Mathematics 5 Quarter 1 Module 9: Solving Real Life Problems Involving Addition and Subtraction of Fractions

Mathematics

Quarter 1 – Module 9: Solving Real Life Problems Involving Addition and Subtraction of Fractions

CO_Q1_Math5_Module9

Mathematics – Grade 5 Alternative Delivery Mode Quarter 1 – Module 9: Solving Real Life Problems Involving Addition and Subtraction of Fractions First Edition, 2020

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Development Team of the Module

Writer: Omar D. Comonical Editors: Zosimo M. Minozo Jr., Catherine L. Cortez, Cathrine O. Cueva, Floriza May Baltar, Ramil R. Magdua, Niann L. Atis, Lilia Martinez, Joseph Randolp Palattao, Bernadeth Daran, and Lilia L. Lagrimas Reviewers: Renato S. Cagomoc, Rolando Lacbo, Joshua Sherwin T. Lim, and Norman E. Sagayap, Miguel V. Dumas, Jr., Lourdes Rama Layout Artist: Angel T. Porlares, Ryan R. Tiu Management Team: Ramir B. Uytico, Arnulfo M. Balane, Rosemarie M. Guino, Joy B. Bihag, Ryan R. Tiu, Sarah S. Cabaluna, Thelma Cabadsan-Quitalig, Elena S. de Luna, Renato S. Cagomoc, Noel E. Sagayap, Geraldine P. Sumbise, Joshua Sherwin T. Lim

Mathematics

Quarter 1 – Module 9: Solving Real Life Problems Involving Addition and Subtraction of Fractions

5

Introductory Message

This Self-Learning Module (SLM) is prepared so that you, our dear learners, can continue your studies and learn while at home. Activities, questions, directions, exercises, and discussions are carefully stated for you to understand each lesson.

Each SLM is composed of different parts. Each part shall guide you step-by-step as you discover and understand the lesson prepared for you.

Pre-tests are provided to measure your prior knowledge on lessons in each SLM. This will tell you if you need to proceed on completing this module or if you need to ask your facilitator or your teacher’s assistance for better understanding of the lesson. At the end of each module, you need to answer the post-test to self-check your learning. Answer keys are provided for each activity and test. We trust that you will be honest in using these.

In addition to the material in the main text, Notes to the Teacher are also provided to our facilitators and parents for strategies and reminders on how they can best help you on your home-based learning.

Please use this module with care. Do not put unnecessary marks on any part of this SLM. Use a separate sheet of paper in answering the exercises and tests, and read the instructions carefully before performing each task.

If you have any questions in using this SLM or any difficulty in answering the tasks in this module, do not hesitate to consult your teacher or facilitator.

Good luck and happy learning!

What I Need to Know

In this module, you are going to gain understanding in solving routine and non–routine word problems that involve addition and subtraction of fractions using appropriate problem-solving strategies and tools.

After going through this module, you are expected to

• solves routine and non–routine problems involving addition and/or subtraction of fractions;
• create routine and non-routine problems involving addition and/or subtraction of fractions; and
• apply solving word problems in real-life situations. M5NS-If-87.2

What I Know

Directions: Choose the letter of the correct answer. Use separate answer sheet.

1. Martin bought 5 1/2 m of white cloth and 2/5 m of blue cloth. How many meters of cloth did he buy in all?
   A. 5 5/6 B. 5 7/8 C. 5 9/10 D. 5 11/12

   
   

2. Anna needs 3 3/4 kg of sugar for her shake. If she had 1 1/2 kg in her house, how many kilograms of sugar does she need to buy?
   A. 1 1/4 B. 2 1/4 C. 3 1/4 D. 4 1/4

   
   

3. Samantha prepared juice. She mixed 1 1/2 liter of orange juice and 3 liters of mango juice. What was the total number of liters that she mixed?
   A. 4 1/2 B. 2 3/4 C. 3 1/2 D. 1 3/4

   
   

4. Mary bought a chocolate cake. She ate 1/8 of it. How much chocolate was left?
   A. 5/8 B. 6/8 C. 7/8 D. 8/8

   
   

5. Kathy’s kitten weighs 1/2 kilogram. Sam’s puppy is 3/4 kilogram. What is the total weight of the two animals?
   A. 1 1/4 B. 1 1/2 C. 1 3/4 D. 2 1/4

   
   

6. Alyssa has 2 meters of ribbon. If she cuts 1 2/5 meters of ribbon, how many meters of ribbon is Alyssa left with?
   A. 2/5 m B. 4/5 m C. 3/5 m D. 1/5 m

