Direct ProportionInverse ProportionPartitative

•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.

Examples:

Score to Rating Number of kilos of rice to the amount that you will pay Your body size to the size of your uniformNumber of kilometres you travelled to the number of your fare

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?

Solution:Given: 1 guide for 3 touristsSolution:

guide:tourists = guide:tourists1 : 3 = 4 : N

N = 4 X 3N = 12

Answer: 12 tourists

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?

Solution:Given: ₱ 45.00 to $1Solution:

dollar:peso = dollar:peso1 : 45 = 6.50 : N

N = 45 x 6.50N = 292.50

Answer: ₱ 292.50

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?

Solution:Given: 3 metres to 5 framesSolution:

metres:frames = metres: frames3 : 5 = N : 20

N =(20 X 3) ÷ 5N = 60 ÷ 5N = 12

Answer: 12 metres

•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.

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?

Solution:Given: 3 men in 3 weeksSolution:

more men:less men = more weeks: less weekN : 3 = 3 : 1

N =(3 X 3) ÷ 1N = 9 ÷ 1N = 9

Answer: 9 men are needed to complete the project.

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

Solution:Given: 20 men in 15 daysSolution:

more men:less men = more days: less days30 : 20 = 15 : N

N =(20 X 15) ÷ 30N = 300 ÷ 30N = 10

Answer: 10 days

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

Solution:Given: 5 pipes in 2 hoursSolution:

more pipes:less pipes = more hours: less hours5 : 1 = N : 2

N =(2 x 5) ÷ 1N = 10 ÷ 1N = 10

Answer: 10 hours

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

1. Divide 100 in to parts 2:3:5.

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

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?

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)

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

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