- The document discusses ratios, proportions, and solving word problems involving direct and partitive proportions. - It provides examples of setting up proportions to find missing terms in ratios and solving word problems involving sales, transportation rates, and other direct comparisons. - Students are asked to practice setting up and solving various word problems that can be modeled using direct and partitive proportions.

3. Forming ratio and
proportion using
colon (:) and
fractions in writing
ratios and
proportions

4. OBJECTIVE
The learner forms ratio and proportion using
colon (:) and fractions in writing ratios and
proportions.

5. READING DRILL:
CALLA LILY
The stately flowers that are commonly used for
decorating the church during weddings are the calla
lilies. Calla lilies are also called Baguio lilies because
they grow abundantly there.
Calla lilies grow singly on long slender stalks.
They may either be yellow or white. They are made
into bridal bouquets or even wreaths.

6. KING BACK
L
What are the different ways
in writing ratios?

7. PROBLEM OPENER
Ronald bought 3 pencils for 10 at Ellen’s School
Supply Store. Ruby bought 6 pencils for 20. Give
the ratio of pencils to the amount of money of
each child.

8. EXERCISE 1
Give the ratio of each of the following orally.
boy scouts to
girl scouts

9. EXERCISE 1
Give the ratio of each of the following orally.
spoon to
fork

10. EXERCISE 1
Give the ratio of each of the following orally.
pebbles to
dice

11. EXERCISE 1
Give the ratio of each of the following orally.
glasses to
mugs

12. EXERCISE 1
Give the ratio of each of the following orally.
trees to
fruits

13. EXERCISE 2
Find the ratio/proportion of the following. Use 2 different
ways in writing them.
1.) Andrea and Hannah collect stamps. Andrea has
6 Philippine stamps and 8 U.S. stamps. Her sister
Hannah has 9 Singapore stamps and 12 Hong
Kong stamps. What is the ratio of Andrea’s stamps
to Hannah’s stamps?

14. 2.) Xander got 17 correct items in a 20-item test.
What is the ratio of his wrong answers to his
correct answers?
3.) In a night market, shorts are being sold at 3
pieces for P225. At this rate, how much will 12
shorts cost?

15. 4.) Luis reads 144 words per minute, how many
words can he read in 6 minutes?
5.) If Nicole has an average of 8 hours playing
games in her computer in 5 days, how many
hours does she play in 20 days?

16. What have you learned?
What is a ratio?
What is a proportion?
What are the ways in writing a ratio?

17. A S S E S S M E N T
Write a ratio or proportion for each of the
following:
1.) A car travels 162 kilometers in 3 hours. How far
can it travel in 12 hours? What is the ratio?
2.) thirty-seven compared to twenty-eight

18. 3) There are 5 kites to seven boys. What is the
ratio?
4) It’s Kim’s birthday. She received 5 boxes and 10
gift bags as gifts. What is the ratio of gifts in bags
and gifts in boxes?
5) In an investiture ceremony, there are 125 star
scouts invested and 230 junior scouts. What is the
ratio?

19. A S S I G N M E N T
Form ratio/proportion for the following:
1) 7 to 8
2) 3 to 5 is equivalent to 6 to 15
3) two barangays to 13 348 people
4) one boat to 3 people is equal to 6 boats to 18
people
5) 45 members of Glee Club to 30 members of Dance
Club

21. Reducing ratios to
lowest terms

22. OBJECTIVE
The learner reduces ratios to lowest
terms.

23. READING DRILL:
CALLA LILY
The stately flowers that are commonly used for
decorating the church during weddings are the calla
lilies. Calla lilies are also called Baguio lilies because
they grow abundantly there.
Calla lilies grow singly on long slender stalks.
They may either be yellow or white. They are made
into bridal bouquets or even wreaths.

