1. Welcome to KU 122 Unit 2 Seminar Louisa Fordyce E-mail: lfordyce@kaplan.edulfordyce@kaplan.edu IM User ID: lrfordyce Office Hours by appointment with 24-hour notice Tech Support: 866-522-7747 Option 2, then Option 0 1

2. PEMDAS Order of operations: Parentheses, Exponents, Multiply, Divide, Add and Subtract When you see problems that have parentheses, exponents, or multiplication and division, they must be solved using the order of operations called PEMDAS 2

3. First How to solve Solve using order of operation: 120 – 3 2 * 4 ÷ (5*4 – 4*6) Start with the parentheses (5*4 – 4*6) 5*4 = 20 (20 – 4*6) 4*6 = 24 (20-24) = -4 Here is what will cause some problems: the 4 is a minus 4 or -4 3

4. 120 – 3 2 * 4 ÷ -4 We’ve taken care of the ( ) so the next step is exponents. 3 2 = 3 squared or 3 * 3 3 2 = 9 120 – 9 * 4 ÷ -4 4

5. The next step is to multiply. The multiply symbol is between the 9 and 4, so multiply those two numbers. 9*4 = 36 120 – 36 ÷ -4 5

6. Next is to divide. The division symbol is between the -36 and -4, so 36 divided by 4 = 9. Class, who knows what happens if you divide two negative numbers? 6

7. If we divide or multiply two numbers that are negative, then the result is a positive. -2 * -2 = +4 -6 ÷ -2 = +3 So -36 ÷ -4 = +9. 120 – 36 ÷ -4 now is written as 120 + 9 The final answer is 129. 7

8. 120 – 3 2 * 4 ÷ (5*4 – 4*6) The numbers inside the ( ) become -4 120 – 3 2 * 4 ÷ -4 3 2 becomes 9 120 – 9 * 4 ÷ -4 120 – 36 ÷ -4 The next step is to divide -36 ÷ -4 120 + 9 = 129, final answer 8

9. Identify the numerator and denominator. 9 < Numerator <Denominator The top number is the numerator. The bottom number is the denominator.

10. Multiplying fractions Multiply the top numbers 6*5 =30 * Multiply the bottom numbers 2*3 =6 Can this fraction be reduced or simplified? (Hint: yes.) 10

11. Reducing “even numbers” “Even numbers” are divisible by 2 can be reduced by dividing both the top and the bottom by 2: 30 ÷ 2 = 15 6 ÷ 2 = 3 We now have Class, can this be reduced or simplified further? 11

12. Yes! 15 and 3 are both divisible by 3. = = 5 (whole numbers can be represented as the number over 1) So when multiplying fractions, multiply across the top, multiply across the bottom, and then reduce if required. 12

13. What if the directions tell you not to simplify? For example, the answer to a problem is We know that can be reduced to But if the directions say do not simplify or do not reduce, leave it as the larger figure. 13

14. Some fractions can’t be reduced. All of these are prime numbers. Class, who knows what a prime number is? 14

15. Prime Numbers Prime numbers can only be divided evenly by 1 and the number itself. 11 is a prime number; it can only be divided by 11 and 1 to equal a whole number. Prime numbers are 1, 3, 5, 7, 11, 13, 17, 23, 29, 31, 37, 43, 47, 53 and so on. 15

16. Rules for dividing fractions Invert second fraction. Multiply across the top (the numerators) Multiply across the bottom (the denominators) Reduce or simplify if possible. Do not simplify if the directions say not to simplify. 16

17. Dividing fractions Dividing fractions is pretty simple. ÷ First, flip or invert the SECOND fraction. Second, change the purpose to multiplication. *Multiply across the top and then the bottom 17

18. What do we need to do to divide these two fractions? 18 ÷

19. Invert the second fraction, then change the function to multiplication 19 ÷ x Multiply across the numerators Multiply across the denominators

20. Can this be reduced? 20

21. Yes! is an improper fraction, meaning that it equals more than a whole number Both top and bottom can be divided by 3 ÷ = = 1 ¼ 21

22. It’s essential to flip or invert the second fraction. If you invert the first fraction, your result will be upside down and incorrect. 22

23. 5/6 ÷ 2/3 = 5/6 * 3/2 = 15/12 = 5/4 = 1 ¼ If you invert the first fraction, 6/5 * 2/3 = 12/15 = 4/5, which isn’t the right answer. 23

24. Dividing a fraction and a whole number First thing to remember: a whole number is actually the number presented as a fraction. = 6, the whole number = 42 24

25. Dividing a fraction and a whole number 6 ÷ = ÷ = * = ? 25

26. = 9 26

27. If the second number is a whole number, you need to express it as the whole number over 1. 2/3 ÷ 6 needs to be written as 2/3 ÷ 6/1 = 2/3 * 1/6 (remember to invert the second fraction) 27

28. Invert the second number and multiply 2/3 * 1/6 = 2/18 Class, can this be simplified if necessary? 28

29. Yes. 2/18 = 1/9 29

30. Adding Fractions First, the denominators or bottoms of both fractions must be the same number. 1/6 + 4/6 = 5/6 JUST ADD THE NUMERATORS, THE TOP NUMBERS. DO NOT ADD THE DENOMINATORS, THE BOTTOM NUMBERS. 30

31. If the fractions are not in the same form, you need to make them match. 1/6 + 2/3 Convert the 2/3 to 4/6 2/3 + 4/6 = 6/6 Can this be simplified? 31

32. Yes. 6/6 = 1 32

33. Determining parts of the whole. One type of problem on the quiz shows a figure with parts shaded. You need to determine what portion of the figure is shaded. The circle is divided into how many sections? 33

34. 34 It is divided into 8 sections. How many of those sections are shaded bright pink?

35. 35 Three of the sections are shaded bright pink. Three of the eight sections are shaded. Class, what portion of the circle is shaded, as expressed as a fraction?

36. 36 Three of the eight sections are shaded, so the answer is 3/8.