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.