Forming ratio and proportion using colon (:) and fractions in writing ratios and proportions
OBJECTIVE
The learner forms ratio and proportion using colon (:) and fractions in writing ratios and proportions.
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.
KING BACK
L
What are the different ways in writing ratios?
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.
EXERCISE 1
Give the ratio of each of the following orally.
boy scouts to girl scouts
EXERCISE 1
Give the ratio of each of the following orally.
spoon to fork
EXERCISE 1
Give the ratio of each of the following orally.
pebbles to dice
EXERCISE 1
Give the ratio of each of the following orally.
glasses to mugs
EXERCISE 1
Give the ratio of each of the following orally.
trees to fruits
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?
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?
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?
What have you learned?
What is a ratio?
What is a proportion?
What are the ways in writing a ratio?
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
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?
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
Reducing ratios to lowest terms
OBJECTIVE
The learner reduces ratios to lowest terms.
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.
KING BACK
L
What are you going to look for in reducing fractions to lowest terms?
Have you gone to farm?
Tell to the class everything that is found in a farm using the picture.
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?
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?
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
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
What have you learned?
Can a ratio be expressed in lowest terms?
How?
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
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
Finding the missing term in a proportion
OBJECTIVE
The learner finds the missing term in a proportion.
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.
KING BACK
L
What are the parts of a proportion?
Do you help your parents at home during weekends?
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?
A
B
PROPORTION is formed by two equal ratios.
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
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?
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
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?
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?
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?
What have you learned?
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
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
Solving word problems involving direct proportion
OBJECTIVE
The learner solves word problems involving direct proportion
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.
KING BACK
L
How do you solve for the missing means or extreme in a proportion?
What do you usually do during weekends?
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?
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.
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.
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?
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: __________
EXERCISE 3
Read and solve.
What have you learned?
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?
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?
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?
Solving word problems involving partitive proportion
OBJECTIVE
The learner solves word problems involving partitive proportion
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.
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
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
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
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
KING BACK
L
How do we solve word-problems involving direct proportion?
Do you share your baon to your friends? How?
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.
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?
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?
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.
EXERCISE 1
Analyze and solve each problem.
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.
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.
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?
What have you learned?
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.
b) How many dogs are there?
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
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.
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?