   
   

7. Lita’s pitcher of water is 1/2 L full. If she adds 1/4 L, how many L of water does she have in all?
   A. 2/4 B. 3/4 C. 2/6 D. 4/4

   
   

8. Alex ordered 10 kilograms of rice. Only 5 1/2 kilograms of rice were delivered. How many kilograms of rice were left undelivered?
   A. 3 1/2 kg B. 5 1/2 kg C. 3 1/2 kg D. 4 1/2 kg

   
   

9. Josie needs 3 1/4 cups of flour for the plain cake and 2 1/3 cups for the pineapple sponge cake. How many cups of flour does she need in all?
   A. 6 7/12 B. 5 7/12 C. 4 7/12 D. 3 7/12

   
   

10. Hanna used 1/4 kg ground meat for spaghetti and 2/3 kg for the hamburger. How much meat did she use?
    A. 9/12 kg B. 8/12 kg C. 1 11/12 kg D. 11/12 kg

    
    

Lesson 1: Solving Real Life Problems Involving Addition and Subtraction of Fractions

In this module, you will learn how to solve the routine and non-routine problems involving addition and subtraction of fractions, using the 4-Step Method that was taught from the previous lessons. Also, this lesson will teach you how to think in more abstract ways and develop your creativity and mathematical reasoning power in understanding and answering non-routine problems using different strategies while finding the correct answer.

Having the ability to solve problems that are experienced in your daily living without following readily identifiable models and process, is a plus knowledge in this lesson.

What’s In

In answering word problem, take note of words clues, to help you figure out which operation will be used.

Study the steps and analyze the given word problems below:

A. Mrs. Garcia had 5 1/4 meters of white cloth. Judith asked 3/4 m of it for their project. How many meters of cloth were left? a. What is asked? The no. of meters of cloth left b. What are given? 5 1/4 meters of white cloth and 3/4 m for Judith’s project c. What operation should be used? Subtraction d. What is the number sentence? 5 1/4 – 3/4 = N e. Show your solution:

Step by step Solution: 5 1/4 – 3/4 = N 21/4 – 3/4 = N 18/4 = N 4 2/4 = N or N = 4 1/2 m of cloth was left (Answer)

B. Anna has 1 1/4 kg of pork and 2 1/2 kg of chicken in her refrigerator. How many kg of meat does she have in her refrigerator? a. What is asked? The no. of kg of meat she has in her refrigerator. b. What are given? 1 1/4 kg of pork and 2 1/2 kg of chicken in her refrigerator c. What operation should be used? Addition d. What is the number sentence? 1 1/4 + 2 1/2 = N e. Step by step Solution: 1 1/4 + 2 1/2 = N 1 1/4 + 2 2/4 = N 3 3/4 = N N = 3 3/4 kgs of meat

Therefore, 3 3/4 kgs of meat

Notes to the Learner

In answering the word problem, follow the sequence Understand, Plan, Solve or what is Asked, Given, Operation, Number Sentence, Solution

What’s New

Try to do the exercises below:

Directions: Read and solve the following problems. Answer in your activity notebook.

1. One weekend, Raul worked 5 3/4 hours on Saturday and 2 2/3 hours on Sunday. How many hours did Raul work for that weekend?
   Understand:
   Plan:
   Solve:
   Check and look back:

   
   

2. Angelika hiked 4 3/8 miles one day and 2 5/16 miles the next day. How many miles did Angelika hike in all?
   Understand:
   Plan:
   Solve:
   Check and look back:

   
   

What Is It

In solving word problem follow the steps:

• ❖ UNDERSTAND
  • Read the problem
  • Determine what is asked in the problem.
  • Determine the important data in the problem (What are given).
• ❖ PLAN
  • Choose a strategy (operation).
  • Draw a picture or make a table.
• ❖ SOLVE
  • Show all your work (number sentence).
  • Label your answer.

Consider the following example problems below:

Example 1:

The pupils of Malikhain Elementary School conducted a contest wherein they will make something out of recyclable materials. The pupils collected 1 2/3 kilogram of used bottles and 1 4/5 kilogram of used newspapers. How many kilograms of recycled materials did the pupils collect?

➢ Understand

a. What is asked?

• The total weight of recyclable materials the pupils collected.

b. What are the given facts?

• 1 2/3 kilogram of used bottles
• 1 4/5 kilogram of used newspaper

➢ Plan

c. What is the operation to be used?

• Addition

➢ Solve

d. What is the number sentence?

