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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: 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. Answer using mixed numbers. Simplify the following complex fractions. Find the average of the following sets of numbers. 2

Compute the following expressions. Prev Next