proportion,direct,inverse,partitive

2. Direct
Proportion
Inverse
Proportion

3. •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

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

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. •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

12. 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. 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. 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. •If a given whole is to be
divided into several parts
given a specified ratio,
partitative proportion is
used.

19. 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. 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. 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