1. Welcome to this IRSC Adult Education Live Virtual Lesson Diana Lenartiene, Ed. S. moderator/instructor

2. Elluminate Meeting/Classroom 2 Introducing… your virtual classroom 6/10/2008; updated: 10/3/11

3. Emoticons Respond to poll Chat Adjust volume

4. 6/10/2008; updated: 10/3/11Elluminate Meeting/Classroom 4

5. 6/10/2008; updated: 8/4/2009Elluminate Meeting/Classroom 5

6. 6/10/2008; updated: 8/4/2009Elluminate Meeting/Classroom 6

7. Ratios We will now view a video on Ratio

8. Ratios A ratio is a comparison between two numbers by division. It can be written in three different ways: 5 to 2 5 : 2 5 2

9. Equal Ratios When two ratios name the same number, they are equal. It ’ s like writing an equivalent fraction. 20 : 30 Equal Ratios: 10 : 15 2 : 3 80 : 120

10. Ratios in Simplest Form Ratios can be written in simplest form. Divide both terms in the ratio by their GCF. Example: 12 to 8 3 to 2 12/8 = 3/2 We have reduced the fraction to lowest terms. To do that, we divided the numerator and denominator by 4.

11. Understanding Proportions We will now watch a video on proportion

12. Vocabulary A proportion is an equation stating that two ratios are equal. To prove that two ratios form a proportion, you must prove that they are equivalent. To do this, you must demonstrate that the relationship between numerators is the same as the relationship between denominators.

13. Examples: Do the ratios form a proportion?, 7 10 21 30 x 3 Yes, these two ratios DO form a proportion, because the same relationship exists in both the numerators and denominators. 8 9, 2 3 ÷ 4 ÷ 3 No, these ratios do NOT form a proportion, because the ratios are not equal.

14. Completing a Proportion Determine the relationship between two numerators or two denominators (depending on what you have). Execute that same operation to find the part you are missing.

15. Example: Cross multiply to see if they are equal! 3= 7 4 8 Multiply 3 x 8 = 24 Multiply 4 x 7 = 28 These ratios are NOT a proportion! Why? Because they were not equal

16. Using Cross Products

17. Cross Products When you have a proportion (two equal ratios), then you have equivalent cross products. Find the cross product by multiplying the denominator of each ratio by the numerator of the other ratio.

18. Example: Do the ratios form a proportion? Check using cross products. 4 12, 3 9 12 x 3 = 36 9 x 4 = 36 These two ratios DO form a proportion because their cross products are the same.

19. Example 2 5 8, 2 3 8 x 2 = 16 3 x 5 = 15 No, these two ratios DO NOT form a proportion, because their cross products are different.

20. Solving a Proportion Using Cross Products Use the cross products to create an equation. Solve the equation for the variable using the inverse operation.

21. Example: Solve the Proportion k 17 = 20 68 Start with the variable. =68 K 17(20) Simplify. =340 Now we have an equation. To get the k by itself, divide both sides by 68. k = 5 68 K 68

22. We will now view a video showing how to Set up and solve word problems using the Proportion formula.

23.  A ratio shows the relation ship of tow things as a Fraction.  A proportion is a statement that two ratios are equal  Proportions allow us to solve problems by using the Proportion formula.  We can set up proportions to solve real world math Problems.

24. Now, you need to make a copy of this screen to send to your teacher for proof of Attendance. This can be done in three easy steps:

27. Thank you for viewing this presentation. Diana Lenartiene, IRSC ABE Instructor If you still have questions, please contact me at: dlenarti@irsc.edu