24. KING BACK
L
What are you going to look
for in reducing fractions to
lowest terms?

25. Have you gone to
farm?
Tell to the class
everything that is
found in a farm
using the picture.

26. PROBLEM OPENER
It took Eugene 2 days to reach Lolo’s
farm. If he left his house last Tuesday, on
what day did he reach Lolo’s farm?

27.  What is the ratio of the sheep to the
cows?
 The chicks to the number of animals?

28. EXERCISE 1
Emmylou and her sister went on a trip to
Hundred Islands. They travelled for 4 days. If
they left last Wednesday, on what day did
they reach Hundred Islands?

29. EXERCISE 2
Express the given ratio in simplest or lowest terms.
1) 6 hours to 12 hours
2) 20 minutes to 1and 1/2 hours
3) 50 centavos to 2 pesos
4) 4 dozens to 25 things
5) 35 km to 5 000 meters

30. EXERCISE 2
Express the given ratio in simplest or lowest terms.
6) 56 clams to 8 mussels
7) 75 atis to 50 guavas
8) 60 seconds to 2 minutes
9) 5000 grams to 2 kilograms
10) 3 keys to 21 doors

31. What have you learned?
Can a ratio be expressed in lowest terms?
How?

32. A S S E S S M E N T
Reduce these ratios to lowest terms.
1) 30:5 4) 49:7
2) 14:15 5) 81:36
3) 9:36

33. A S S I G N M E N T
Reduce the ratios to lowest terms.
a) 18:20
b) 6:18
c) 12:3
d) 28:50
e) 11:44

35. Finding the missing
term in a
proportion

36. OBJECTIVE
The learner finds the missing term in
a proportion.

37. READING DRILL:
CALLA LILY
The stately flowers that are commonly used for
decorating the church during weddings are the calla
lilies. Calla lilies are also called Baguio lilies because
they grow abundantly there.
Calla lilies grow singly on long slender stalks.
They may either be yellow or white. They are made
into bridal bouquets or even wreaths.

38. KING BACK
L
What are the parts of a
proportion?

39. Do you help
your parents at
home during
weekends?

40. PROBLEM OPENER
During weekends, Zeny helps her mother sell
buko juice. For every buko, Zeny
adds 4 liters of water. How many liters of
water does she need for 3 bukos so that
the taste will be the same?

41. A B
 What is the ratio in A? in B?
 Is the second ratio equal to the first ratio?
Why?

42. Therefore, 1:4 = 3:12 or
1
4
=
3
12
PROPORTION is formed by two equal ratios.

43. 1
4
=
3
N
Buko
Liters of
water
Solution= 1 x N = 3 x 4
1N = 12
N= 12 ÷ 1
Solution= 1 x N = 4 x 3
1N = 12
N=12 ÷ 1
N=12
or 1:4 = 3:N

44. EXERCISE 1
Illustrate the problem before writing the
proportion.
Zeny and her mother also sells hotcakes
on weekends. Mother’s recipe calls for 3
eggs to make 5 hotcakes. Zeny wants to
make 25 hotcakes. How many eggs will
she need?

45. EXERCISE 2
Tell whether the following given ratios are proportions. Write
Yes if they are and No if not, change one term to make them
proportions.
a) 4/5 and28/35
b) 18:45 and 4:12
c) 20/48 and l5/36
d) 3:21 and 6:40
e) 9:12 and 27:32

46. EXERCISE 3
Solve for the missing term.
1) What number compared to 10 is
the same as 28 compared to 5?
2) Lisa saves 60 in 4 weeks. At this
rate, how long will it take her to save
300.00?

47. EXERCISE 3
Solve for the missing term.
3) Six compared to 11 is the same as 84
compared to what number?
4) A motorist traveled 240 km in 3 hours.
At the same rate, how long will it take to
travel 400
km?

48. EXERCISE 3
Solve for the missing term.
5) A scale 3.5 cm on a map represents an
actual distance of 175 km. What actual
distance does a scale distance of 5.7 cm
represent?

49.  What is a proportion?
 What are the terms or elements in a
proportion?
 How do we find the missing element in
a proportion?
What have you learned?