• 1 2/3 + 1 4/5 = N

e. Show your solution and answer.

• 5/3 + 9/5 Rename the mixed number to an improper fraction by multiplying the denominator by the whole number, then add the product to the numerator.
• 25/15 + 27/15 Find the LCD. Then, rename the fraction to a similar fraction.
• (25+27)/15 = 52/15 Add the numerator and copy the denominator.
• 52/15 = 3 7/15 Rename the improper fraction to a mixed form.

➢ Answer: The pupils collected 3 7/15 kilograms of recyclable materials.

Example 2:

Samuel has an aquarium. One-third of the fishes in a tank are catfish, 2/9 of the fishes are kois and the rest are goldfish. There are 40 goldfishes in the tank. How many fishes are there in a tank?

In solving non-routine problem, there are no particular way(s) in finding the correct answer. Below are the methods which involve ways of thinking and variety of strategies to reach a solution. You may only need to use one strategy or a combination of strategies.

• Look for a pattern
• Guess and check
• Make and solve a simpler problem
• Work backwards
• Act it out/make a model
• Break up the problem into smaller ones and try to solve these first
• Draw a picture or diagram
• Make an organized list
• Make a table
• Write an equation/mathematical sentence
• Use manipulatives
• Use logical reasoning

Let us try to solve example problem 2 using a model/a diagram in solving the problem of Samuel.

1 whole divided by 3 equal parts 1/3

3 equal parts: catfish, kois and goldfish

[chart: bar model diagram; 3 equal parts: catfish, kois and goldfish] catfish

The 3 equal parts given, two−ninths (2/9) parts are for kois and rest for the other type of fish. Divide the 3 equal parts into 9 total equal parts, 2/9 as shown below.

Given: 40 = goldfish (2/9) = kois

[chart: bar model diagram; fish tank model with catfish, kois and 40 goldfish] catfish kois 40 goldfish How many fish are there in all?

1 – 1/3 – 2/9 = 9/9 – 3/9 – 2/9 = 4/9

So, 40 is 4/9 of the total number of fish, which represents 4 units in the model. If we divide the 40 goldfish per unit, that is 10 fish each. Since, there are 9 units that makes it 90 fish.

[chart: bar model diagram; 4 units shaded as catfish and kois, 5 units as goldfish, each goldfish unit labeled 10] 10 10 10 10 4 units = 40 1 unit = 40 ÷ 4 = 10 9 units = 9 x 10 = 90

Therefore, there are 90 fishes in the tank.

Example 3: Here is another problem using logical reasoning/mathematical sentence.

BJ needed 1 2/3 ft of bamboo for their project. His classmates is asking for 1 1/4 ft. How long is the bamboo that they need?

Given: 1 2/3 ft – length of bamboo that BJ need; 1 1/4 ft – length of bamboo that BJ’s classmates need Task: find out how long is the bamboo that they need. Solution: 1 2/3 ft + 1 1/4 ft = N

Change mixed fraction to improper fraction: 1 2/3 + 1 1/4 ⟹ 5/3 + 5/4 = N

Find the least common denominator: 5/3 + 5/4 = ⟹ 20/12 + 15/12 = 35/12 or 2 11/12 ft.

Therefore, BJ needed 2 11/12 ft of bamboo for himself and his classmate.

Example 4:

Vane, Joan and Rutche cleaned the wall together and finished it in 4 1/2 hours. If Rutche helped for 1 3/4 hours and Vane for 1 2/3 hours, what is the working time for Joan?

Asked: N = time of Joan in helping clean the wall Given: time working together = 4 1/2 hours Rutche = 1 3/4 hours, Vane = 1 2/3 hours Plan: Subtraction Solution: 4 1/2 – 1 3/4 – 1 2/3 = N; you may continue to solve in your activity notebook N = 1 1/12 hours, time of Joan in cleaning the house

Example 5: Read and understand the problem below.

During a school fair, Remy served mango juice and buko juice. He inspected the jar to find how much of each kind of juice was left over after the fair. This is what he saw:

• Three jars had mango juice and three jars had buko juice.
• Two jars are 1/4 full-one jar containing mango and the other jar containing buko juice. The jar that had the least amount contained mango juice.
• One jar of buko juice is 1/3 full. This jar is twice as full as another jar of mango juice.

After cleaning up, he poured all the left over into another jar-all the mango juice into the red jar, and the buko juice into the blue jar. The blue jar became full while the red jar needs 1/8 more to be full.

