2. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
Fraction Notation: Addition, Subtraction, and Mixed Numerals 4
4.1
Least Common Multiples
4.2
Addition, Order, and Applications
4.3
Subtraction, Equations, and Applications
4.4
Solving Equations: Using the Principles Together
4.5
Mixed Numerals
4.6
Addition and Subtraction of Mixed Numerals; Applications
4.7
Multiplication and Division of Mixed Numerals; Applications
4.8
Order of Operations and Complex Fractions
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Slide 2

3. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
4.8
Order of Operations and Complex Fractions a
Simplify expressions containing fraction notation
using the rules for order of operations. b
Simplify complex fractions. b
Simplify fraction notation like n/n to 1, 0/n to 0, and
n /1 to n.
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Slide 3

4. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
4.8
Order of Operations and Complex Fractions a
Simplify expressions containing fraction notation
using the rules for order of operations.
Like expressions containing integers, expressions containing fraction notation follow the rules for order of operations.
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Slide 4

5. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
4.8
Order of Operations and Complex Fractions
1. Do all calculations within parentheses ( ), brackets [ ] , braces { }, absolute-value symbols, numerators, or denominators.
2. Evaluate all exponential expressions.
3. Do all multiplications and divisions in order from left to right.
4. Do all additions and subtractions in order from left to right. a
Simplify expressions containing fraction notation
using the rules for order of operations.
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Slide 5

6. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
4.8
Order of Operations and Complex Fractions a
Simplify expressions containing fraction notation
using the rules for order of operations. 1
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Slide 6

7. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
4.8
Order of Operations and Complex Fractions a
Simplify expressions containing fraction notation
using the rules for order of operations. 1
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Slide 7

8. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
4.8
Order of Operations and Complex Fractions a
Simplify expressions containing fraction notation
using the rules for order of operations. 3
Simplify.
The parentheses here are not grouping symbols, so we begin by evaluating the exponential expression.
Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
Slide 8

9. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
4.8
Order of Operations and Complex Fractions a
Simplify expressions containing fraction notation
using the rules for order of operations. 3
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Slide 9

10. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
4.8
Order of Operations and Complex Fractions b
Simplify complex fractions.
A complex fraction is a fraction in which the numerator and/or denominator contain one or more fractions.
Since a fraction bar represents division, complex fractions can be rewritten using the division symbol
Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
Slide 10

11. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
4.8
Order of Operations and Complex Fractions b
Simplify complex fractions. 4
Simplify.
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Slide 11

12. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
4.8
Order of Operations and Complex Fractions b
Simplify complex fractions. 4
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Slide 12

13. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
4.8
Order of Operations and Complex Fractions b
Simplify complex fractions. 4
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Slide 13

14. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
4.8
Order of Operations and Complex Fractions b
Simplify complex fractions.
When the numerator or denominator of a complex fraction consists of more than one term, first simplify the numerator and/or denominator separately.
Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
Slide 14

15. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
4.8
Order of Operations and Complex Fractions b
Simplify complex fractions. 6
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Slide 15

16. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
4.8
Order of Operations and Complex Fractions b
Simplify complex fractions. 6
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Slide 16

17. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
4.8
Order of Operations and Complex Fractions b
Simplify complex fractions. 6
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Slide 17

18. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
4.8
Order of Operations and Complex Fractions b
Simplify complex fractions. 7
Harvesting Walnut Trees.
A woodland owner decided to harvest five walnut trees in order to improve the growing conditions of the remaining trees. The logs she sold measured
What is the average length of the logs?
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Slide 18

19. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
4.8
Order of Operations and Complex Fractions b
Simplify complex fractions. 7
Harvesting Walnut Trees.
Recall that to compute an average, we add the numbers and then divide the sum by the number of addends.
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Slide 19

20. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
4.8
Order of Operations and Complex Fractions b
Simplify complex fractions. 7
Harvesting Walnut Trees.
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Slide 20