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# 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:

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:

Terminology
order of operations
complex fractions

Exercise Set 3.5

Compute the following exponents.

Simplify the following exponents.