50. A S S E S S M E N T
Solve for the missing term in each
proportion.
1) 6:n = 8:12 4) y:6 = 28:84
2) m:7 = 6:21 5) 14:21 = 2:n
3) 20:24 = x:6

51. A S S I G N M E N T
Find the missing term to make the
proportion true.
a) 9:N = 27:15
b) N:8 = 12:32
c) 5:3 = 25:N

53. Solving word
problems involving
direct proportion

54. OBJECTIVE
The learner solves word problems
involving direct proportion

55. READING DRILL:
CALLA LILY
The stately flowers that are commonly used for
decorating the church during weddings are the calla
lilies. Calla lilies are also called Baguio lilies because
they grow abundantly there.
Calla lilies grow singly on long slender stalks.
They may either be yellow or white. They are made
into bridal bouquets or even wreaths.

56. KING BACK
L
How do you solve for the
missing means or extreme in
a proportion?

57. What do you
usually do
during
weekends?

58. PROBLEM OPENER
Roy and Al sell newspapers on weekends to
earn extra money. For every 3 newspapers
that Roy sells, Al sells 5. If Roy sold 15
newspapers, how many did Al
sell?

59. Analyze the problem.
a.) What is asked in the problem?
b.) What are given?
c.) Illustrate the problem.
Roy
Al
Note that the quantities change in the same direction. As the
number of newspapers that Roy sells increases, the number of
newspapers that Al sells also increases. This proportion is called
DIRECT PROPORTION.

60. In direct proportion, when one quantity increases,
the other quantity increases at the same rate and
vice versa.
To solve word problems with direct proportion:
-List down the given facts and identify the missing
term.
-Set the proportion for the problem.
-Solve for the missing term.

61. EXERCISE 1
Work in groups. Illustrate the problem and write
the proportion.
The sign on the store window says,
“Magazine for sale, buy 3, take 2.” How
many magazines must I buy If I want to
take 10 magazines for free?

62. EXERCISE 2
Solve the problems.
a) A motorist travels 275 km in 5 hours. How far can he
travel in 9 hours at the same speed?
Proportion: __________
Answer: __________
b)Two buses can transport 130 people. How many buses
are needed to transport 780 pupils?
Proportion: __________
Answer: __________

63. EXERCISE 3
Read and solve.
The ratio of the areas of 2 squares is 1:4.
The area of the smaller square is 36 𝑐𝑚2
.
How long is each side of the bigger
square?

64.  What must you remember when setting
a direct proportion?
What have you learned?

65. A S S E S S M E N T
Analyze each problem and write a proportion to solve
it. Draw a diagram to help you when necessary.
1) A tree casts a shadow of 12 meters when a
5-metre pole casts a shadow of 4 meters.
How tall is the tree?
2) At the rate of 3 items per 100, how much
will 12 items cost?

66. 3) A car travels 72 km on 8 liters of gasoline.
At the same rate, about how far can it travel
on 11 liters of gasoline?

67. A S S I G N M E N T
Write a proportion for each problem, then find the missing term.
a) The ratio of 2 numbers is 3:5. The larger number is 30. What is the
smaller number?
b) There are 3 teachers to 125 pupils during the school program.
How many teachers were
there if there were 2 500 pupils?
c) The ratio of male teachers to female teachers in our school is 2:9.
If there are 108 female teachers, how many teachers are male?

69. Solving word
problems involving
partitive proportion

70. OBJECTIVE
The learner solves word problems
involving partitive proportion

71. READING DRILL:
CALLA LILY
The stately flowers that are commonly used for
decorating the church during weddings are the calla
lilies. Calla lilies are also called Baguio lilies because
they grow abundantly there.
Calla lilies grow singly on long slender stalks.
They may either be yellow or white. They are made
into bridal bouquets or even wreaths.

