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Exponents and Order of Operations;Complex Fractions
Exponents and Order of Operations; Complex Fractions
Example 5 Simplify the following complex fractions.
Solution a . Multiplying by and simplifying the resulting fraction:
multiplying by 12/12 

simplifying (cancelling)  
simplifying fractions 
b. Multiplying by 12/12 and simplifying the resulting fraction:
multiplying by 12/12  
distributive property  
simplifying fractions  
simplifying 
c. Multiplying by 12/12 and simplifying the resulting fraction:
multiplying by 12/12  
distributive property  
simplifying fractions  
multiplying  
simplifying 
d. Multiplying by
30/30
and simplifying the resulting fraction (first convert
mixed numbers to fractions ):
converting to fractions  
multiplying by 30/30  
distributive property  
simplifying fractions  
multiplying  
simplifying 
Example 6 Find the average of
Solution
Recall that the average of a group of numbers is the sum of those
numbers
divided by the amount of numbers. To find the sum of these three mixed
numbers, first add their fractional portions :
Therefore the sum is given by:
Thus, the average of the three numbers is given by the complex fraction :
computing the sum  
writing as a fraction  
multiplying by 3/3  
simplifying  
converting to mixed number 
We conclude this section with order of operations with decimals . The rules are
identical to those
with fractions and mixed numbers.
Example 7 Compute the following expressions.
Solution a. Computing using the order of operations:
multiplying decimals  
writing subtraction as addition  
adding decimals 
b. Computing using the order of operations:
subtracting decimals  
computing the exponent 
c. Computing using the order of operations:
subtracting decimals  
computing the exponent 
d. Computing using the order of operations:
writing as addition  
adding decimals  
multiplying decimals 
Terminology
order of operations
complex fractions
Exercise Set 3.5
Compute the following exponents.
Simplify the following exponents.
Compute the following expressions . Express your answers as fractions.
Compute the following expressions. Answer using mixed numbers.
Simplify the following complex fractions.
Find the average of the following sets of numbers.
2
Compute the following expressions.
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