What are the amounts of the 3 jars of mango juice and the 3 jars of buko juice that Remy saw before the clean-up?

Here’s a way to solve the problem of Remy.

Conditions	Illustrations
Three jars had mango juice and three jars had buko juice.	[illustration: six empty jars, three under the label Mango Juice and three under the label Buko Juice] Mango Juice Buko Juice
Two jars are 1/4 full-one jar containing mango and the other jar containing buko juice.	[illustration: jars; first jar of the mango group and first jar of the buko group each labeled 1/4] Mango Juice Buko Juice
One jar of buko is 1/3 full. This jar is twice as full as another jar of mango juice.	[illustration: mango jars labeled 1/4, 1/6, ?; buko jars labeled 1/4, 1/3, ?] Mango Juice Buko Juice 1/3 of the buko juice ÷ 2 1/3 x 1/2 = 1/6

Conditions	Illustrations
[transcriber’s note: table continued from the previous page]
After cleaning up, he poured all the left over into another jar-all the mango juice into the red jar, and the buko juice into the blue jar. The blue jar became full while the red jar needs 1/8 more to be full.	[illustration: mango jars labeled 1/4, 1/6, ?; buko jars labeled 1/4, 1/3, ?; a red jar labeled Needs 1/8 to be full; a blue jar labeled Full] Mango Juice Buko Juice Needs 1/8 to be full Full
What are the amounts of the three jars of mango juice and the three jars of buko juice that Remy saw before the clean-up?	[illustration: mango jars labeled 1/4, 1/6, 11/24; buko jars labeled 1/4, 1/3, 5/12] Mango Juice Buko Juice Solution: Total amount of juice in the red jar: 1 − 1/8 = 7/8 Amount of the third jar of mango juice: 7/8 − (1/4 + 1/6) = ? 7/8 − 5/12 = 11/24 Therefore, the amount of the three jars of mango juice are 1/4, 1/6 and 11/24. Solution: Amount of the third jar of buko juice: 1 − (1/4 + 1/3) = ? 1 − 7/12 = 5/12 Therefore, the amount of the three jars of buko juice are 1/4, 1/3 and 5/12.

What’s More

Do the exercises below:

A. Directions: Solve each problem involving the addition/subtraction of fractions. Write the answers only on separate sheet of paper.

1. Dorry’s house is 3/4 kilometer from the church. One day, she took a tricycle to the church. After covering a distance of 1/8 kilometers, the tricycle stopped and Dorry had to walk. How far did she walk?

   
   

2. Catherine and Bernard shared a cake. Catherine ate 1/3 of it and Bernard ate 3/8 of it. What fraction of the cake did they eat?

   
   

3. Cindy bought 10 4/5 kilograms of ground meat. She used 3 2/3 kilograms to make lumpia. How many kilograms of ground meat was left?

   
   

4. On her way to school, Jasmine travels 6 3/8 kilometers by bus and 5 2/5 kilometers by tricycle. How far does she travel from her home to school?

   
   

5. A tailor used 2 3/4 meters of cloth for a pair of pants and 1 9/10 meters of a skirt. How many meters of cloth were used?

   
   

B. Directions: Read and analyze the following problem. You may solve using any method. Write your answer on a separate sheet of paper.

1. Ben weighs 44 1/2 kg, Tony weighs 41 5/8 kg and Jun weighs 22 1/4 kg. How much more did Tony and Jun weighs than Ben?

   
   

2. A certain caterpillar crawls in a clothesline that is 1 meter long. Starting at one end of the clothesline, the caterpillar crawls at a distance of 1/3 m during daytime but slides back at 1/4 m during night time. In how many days will the caterpillar reach the end of the clothesline?

   
   

3. The children’s play station is open whole day only during Saturday. VJ’s mother only allow him to play 2/5 hour in the morning and 7/10 hours in the afternoon. But VJ requested her mother to stay an additional 3/4 hour in the morning and 3/5 hour in the afternoon since it is Saturday. How long did VJ stay in the children’s play station if his mother allowed him to stay on the additional hour he requested? If his mother will not allow him, how many hours did he stay in the children’s play station?

   
   

4. Dennis has 10 cans of milk with a total weight of 6 3/4 kilograms. He will pack these cans of milk into 3 boxes where each box can only contain up to 2 1/2 kilograms. How can Dennis pack these cans into the box if the weight of the cans of milk (in kg) are 2/3, 5/8, 2/5, 1/3, 1 1/4, 7/8, 1/2, 3/5, and 3/4?

