in the quotient directly above the decimal point in the dividend. Step 2: Divide as with whole numbers. (do on board first).

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Martin-Gay, Basic Mathematics, 4e 44 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Example Divide: 219.2÷8. divisor dividend quotient Check:

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Martin-Gay, Basic Mathematics, 4e 55 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Example Divide: 0.6÷4. divisor dividend quotient Check:

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Martin-Gay, Basic Mathematics, 4ed 66 Dividing Decimals Dividing by a Whole NumberPractice Problems One Step 1: Place the decimal point in the quotient directly above the decimal point in the dividend. Step 2: Divide as with whole numbers. P 287 Practice Problem One Do on board

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Martin-Gay, Basic Mathematics, 4ed 77 Dividing Decimals Dividing by a Whole Number Practice Problems Two Step 1: Place the decimal point in the quotient directly above the decimal point in the dividend. Step 2: Divide as with whole numbers. P 287 Practice Problem Two

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Martin-Gay, Basic Mathematics, 4ed 88 Dividing Decimals Dividing by a Whole NumberPractice Problems Three Step 1: Place the decimal point in the quotient directly above the decimal point in the dividend. Step 2: Divide as with whole numbers. P 288 Practice Problem 3a

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Martin-Gay, Basic Mathematics, 4ed 99 Dividing Decimals Dividing by a Whole NumberPractice Problems Three Step 1: Place the decimal point in the quotient directly above the decimal point in the dividend. Step 2: Divide as with whole numbers. P 288 Practice Problem 3b Do on board

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Martin-Gay, Basic Mathematics, 4e 10 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Dividing by a Decimals If the divisor is not a whole number, before we divide we need to move the decimal point to the right until the divisor is a whole number.

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Martin-Gay, Basic Mathematics, 4e 11 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Example Divide: 6.888÷2.8. becomes 2.46

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Martin-Gay, Basic Mathematics, 4ed 12 Dividing Decimals Dividing by a DecimalPractice Problems Step 1: Move the decimal point in the divisor to the right until the divisor is a whole number. Step 2: Move the decimal point in the dividend to the right the same number of places as the decimal point was moved in step 1. Step 3: Divide. Place the decimal point in the quotient directly over the moved decimal point in the dividend P 289 Practice Problem 4 Move decimal 1 place to the right. Do on board

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Martin-Gay, Basic Mathematics, 4ed 13 Dividing Decimals Dividing by a DecimalPractice Problems Step 1: Move the decimal point in the divisor to the right until the divisor is a whole number. Step 2: Move the decimal point in the dividend to the right the same number of places as the decimal point was moved in step 1. Step 3: Divide. Place the decimal point in the quotient directly over the moved decimal point in the dividend P 289 Move decimal 2 places to the right. Practice Problem 5 Do on board

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Martin-Gay, Basic Mathematics, 4ed 14 Dividing Decimals Dividing by a DecimalPractice Problems Step 1: Move the decimal point in the divisor to the right until the divisor is a whole number. Step 2: Move the decimal point in the dividend to the right the same number of places as the decimal point was moved in step 1. Step 3: Divide. Place the decimal point in the quotient directly over the moved decimal point in the dividend P 290 Move decimal 2 places to the right. Practice Problem 6 (round quotient to the nearest hundredth) Do on board

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Martin-Gay, Basic Mathematics, 4e 15 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Dividing by Powers Dividing Decimals by Powers of 10 such as 10, 100 or 1000 Move the decimal point of the dividend to the left the same number of places there are zeros in the power of 10.

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Martin-Gay, Basic Mathematics, 4e 16 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Example Divide. a. b. = 0.5486 Move the decimal point 3 places to the left. = 0.068 Move the decimal point 1 place to the left.

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Martin-Gay, Basic Mathematics, 4e 17 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Dividing Decimals by Powers of 10 TypeExample Dividing Decimals by Powers of 10 such as 10, 100, 1000...: Move the decimal point to the left the same number of places as there are zeros in the power of 10. Practice Problem 8 Practice Problem 9 P 291

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Martin-Gay, Basic Mathematics, 4e 18 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Solving Problems by Dividing Decimals Practice Problem 10 SOLUTION A bag of fertilizer covers 1250 square feet of lawn. Tim Parker’s lawn measures 14,800 square feet. How many bags of fertilizer does he need? If he can buy only whole bags of fertilizer, how many whole bags does he need? Tim needs 11.84 bags. P 29 Divide one more place and use that digit for rounding. Tim will need 12 whole bags. Go out 2 more places Go out only 1 more places

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Martin-Gay, Basic Mathematics, 4e 19 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Order of Operations 1. Perform all operations within parentheses ( ), brackets [ ], or other grouping symbols such as fraction bars or square roots, starting with the innermost set. 2. Evaluate any expressions with exponents. 3. Multiply or divide in order from left to right. 4. Add or subtract in order from left to right.

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Martin-Gay, Basic Mathematics, 4e 20 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Example Simplify 1.4(2 – 1.8).

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Martin-Gay, Basic Mathematics, 4e 21 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Order of Operations 1. Perform all operations within parentheses ( ), brackets [ ], or other grouping symbols such as fraction bars or square roots. 2. Evaluate any expressions with exponents. 3. Multiply or divide in order from left to right. 4. Add or subtract in order from left to right. Practice Problem 11 SOLUTION P 292 Simplifying Expressions with Decimals

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Martin-Gay, Basic Mathematics, 4e 22 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Simplifying Expressions with Decimals Order of Operations 1. Perform all operations within parentheses ( ), brackets [ ], or other grouping symbols such as fraction bars or square roots. 2. Evaluate any expressions with exponents. 3. Multiply or divide in order from left to right. 4. Add or subtract in order from left to right. Practice Problem 12 SOLUTION P 292

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Martin-Gay, Basic Mathematics, 4e 23 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Simplifying Expressions with Decimals Order of Operations 1. Perform all operations within parentheses ( ), brackets [ ], or other grouping symbols such as fraction bars or square roots. 2. Evaluate any expressions with exponents. 3. Multiply or divide in order from left to right. 4. Add or subtract in order from left to right. Practice Problem 13 SOLUTION P 292

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Martin-Gay, Basic Mathematics, 4e 24 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. DONE

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Martin-Gay, Basic Mathematics, 4e 25 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Estimating When Dividing Decimals Example: Divide: 0.54÷12. Then estimate to whether the proposed result is reasonable. Exact Estimate The estimate is 0.05, so 0.045 is reasonable.

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