Kinds of proportion

proportion,direct,inverse,partitive

1. KINDS OF PROPORTION

2. Direct Proportion Inverse Proportion Partitative Proportion

3. DIRECT PROPORTION If an increase in quantity results to an increase in another, then the two quantities are in direct proportion. This holds true if a decrease in one quantity results to a decrease in another quantity.

4. Examples: Score to Rating Number of kilos of rice to the amount that you will pay Your body size to the size of your uniform Number of kilometres you travelled to the number of your fare

5. SAMPLE PROBLEMS 1. When Mrs. Cruz went to abroad for an educational tour, she noticed that each guide goes along with three tourists. If there are 4 guides, how many tourists would they bring around?

6. Solution: Given: 1 guide for 3 tourists Solution: guide:tourists = guide:tourists 1 : 3 = 4 : N N = 4 X 3 N = 12 Answer: 12 tourists

7. SAMPLE PROBLEMS 2. The exchange rate of peso to a dollar in 2015 is ₱45.00 to $1. How much will you get for $6.50?

8. Solution: Given: ₱ 45.00 to $1 Solution: dollar:peso = dollar:peso 1 : 45 = 6.50 : N N = 45 x 6.50 N = 292.50 Answer: ₱ 292.50

9. SAMPLE PROBLEMS 3. For every 3 metres of bamboo sticks, 5 frames of Christmas lanterns can be made. How many metres are needed to make 20 frames?

10. Solution: Given: 3 metres to 5 frames Solution: metres:frames = metres: frames 3 : 5 = N : 20 N =(20 X 3) ÷ 5 N = 60 ÷ 5 N = 12 Answer: 12 metres

11. INVERSE PROPORTION If an increase in quantity results to a decrease in another, then the two quantities are in inverse proportion. This holds true if a decrease in one quantity results to a increase in another quantity.

12. SAMPLE PROBLEMS 1. Three men can complete a project in 3 weeks. How many men will be needed if the project is to be completed in a week?

13. Solution: Given: 3 men in 3 weeks Solution: more men:less men = more weeks: less week N : 3 = 3 : 1 N =( 3 X 3) ÷ 1 N = 9 ÷ 1 N = 9 Answer: 9 men are needed to complete the project.

14. SAMPLE PROBLEMS 2. Twenty men can paint a building in 15 days. How many days will it take 30 men to paint the same building?

15. Solution: Given: 20 men in 15 days Solution: more men:less men = more days: less days 30 : 20 = 15 : N N =(20 X 15) ÷ 30 N = 300 ÷ 30 N = 10 Answer: 10 days

16. SAMPLE PROBLEMS 3 . Five pipes can fill a tank in 2 hours. In how many hours can 1 pipe fill the same tank?

17. Solution: Given: 5 pipes in 2 hours Solution: more pipes:less pipes = more hours: less hours 5 : 1 = N : 2 N =(2 x 5) ÷ 1 N = 10 ÷ 1 N = 10 Answer: 10 hours

18. PARTITATIVE PROPORTION If a given whole is to be divided into several parts given a specified ratio, partitative proportion is used.

19. SAMPLE PROBLEMS 1 . Divide 100 in to parts 2:3:5.

20. Solution: Given: 100 into parts 2:3:5 Solution : 2 units + 3 units + 5 units = 10 units 1 unit = 100 ÷ 10 1 unit = 10 Therefore, 10 x 2 units = 20 10 x 3 units = 30 10 x 5 units = 50 Answer: 20, 30 and 50

21. SAMPLE PROBLEMS 2 . Ruby, Rose and Ann are business partners. They agreed to divide their profits in the ratio 1:2:3. How much should each receive if the total profit is ₱6000?

22. Solution: Given: ₱6000 into parts 1:2:3 Solution : 1 unit + 2 units + 3 units = 6 units 1 unit = 6000 ÷ 6 1 unit = 1000 Therefore, 1000 x 1 unit = 1000 1000 x 2 units = 2000 1000 x 3 units = 3000 Answer: Ruby( ₱1000), Rose( ₱2000), Ann (₱3000)

23. SAMPLE PROBLEMS 3. Divide a 72-m rope into 3 with the ratio 1:2:5. What is the measure of each rope?

24. Solution: Given: 72-m rope in the ratio 1:2:5 Solution : 1 unit + 2 units + 5 units = 8 units 1 unit = 72 ÷ 8 1 unit = 9 Therefore, 9 x 1 unit = 9 9 x 2 units = 18 9 x 5 units = 45 Answer : 9m, 18m, 45m