1. KU122: Introduction to Math Skills and Strategies Kirsten Muller, M. A., M. Ed. Unit 2 Seminar

2. Fraction Notation 2.1Fraction Notation and Simplifying 2.2Multiplication and Division 2.3Addition and Subtraction; Order 2.4Mixed Numerals 2.5Applications and Problem Solving 2.6Order of Operations; Estimation Slide 2/35 2 CHAPTER

3. Fraction Notation and Simplifying Identify the numerator and the denominator of a fraction and write fraction notation for part of an object. Simplify fraction notation like n/n to 1, 0/n to 0, and n/1 to n. Multiply a fraction by a fraction. Use multiplying by 1 to find different fraction notation for a number. Simplify fraction notation. 2.a b c d e

4. A Objective A Identify the numerator and the denominator of a fraction and write fraction notation for part of an object. Slide 4/35

5. The following are some examples of fractions: This way of writing number names is called fraction notation. The top number is called the numerator and the bottom number is called the denominator. Slide 5/35

6. Example What part of the circle is shaded? Solution The object is divided into 8 equal parts. 3 of the parts are shaded of the circle is shaded. Slide 6/35

7. Example C What part is shaded? Solution Each cylinder is divided into 2 equal parts. The unit is ½. The denominator is 2. We have 5 of the units shaded. ells us the numerator is 5. is shaded Slide 2- 7

8. Example D Simplify. Solution Slide 8/35

9. The Number 0 in Fraction Notation for any whole number n that is not 0. Slide 9/35

10. Example Simplify. Solution Slide 2- 10

11. A Denominator of 0 is not defined for any whole number n. Slide 11/35

12. Any Whole Number In Fraction Notation Any whole number divided by 1 is the whole number. That is, for any whole number n. Slide 12/35

13. Example F Simplify. Solution Slide 13/35

14. To multiply a fraction by a fraction, a) Multiply the numerators to get a new numerator, and b) Multiply the denominators to get the new denominator. Slide 14/35

15. Example Multiply. Solution: Slide 2- 15

16. Objective Multiply a fraction by a fraction. Slide 17/35c

17. To multiply a fraction by a fraction, a) Multiply the numerators to get a new numerator, and b) Multiply the denominators to get the new denominator. Slide 2- 17

18. Example Solution: Slide 18/35

19. Example Find a name for with a denominator of 36. Solution Since 9 × 4 = 36, we multiply by : Slide 20/35

20. Example Find a name for with a denominator of 48. Solution Since 12 × 4 = 48, we multiply by : Slide 21/35

21. Example Simplify. 1. 2. 3. 1. 2. 3. Slide 2- 21 The number 1 allows for pairing of factors in the numerator and the denominator.

22. Example Simplify: Solution The fraction is not simplified since common factors remain in the numerator and denominator. To find the 42, we divided 210 by 5. To find the 49, we divided 245 by 5. To find the 6, we divided 42 by 7. To find the 7, we divided 49 by 7.

23. Multiplication and Division Multiply and simplify using fraction notation. Find the reciprocal of a number. Divide and simplify using fraction notation. Solve equations of the type a · x = b and x · a = b, where a and b may be fractions. 2.a b c d

24. Objective D Multiplying by 1. Slide 25/35

25. Slide 26/35 Reciprocals If the product of two numbers is 1, we say that they are reciprocals of each other. To find the reciprocal of a fraction, interchange the numerator and denominator. Number  Reciprocal

26. Example C Find the reciprocal. 1. 2.3.4. Solution 1. The reciprocal of is 2. The reciprocal of is 3. The reciprocal of is 4. The reciprocal of is Slide 2- 26

27. Slide 28/35 0 Has No Reciprocal The number 0, or has no reciprocal. (Recall that is not defined.)

28. Objective C Divide and simplify using fraction notation. Slide 2- 28

29. Slide 2- 29 To divide fractions, multiply the dividend by the reciprocal of the divisor. Multiply by the reciprocal of the divisor.

30. Example D Divide and simplify. Solution Slide 31/35

31. Example E Divide and simplify. Solution Slide 31/35

32. MML Quizzes You have to take your quizzes using MML. You only have 12 hours to take them (but they will NOT take 12 hours to complete). Just don’t start taking it until you are ready. Do the tutorials, read the chapter, and do the practice problems before you start the quiz.

33. My Math Lab (MML) You need to log into the MML to get registered before you can start taking any quizzes or viewing the tutorials. Please do so as soon as possible. For more information on using the MML, look at the MML Resources area under Course Home on the class website.

34. Unit 2 Assignments The following assignments are due by 11:59pm ET on Tuesday: 1.) Live seminar 2.) Discussion Board 3.) Practice Problems 4.) MML Ungraded Tutorials 5.) MML Quiz