Mathematics 6 Quarter 2 Week 2 FINAL

LILOY II DISTRICT
MATHEMATICS VI
LEARNING ACTIVITY SHEET
QUARTER 2 WEEK 2
NAME:_________________________________________________________________GRADE/SECTION:_________________
SCHOOL: _______________________________________________________________ DATE: __________________________
Finding the Missing Term in a Proportion and Solving Problems Involving Kinds of Proportions
(Direct, Inverse, and Partitive)
When two ratios are equal, a proportion is formed. A proportion is a statement of equality between two ratios. Each part of a
proportion is a term. The first and the last terms are called extremes while the second and the third terms are called means. In the
proportion 2 : 3 = 4 : 6 , where 3 and 4 are called the means , and where 2 and 6 are the extremes. The product of the means must
be equal to the product of the extremes, in order to say that two ratios are equal or it is a proportion.
There are three types of proportion:

1. Direct proportion, when one quantity increases ,the other quantity increases at the same rate and vice versa.
 The product of the means should be equal to the product of the extremes or the cross products should be equal. Wherein first and
third term are the same quantities, while second term andfourth term are of the same quantities.
2. Inverse or indirect proportion, when one quantity increases, the other quantity decreases , and vice versa.
 The product of the means should be equal to the product ofthe extremes or the cross products should be equal but you must
follow this set-up :
3. Partitive proportion, a whole is divided into parts that is proportional to the given ratio
 First add the quantities in the ratio, Second divide the sum by the whole number, Third multiply the quotient to each of the
quantity in the ratio.
Illustrative Examples:
1. Find the missing term in a direct proportion.
a. 2 : 3 = N : 12
Step 5. Solve for the missing term:
2. Find a missing term in an inverse proportion.

a. 2 : 4 = 9 : N
Step 1. Identify the Means: 4, 9 : Extremes: 2, N
Step 2. Multiply the Means: 4 x 9 = 36
Step 3. Multiply the Extremes: 2 x N = 2N
Step 4. Equate the Means and the Extremes: 36 = 2N or 2N = 36
Step 5. Solve for the missing term:
3. Find a missing term in a partitive proportion.

a. If 60 mangoes are divided into the ratio of 3 : 4 : N, what is N?
Step 1: Identify the known ratio: 3 , 4
Step 2: Multiply the known ratio : 3 x 4 = 12
Step 3: Make the product of the known ratios as the denominator of each ratio:
3 and 4
12 12
Step 4: Simplify each ratio:
3 1 and 4 1
12 4 12 3
Step 5: Get the exact value of each ratio from the given totality:
1 of 60 mangoes = (1 x 60) = 15 mangoes

4 4
1 of 60 mangoes = (1 x 60) = 20 mangoes
3 3
Step 6: Add the exact value of known ratios:
15 + 20 = 35 mangoes
Step 7: Subtract the sum of the exact values of the known ratios from the given totality to solve for the missing term:
60 mangoes – 35 mangoes = 25 mangoes
Step 8: Write the new values in terms of ratio:
15 : 20 : 25
Step 9: Simplify your answer by dividing the Greatest Common Factor (GCF) to each ratio to solve for the missing term
Learning competencies:
*Finding the missing ter m in a proportion either a direct proportion, inverse proportion and partitive proportion.(M6NS-IIb-133)
*Solving word problems in a proportion either a direct proportion, inverse proportion and partitive proportion. (M6NS-IIc-134)
EXERCISES: READ AND UNDERSTAND AND SOLVE. Write your answer in the space before the number
A. Solve for the following in the direct proportion.
______________1) 3 : ____ = 6 : 10
_________________2) 5 : 12 = 35 : N
______________3) 2 = N
9 81
______________4) A motorist travels 270 km in 5 hours. How far can he travel in 9 hours at the same
speed?
B. Solve for the following in an inverse or indirect proportion.
______________5) Mr. Datu has enough money to pay 8 workers for 15 days. If he adds 4 more
Workers,for how long can he pay them at the same rate?
______________6) Four farmers can plow a land in 6 days, in how many days can they finish the job if
there are 8 farmers?
______________ 7) A carpenter working 8 hours a day could finish the work in 5days. How many days
could he finish a similar piece of work by working overtime for 10 hours a day?
C. Solve for the following partitive proportion (for number 8 t0 10)
______________8) Php 90,000 incentive to be divided in a ratio of 5 : 3 : 1 How much will each
receive?
______________9)
_____________10)
ASSESSMENT: Solve the following problems below using the steps in solving problems involving proportions. Encircle the
letter of the correct answer.
1. A package promo allows 3 persons to ride on a zip line for ₱750. How much will 12 friends pay to ride on a zip line?
A. ₱2000 B. ₱3000 C. ₱4000 D. ₱5000
2. You cut a 3 m string into three parts using the ratio 1 : 2 : 3. How long will be the shortest part?
A. ½ B. 1 C. 1 ½ D. 2
3. Morie wants to donate his 200 books to three Kindergarten Schools in a 1 : 4 : 5 ratio. How many books will each Kindergarten
School receive?
A. 20:80:100 B. 30:40:50 C. 40:50:60 D. 40:50:100
4. Jason paid ₱1, 680.00 for the three “Bayanihan” painting. His brother Joshua wanted to buy 8 “Bayanihan” paintings. How
much would Joshua pay?
A. ₱2240 B. ₱3340 C. ₱4480 D. ₱5500
5. Michael wanted to go to his brother’s house which is 24 km from his house. If he drives his car with a speed of 60 kph, he will
be there in 24 minutes. If he makes his speed slower to 40 kph, how long would Michael take to reach his brother’s house?
A. 24 min. B. 28 min. C. 32 min. D. 36 min.
6. If three durian seedlings cost ₱20.00. How much is the cost for twelve durian seedlings?
A. ₱80 B. ₱100 C. ₱120 D. ₱140
7. During this pandemic the bus fare for an 80 km trip is ₱65.00. How much is the bus fare for a 320 km trip?
A. ₱260 B. ₱360 C. ₱460 D. ₱560
8. If 6 women can trim a flower garden in two days. How long will 3 women do it?
A. 4 days B. 5 days C. 10 days D. 20 days
9. A sack of food is enough to cater 10 persons for 3 days. How long will it last for 5 persons?
A. 4.5 days B. 5 days C. 5.5 days D. 6 days
10. It takes 5 sales representative for 6 days to sell 5,000 boxes of face mask. If 1 more sales representative are added, how long
will it take them? A. 2 days B. 3 days C. 4 days D. 5 days
Reflection:
1. What part of the activity do you find easy? Why? ____________________________________________
2. What part of the activity do you find difficult? Why? _________________________________________

Key answer mathematics 6 (quarter 2 week 2)
Exercises:
1. 5
2.
3. 18
4.
5. 10
6.
7. 4
8.
9. ₱ 30,000.00
10.
Assessment:
1. B
2.
3. A
4.
5. D
6.
7. A
8.
9. D
10.
Prepared by:
BEBIAN AQUE BALUCOS

Grade 6 Adviser

Mathematics 6 Quarter 2 Week 2 FINAL

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LILOY II DISTRICT

There are three types of proportion:

Step 5. Solve for the missing term:

2. Find a missing term in an inverse proportion.

3. Find a missing term in a partitive proportion.

Step 2: Multiply the known ratio : 3 x 4 = 12

1 of 60 mangoes = (1 x 60) = 15 mangoes

2. What part of the activity do you find difficult? Why? _________________________________________

BEBIAN AQUE BALUCOS

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