Math 84 Activity # 1 Your name: Order of Operations Goals: 1) Evaluate Real numbers with Exponents. ) Use the Order of Operations to Evaluate Expressions. ) Review Exponents and Powers of Ten Integer exponents provide a shorthand notation for representing repeated multiplication of real numbers. For example, 5 = 5 5 5 = 15, where 5 is called the base and is called the exponent or power. The power indicated the number of times we should multiply the base to itself. READ this packet don t JUST do the problems. Task 1: Evaluate Real numbers with Exponents. Evaluate each of the following expressions containing exponents and simplify. 4 a) b) 4 c) 8 Task : expression: 5+ 4 Order of Operations. Problem: Evaluate the following arithmetic a) How many operations are there in the above expression? b) What are these operations? Will it matter which operations we perform first? Well, let s observe the following solutions from two different students Student 1 Student 5+ 4 5+ 4 = 9 = 5+ 8 = 18 = 1 It appears that each of these students interpreted the expression different and as a result, they obtain two different answers. Student 1: performed the operation of addition then multiplication. 1
Student : performed the operation of multiplication then addition. Since there can be only one correct answer when performing arithmetic operation, we need to know what to do first: add, subtract, multiply or divide. The rules are called as Order of Operations c) If the correct answer to the expression 5+ 4 is 1, which student got the correct answer? d) Which operations should have done first? If we want to add two numbers first and then multiply, we use grouping symbols such as parentheses to enclose the addition and write( 5+ 4). So, e) ( 5+ 4) =? In other words, any operation in a grouping symbol should be done first. Grouping symbols can include parentheses( ), brackets[ ], and braces{ } f) Simplify: 9+ 6 ( 8 5) g) Simplify: ( 14 5) [ 9 6] If an expression has multiple grouping symbols, begin with the innermost grouping symbol and work outward. 4+ 8 h) Simplify: ( ) i) Simplify: 0 6+ ( 5 )
j) Simplify: 6 9 Note: the correct answer to (j) should be 8. Multiplication and division should be performed in order from left to right. In other words, when there are multiplication and division, you need to work from left to right, which ever appears first. Similarly, when there are addition and subtraction, you need to work from left to right, which ever appears first. k) Simplify: 9 5 ( 8 ) + 6 + 6 5+ 4 7 l) Simplify: ( ) Rules of Operations Step 1: Simplify all operations inside a grouping symbol. (If an expression has multiple grouping symbols, begin with the innermost grouping symbol and work outward). Step : Simplify all exponents, working from left to right. Step : Perform all multiplications and divisions, working from left to right. Step 4: Perform all addition and subtractions, working from left to right.
Organizational Tip: Use a SEPERATE line for every operation performed If a problem includes a fraction bar, perform all calculations above and below the fraction bar before dividing the numerator by the denominator. Simplify each of the following expressions using the order of operations m) 18 6 + o) ( ) 89 5 n) 6 4 (5 + 10 ) p) ( ) 4 + 6 14 Task : packet. Create your own problem, using at least three operations, and one set of parenthesis. Don t try to make the problem to difficult, but don t make it too easy. Perhaps use something that has stumped you in this Your problem: (Check it for above requirements and then rewrite it on scrap paper and write up a complete solution! 4
Study tip This problem can be used to help you review for an exam Your answer: Task 4: Rewrite the following in standard notation: a. 5³ b. 10⁴ c. 10³ d. ⁴ Extra Practice ( ) ( ) + 9 1 1 18 + 4 4 5 + (needs to be done on separate paper) Tool kit entry for Order of Operations (what MUST you remember from this activity)? 5