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

Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.

4.5

Dividing Decimals and Order of Operations

Martin-Gay, Basic Mathematics, 4e 22


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 NumberStep 1: Place the decimal point in the quotient

directly above the decimal point in the dividend.

Step 2: Divide as with whole numbers.



Dividing Decimals

Dividing by a Whole Number Example

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).

.8.112

.5

.11210

8

18

9

180



Example

Divide: 219.2÷8.

27.4 8 219.2

16

59

56

32

32

0

divisor dividend

quotient

Check: 27.4

8

219.2



Example

Divide: 0.6÷4.

0.15 4 0.60

4

20

20

0

divisor dividend

quotient

Check: 0.15

4

0.60

Martin-Gay, Basic Mathematics, 4ed 66

Dividing Decimals

Dividing by a Whole Number Practice Problems One



P 287

62.517 2.86

Practice Problem One

Do on board


Dividing Decimals

Dividing by a Whole Number

Practice Problems Two



P 287

Practice Problem Two

919.26 91.2

.19.269

2

188 1

9

8 109

1

90


Dividing Decimals

Dividing by a Whole Number Practice Problems Three



P 288

84.

05.0

Practice Problem 3a

.40.080

40

5

0

.4.08


Dividing Decimals

Dividing by a Whole Number Practice Problems Three



P 288

Practice Problem 3b

1262.13

135.1

Do on board



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.



Example

Divide: 6.888÷2.8.

becomes 2.8 6.888 28 68.88

56

128

112

168

168

0

2.46


Dividing Decimals

Dividing by a Decimal Practice 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

6.588.166

8.29 .8.166856

88.1666.5Move decimal 1 place to the right.

Do on board


Dividing Decimals





P 289

.60.19716

976.116.Move decimal 2 places to the right.

Practice Problem 5

16.0976.1

35.12Do on board


Dividing Decimals





P 290

.00.234057

40.2357.Move decimal 2 places to the right.

Practice Problem 6 (round quotient to the nearest hundredth)

57.04.23

05.41Do on board



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.



Example

Divide.

a.

b.

548.6

1000

0.68

10

= 0.5486 Move the decimal point 3 places to the left.

= 0.068 Move the decimal point 1 place to the left.



2454.3100

54.324

1283.01000

3.128

Dividing Decimals by Powers of 10

Type Example

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 9056.0

10

56.0

P 291



148001250

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?

00.148001250

84.11

Tim needs 11.84 bags.

P 29

1480012500.148001250

8.11

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



Order of Operations

Order of Operations1. 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.



Example

Simplify 1.4(2 – 1.8).

21.4( )1.8 1.4(0.2)

0.28



Order of Operations

1. Perform all operations within parentheses ( ), brackets [ ], or other grouping symbols such as fraction bars or square roots.




Practice Problem 11

SOLUTION101008.897 )10(978.8

7.89

P 292

10100897.8 :Simplify

Simplifying Expressions with Decimals




Order of Operations





Practice Problem 12

SOLUTION 8.12.369.8 )4.1(69.8

166.12

P 292

1.8-3.28.69 :Simplify




Order of Operations





Practice Problem 13

SOLUTION

P 292

02.0

101.2-20.06 :Simplify

2

02.0

101.2-20.06 2 02.0

101.44-20.06

02.0

144.-20.06

02.0

19.916 8.995



DONE



Estimating When Dividing Decimals

Example:

Divide: 0.54÷12. Then estimate to whether the proposed result is reasonable.

0.045 12 0.540

48

60

60

0

Exact Estimate 0.05 10 0.50

50

0

The estimate is 0.05, so 0.045 is reasonable.

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

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