1. C EXPONENTS, ORDER OF OPERATIONS, AND AVERAGE Math081 Catherine Conway

2. Exponents Definition: An exponent is a whole number that indicates how many times the base is to be used as a factor. Exponents indicate repeated multiplication. 3 4 = 3· 3· 3· 3 base exponent Expanded form Definition: Any number other than 0 raised to the 0 power is 1. That is, if a represents any nonzero number, then it is always true that a 0 = 1

3. Practice: Pg 79 #10, 13, 17, 21 #10: Name the base and exponent for 0 4. #13: Simplify 2 3. #17: Simplify 9 0. #21: Simplify 10 1. Base is 0 and exponent is 4 2 3 = 8 9 0 = 1 10 1 = 10

4. Order of Operation When evaluating mathematical expressions, a certain order must be followed when simplifying. 1.If the expression contains grouping symbols, such as ( ), [ ], or a fraction bar, then perform the operation inside the grouping or above and below the fraction bar. 2.Then evaluate, or simplify, any numbers with exponents. 3.Then do all multiplications and divisions in order from left to right. 4.Finally, do all additions and subtractions from left to right.

5. Order of Operation – PEMDAS 1.If the expression contains grouping symbols, such as ( ), [ ], or a fraction bar, then perform the operation inside the grouping or above and below the fraction bar. 2.Then evaluate, or simplify, any numbers with exponents. 3.Then do all multiplications and divisions in order from left to right. 4.Finally, do all additions and subtractions from left to right. P E M or D A or S P lease - E xcuse - M y - D ear - A unt - S ally

6. Simplify: 8 x 5 – 3 x 6 8 x 5 – 3 x 6 40 – 18 22 Multiply (from left to right) Subtract PEMDA S

7. Simplify: 40 – 3(6 + 1) 40 – 3(7) 40 – 21 19 Multiply Subtract PEMDA S 40 – 3(6 + 1) Parentheses – perform operation inside (addition)

8. Simplify: 72 ÷ 3 2 – 5 + 2· 1 2 72 ÷ 9 – 5 + 2· 1 8 – 5 + 2 3 + 2 Divide and Multiply Subtract P EMDA S 72 ÷ 3 2 – 5 + 2· 1 2 Exponents 5 Add

9. Simplify: 5 + 2[12 – 4(9 – 7)] 5 + 2[12 – 4(2)] 5 + 2[4] 5 + 8 Parenthese 2 (multiply then subtract) Multiply P EMDA S 5 + 2[12 – 4(9 – 7)] Parentheses 1 (subtract) 13 Add

10. Average – descriptive statistics Mean : The average (arithmetic mean) for a set of data values. To find the mean, add all the numbers and then divide the sum by the number of numbers in the set. Median : The middle values for a set of data listed from smallest to greatest. If there is an odd number of numbers, the median is the middle value. If there is an even number of numbers, the median is the average of the two numbers in the middle. Mode : The number that occurs the most often. ( can be more than 1 mode ) If all the numbers in the set occur the same number of times, there is no mode. If two or more numbers have the same number of occurrence, then the mode will be those numbers. Range : The difference between the largest number and the smallest number within a set of data.

11. Example: 778765798785 799493 755695 56 + 65 + 75 + 77 + 79 + 79 + 85 + 87 + 87 + 93 + 94 + 95 12 = 81 (mean) 79 + 85 2 = 82 (median) 79, 87 (mode) 95 – 56 = 39 (range)

12. Pg. 79 #43, 47, 56, 58, 70, 73 12,768 57 12 416 66 7

13. Pg. 80 #86, 87, 90, 91, 93, 94 For 86 and 87, find mean and range #86: 2, 4, 6, 8, 10 #87: 1, 3, 9, 11 For 90 and 91, find median and range #90: 42, 48, 50, 64 #91: 10, 20, 50, 90, 100 For 93 and 94, find mode and range #93: 14, 18, 27, 36, 18, 73 #94: 11, 27, 18, 11, 72, 11 6 and 8 6 and 10 49 and 22 50 and 90 18 and 59 11 and 61