72. Choose the letter of the correct answer.
1. Calla lilies are commonly used for :
a. corsages
b. garlands
c. church decoration
2. They are also called
a. water lily
b. rose lily
c. Baguio Lilies

73. 3. In Baguio, these lilies grow
a. abundantly
b. scarcely
c. singly
4. Calla lilies grow
a. in clusters
b. singly
c. in pairs
5. The selection is about
a. gumamela
b. calla lilies
c. sampaguita

74. 6. Their stalks are
a. slender
b. stout
c. wide
7. They may either be
a. white or red
b. red or yellow
c. yellow or white
8. Brides use Calla lilies in their:
a. wreaths
b. corsage
c. bouquets

75. 9. Calla lilies are also used for:
a. corsage for the head
b. corsage for the dress
c. wreath for the dead
10. Calla lilies are:
a. stately
b. fancy
c. unattractive

76. KING BACK
L
How do we solve word-
problems involving direct
proportion?

77. Do you share
your baon to
your friends?
How?

78. PROBLEM OPENER
Joy and Dale are twins. They always share their
things equally. Even their mother gave them the
same amount of anything, whether money, toys,
candies, and others. But one day, their father gave
them 5 chocolates, 2 chocolates for Joy and 3
chocolates for Dale.

79. Analyze the problem.
a.) What do you think each of the girls felt?
b.) Why did their mother give them things
equally?
c.) If you were one of the girls, what will you
do?
d.) Is it right to have the same amount of things
as your other siblings? Why?

80. Joy and Dale found out that there are things that
cannot be shared equally. So one day, their mother
gave them P150 so that the ratio is 2:3, 2 parts for
Dale and 3 parts for Joy. How much did each girl
receive?
1. What is asked in the problem?
2. What are the given facts?
3. How can we find the answer?

81. PARTITIVE PROPORTION
In partitive proportion, a whole is divided
into parts that is proportional to the given
ratio.
To solve word problems involving partitive
proportion, divide the given total or
difference by the sum or difference of the
ratio, then multiply the answer by each of
the terms.

82. EXERCISE 1
Analyze and solve each problem.
1.Two numbers are in the ratio 5:3. If the sum
is 88, find the two numbers.
2. The ratio of chairs to tables is 2:7. There are
180 chairs and tables in a party. How many are
there of each kind?
3. The sum of two numbers is 215. If the ratio
is 2:3, find the larger number.

83. EXERCISE 2
Analyze and solve each problem.
1. Two numbers are in the ratio of 4:7. If the
sum is 330, what are the numbers?
2. The ratio of Math books to Filipino books in
a class is 8 to 5. How many Math books are
there if there are 247 books in all?
3. The difference of two numbers is 12. Find the
numbers if their ratio is 1:2.

84. EXERCISE 3
Solve the given problems.
1) The salary of two workers is in the ratio 3:4. They received
12,250.00. How much did each worker receive?
2) The ratio of men to women at a college is 7 to 5. How
many women students are there if there are 350 men?
3) The ratio of Math books to other books in a class is 8 to 5.
How many Math books are there if there are 247 books in
all?

85. How do you solve word problems
involving partitive proportion?
What are the processes involved?
What have you learned?

86. A S S E S S M E N T
Read and analyze, then solve the
problems.
1) The ratio of cats to dogs is 6:5. There are
495 dogs and cats in a certain barangay.
a)How many cats are there?
b) How many dogs are there?

87. 2) Three numbers are in the ratio 2:5:7. If their
sum is 504, what are the three numbers?
a) first number
b) second number
c) third number

88. A S S I G N M E N T
Analyze and solve the problems carefully.
1) The ratio of doors to windows is 1:5. There are 186
doors and windows in a building. How many
doors are there? windows?
2) The ratio of the angles of a triangle is 3:4:5. Find
the measure of each angle.

89. 3) Three numbers are in the ratio 1:4:7.
Find the second number if their sum is 276.
4) The difference between two numbers is
40. They are in the ratio 9:7. What are the
numbers?