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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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