Post on 17-Dec-2015
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
4.5
Dividing Decimals and Order of Operations
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 NumberStep 1: Place the decimal point in the quotient
directly above the decimal point in the dividend.
Step 2: Divide as with whole numbers.
Martin-Gay, Basic Mathematics, 4e 33
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
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
Martin-Gay, Basic Mathematics, 4e 44
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
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
Martin-Gay, Basic Mathematics, 4e 55
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
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
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
62.517 2.86
Practice Problem One
Do on board
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
919.26 91.2
.19.269
2
188 1
9
8 109
1
90
Martin-Gay, Basic Mathematics, 4ed 88
Dividing Decimals
Dividing by a Whole Number Practice 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
84.
05.0
Practice Problem 3a
.40.080
40
5
0
.4.08
Martin-Gay, Basic Mathematics, 4ed 99
Dividing Decimals
Dividing by a Whole Number Practice 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
1262.13
135.1
Do on board
Martin-Gay, Basic Mathematics, 4e 1010
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.
Martin-Gay, Basic Mathematics, 4e 1111
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Example
Divide: 6.888÷2.8.
becomes 2.8 6.888 28 68.88
56
128
112
168
168
0
2.46
Martin-Gay, Basic Mathematics, 4ed 1212
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
Martin-Gay, Basic Mathematics, 4ed 1313
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
.60.19716
976.116.Move decimal 2 places to the right.
Practice Problem 5
16.0976.1
35.12Do on board
Martin-Gay, Basic Mathematics, 4ed 1414
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 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
Martin-Gay, Basic Mathematics, 4e 1515
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.
Martin-Gay, Basic Mathematics, 4e 1616
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
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.
Martin-Gay, Basic Mathematics, 4e 1717
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
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
Martin-Gay, Basic Mathematics, 4e 1818
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
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
Martin-Gay, Basic Mathematics, 4e 1919
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
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.
Martin-Gay, Basic Mathematics, 4e 2020
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Example
Simplify 1.4(2 – 1.8).
21.4( )1.8 1.4(0.2)
0.28
Martin-Gay, Basic Mathematics, 4e 2121
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
SOLUTION101008.897 )10(978.8
7.89
P 292
10100897.8 :Simplify
Simplifying Expressions with Decimals
Martin-Gay, Basic Mathematics, 4e 2222
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 8.12.369.8 )4.1(69.8
166.12
P 292
1.8-3.28.69 :Simplify
Martin-Gay, Basic Mathematics, 4e 2323
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
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
Martin-Gay, Basic Mathematics, 4e 2424
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
DONE
Martin-Gay, Basic Mathematics, 4e 2525
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.
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.