Quarter 3-W5 - Properties of Proportion.pptx

This presentation is for grade 9

1. Pulo National High School WELCOME to MATHEMATICS 9 CLASS ! Gina Acayen -Trinidad Teacher

2. LESSON TITLE : Properties of Proportion

3. Objectives: At the end of the lesson the students should be able to : applies the fundamental theorems of proportionality to solve problems involving proportions.. (M9GE-IIIf-2)

4. Fundamental Rule of Proportion If a:b= c:d, then = provided that b 0;d 0.  

5. Properties of Proportion Cross Multiplication Property If = then ad= bc provided that b 0;d 0.  

6. 2. Alternation Property A. If = then = provided that b 0;c 0; d 0. This property can be derived by multiplying both sides of the equation by . Example: = multiply by   =  

7. 2. Alternation Property B. If = then = provided that a 0;b 0;c 0 d 0, . This property can be derived by multiplying both sides of the equation by . Example: = multiply by   =  

8. 3. Inverse Property B. If = then = provided that a 0;b 0;c 0 d 0, . This property can be derived by getting the reciprocal of both ratios . Example: = getting the reciprocal =    

9. 4 . Addition Property If = then = provided that a 0;b 0;c 0 d 0, . This property can be derived by adding 1 to both sides of the equation Example: = adding 1 to both sides   =  

10. 5. Subtraction Property If = then = provided that a 0;b 0;c 0 d 0, . This property can be derived by subtracting 1 to both sides of the equation. Example: = Subtracting 1 to both sides   - = -  

11. 6. Sum Property If = = then = = = = k ; where k is a constant at proportionality and b 0;d 0 f 0, .  

12. 1.) 2:4= 8:x 2.) 2:x= x:8   Direction: Solve for x in each proportion.    

13. 1.) Find the fourth term in a proportion if the first three terms are 12, 17, and 36. Direction: Solve each problem. 2.) The length and width of a rectangular garden are in the ratio 4:3.If the length is 24 feet, what is the width?

14. A. Direction: Solve for x in each proportion. 1 .) Find the fourth term in a proportion if the first three terms are 18, 35, and 72. 2.) The length and width of a rectangular garden are in the ratio 6:3.If the length is 24 feet, what is the width?     B. Direction: Solve the following problem.

15. a.)   Determine the value/s of indicated quantities from the given proportions.

16. b.)  

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18. Direction: Solve the following. 1. Use the proportion = to complete each proportion.   1.) =   2.) =   3.) =   4.) =  

19. 2. Find the value of y in the following proportions. a.) =   b.) =   c.) =   d.) =   3. If m : n = 5 : 3, find 3m+ 4n : 6m- 2n.