Ratio & proportion
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The document discusses ratios, proportions, and scale drawings. It begins by defining a ratio as a comparison of two or more quantities without units. Ratios can be written in different forms such as a:b or a to b. A proportion is an equation stating that one ratio is equal to another. Direct proportion means that as one quantity increases, the other also increases by the same factor. Inverse proportion means that as one quantity increases, the other decreases. Scale drawings use a scale ratio to show the relationship between an object's depicted size and its actual size. Examples are provided to demonstrate calculating ratios, proportions, direct and inverse proportions, and using scale ratios.
Ratio & proportion
- 2. DO NOW (not later): • Compare the number of boys to girls in the class.
- 3. • The number of boys = • The number of girls = • If we compare boys to girls we get ___ boys to _____ girls.
- 4. What do we call a comparison between two or more quantities? We just found the RATIO RATIO of boys to girls. Is the ratio of girls to boys the same ? No, when writing a ratio, ORDER matters.
- 5. AIM: What is a ratio?
- 6. DEFINITION OF RATIO A ratio is the comparison of two or more numbers (quantities). A ratio has no units
- 7. Which ratio shows the ratio of 3 butterflies to 1 apple?
- 8. Three Ways to write a Ratio
- 9. Three ways to write a ratio •
- 10. Write A Ratio Rewrite into a ratio : a) 15 metre to 2 km 15 m : 2 km ( ratio no units, and km change to m ) 15 : 2000 ( write into simplest form ) 3 : 400 b) 135 seconds : 1.5 minutes ( minute change to second ) 135 : 90 ( write into simplest form ) 3:2
- 11. Write A Ratio If P : Q = 3 : 5, and Q : R = 2 : 1, find the ratio P : R ! P : Q : R (1) 3 : 5 (2) 2 : 1 The value of Q are 5 and 2. So, we need to make it equal . Find LCM of 2 and 5 ! It is 10 Ratio becomes : P : Q : R (1) 6 : 10 (2) 10 : 5 So, the ratio of P : R = 6 : 5
- 12. WRITE A RATIO In a new car dealer’s lot, there were 23 silver, 18 white, 2 maroon, 8 red, and 12 blue vehicles. Write the ratio of silver vehicles to total vehicles. silver 23 total 63 Write the ratio of white to blue vehicles. white 18 3 blue 12 2
- 13. Decrease and Increase in Ratio If the number of teachers in a college is increased from 50 to 60. Then the ratio of new staff and old staff is : Numbers of new staff Number of old staff 60 50 6 5 We say that, number of teachers has been increased in ratio 6 : 5
- 14. RULE TO INCREASE OR DECREASE Improper fraction Proper fraction
- 15. PROPORTION
- 16. Definition of Proportion • A proportion is an equation that says one ratio is equal to another. 3 39 ratio = ratio 4 52
- 17. DIRECT PROPORTION Two quantities x and y are said to be in direct proportion if they increase (decrease) together in such a manner that the ratio of their corresponding values remains constant.
- 18. Understanding Direct Proportion Question : Price of 8 oranges Rp 2600. What is the price of 6 oranges ? based on units Calculation Price 8 oranges = Rp 2600 Price 1 orange = Rp 2600 : 8 = Rp 325 Price 6 oranges = 6 x Rp 325 = Rp 1950
- 19. Understanding Direct Proportion Price of 8 oranges Rp 2600. What is the price of 6 oranges ? Calculation Based on ratio Number of oranges Price ( Rp ) 8 2600 6 X
- 20. Understanding Direct Proportion If you drive 90 miles in 2.5 hrs, how long should it take for you to complete the final 200 miles of a trip? mile hour 90 2,5 200 X
- 21. Understanding Direct Proportion Six identical CNC machines can produce 768 pistons in one day. If two of the CNC machines break down, how many pistons can be produced in a day? Piston Machine 6 768 4 X
- 22. INVERSE PROPORTION In the inverse proportion, if the quantity x increases, the quantity y decreases, or when the quantity x decreases, the quantity y increases.
- 23. Understanding Inverse Proportion Some candies are distributed to 15 kids and each kid gets 4 candies. If there are only 12 kids, how many candies does each kid get Calculation based on the result of multiplication. Kid candy 15 4 12 C 15 x 4 = 12 x C 60 = 12 C C = 5 candies
- 24. Understanding Inverse Proportion 4 employees can complete a basic auto interior restoration in 6 work days. If only two employees are available for a similar project, how long will it take? Employee day 4 6 2 D 4x6 =2xD 24 =2D C = 12 days
- 25. Understanding Inverse Proportion 6 childrens need 30 minutes time to tidy up the books in their schools library. How many children must be added so that the job could be done in 20 minutes? Children Minute 6 30 X 20 6 . 30 = X . 20 Children must be added 180 = 20 X : X = 9 childrens 9 – 6 = 3 students
- 27. P S R P = Picture ( size on picture/map) S = Scale ( in Ratio ) R = Real ( the real size of that object)
- 28. Example •
- 30. EXERCISE 39 PAGE 63 - 64