© 2012 pearson prentice hall. all rights reserved 4.5 fractions, decimals, and order of operations
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© 2012 Pearson Prentice Hall. All rights reserved
4.5
Fractions, Decimals, and Order of Operations
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Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
To write a fraction as a decimal, divide the numerator by the denominator.
Writing Fractions as Decimals
3 = 3 4 = 0.754
2 = 2 5 = 0.405
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Write as a decimal.
Write the fractional partonly as a decimal.
Thus
Example
0.187516 3.0000
16
140
128
120
112
80
80
0
33
16
33 3.1875
16
44
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Write as a decimal.
Write 2/5 as an equivalent fraction with a denominator of 10.
Example
2
5
2 2 2 40.4
5 5 2 10
55
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Comparing Fractions and Decimals
To compare decimals and fractions, write the fraction as an equivalent decimal.
Compare 0.125 and .14
1 = 0.254
Therefore, 0.125 < 0.25
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Example
Insert <, >, or = to form a true statement.
Write 7/8 as a decimal and compare.
70.87
80.875
8 7.000
64
60
56
40
40
0
0.87 0.875
0.87 0< .875
< 7
0.87 8
77
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Order of Operations
1. Perform all operations within parentheses ( ), brackets [ ], or other grouping symbols such as fraction bars, 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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Example
Simplify 1.4(2 – 1.8).
21.4( )1.8 1.4(0.2)
0.28
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Example
Simplify 25.68 (0.9) 100
0.2
2 25.68 (0.9) 100 5.68 ( ) 100
0.2 0.25.68 0.81 100
0.25.68 0.0081
0.25.68
0.9
81
0.228.4405
1010
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Using the Order of Operations
Simplify ( – 2.3)2 + 4.1(2.2 + 3.1)
Simplify inside parentheses.
( – 2.3)2 + 4.1(2.2 + 3.1) = ( – 2.3)2 + 4.1(5.3)
= 5.29 + 4.1(5.3) Write ( – 2.3)2 as 5.29.
= 5.29 + 21.73 Multiply.
= 27.02 Add.
1111
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Finding the Area of a Triangle
base
height
AA basebase • • heightheight==11
22
AA bhbh==1
2
1212
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Finding the Area of a Triangle
base = 9. 4 feet
height = 8 feet
AA basebase • • heightheight==11
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19.4 8
20.5 9.4 8
37.6 square feet
A
A
A
1313
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Using Decimals as Replacement Values
Evaluate 3 4 for 3.7x x
3 4 3( ) 4
11.
3.7
1 4
7.1
x