   
   

What I Have Learned

To solve word problems, follow these steps:

1. Analyze carefully the given real-life problem,
   -State what is asked.
2. Indicate what are the given data.
   -Determine what operation to use.
   -Write the number sentence.
3. Solve.
4. Check the answer.

Answer the following problems below. Write the final answer with your solution in a separate sheet.

1. Mr. Guevara’s tablecloth, which was 3 1/8 meters long, got stained near the edge. He cut the 3/8 meters which got stained. How long is the tablecloth now?
   Follow the steps 1-4 stated in solving the problem given above.

1. Understand
2. Plan
3. Solve
4. Check and look back

Using Problem No. 1, make use of a model to solve the problems below.

1.1) If the length of the table is 3 1/2 m, will the new length of the tablecloth be enough to cover the length of the table?

1.2) If the table is 2 1/2 m long and the 3 1/8 meters long tablecloth cover got stained of about half of the measure of the table, will there be enough cloth to cover the table after cutting the stained part?

2. Ronnie went to his hometown to visit his grandparents. His hometown is 36 3/5 km away from his house. He walked 1 1/4 km and travels a distance of 6 1/2 km by a jeep to get to the bus station. He covers the remaining distance by bus and a short walk of 1/5 kilometer. How many kilometers did Ronnie travel by bus?

What I Can Do

A. Directions: Write TRUE if the answer shown in the parenthesis is correct and FALSE if it is not.

1. Anna bought 5 1/2 kilogram of rice. She cooked 1 1/4 kilogram. How many kilograms of rice were left? (2 1/2 kilograms of rice)

   
   

2. Rose was requested by her mother to buy for her 1/4 kg. of cabbage, 1/3 kg. of ginger, and 1/2 kg. of tomatoes. How many kilograms of vegetables did Rose buy in all? (1 1/12 kg. of vegetables)

   
   

3. Mr. San Agustin spends 2/8 for his house rental and 4/8 for his food and other expenses. How much were the total expenses of Mr. san Agustin? (3/4 was the total expenses)

   
   

4. During Family Day at Marie’s School, her brother ran 8 5/9 meters and her dad ran 15 1/9 meters. How far did the two runs? (23 2/3 meters were the total distance)

   
   

5. Anton hiked for 2 1/2 hours on Saturday, 3 1/4 hours on Sunday. How many hours did Anton hike for two days? (5 1/2 hours were the total Anton hiked for two days)

   
   

6. “Bokayo” is one of the favorite delicacies in our locality. Its ingredients are brown sugar and shredded young coconut. If there are 1 3/4 cups of brown sugar and 2 1/2 cups of shredded young coconut, how many cups of ingredients are there in all? (3 3/4 were the total ingredients in all)

   
   

7. A unit fraction is a fraction whose numerator is 1. Some of the examples: 1/2, 1/3, 1/4, 1/5, 1/10, and 1/100. Ancient Egyptians wrote the fraction by expressing it as a sum of different unit fractions. For instance, 1/2 = 1/3 + 1/6 and 2/5 = 1/10 + 1/20 + 1/4. Express the following fractions as a sum of unit fractions. Explain the strategy you use in finding the answers.

   
   

Did you find any pattern?

a) 2/3 b) 4/5 c) 3/7

Assessment

Do the test below apply what you have learned on the previous activities.

Directions: Choose the letter of the correct answer on a separate answer sheet.

1. Martin bought 5 1/2 m of white cloth and 2/5 m of blue cloth. How many meters of cloth did he buy in all?
   A. 5 5/6 B. 5 7/8 C. 5 9/10 D. 5 11/12

   
   

2. Anna needs 3 3/4 kg of sugar for her shake. If she had 1 1/2 kg in her house, how many kilograms of sugar does she need to buy?
   A. 1 1/4 B. 2 1/4 C. 3 1/4 D. 4 1/4

   
   

3. Samantha prepared juice. She mixed 1 1/2 liter of orange juice and 3 liters of mango juice. What was the total number of liters that she mixed?
   A. 4 1/2 B. 2 3/4 C. 3 1/2 D. 1 3/4

   
   

4. Mary bought a chocolate cake. She ate 1/8 of it. How much chocolate was left?
   A. 5/8 B. 6/8 C. 7/8 D. 8/8

   
   

5. Kathy’s kitten weighs 1/2 kilogram. Sam’s puppy is 3/4 kilogram. What is the total weight of the two animals?
   A. 1 1/4 B. 1 1/2 C. 1 3/4 D. 2 1/4

   
   

6. Alyssa has 2 meters of ribbon. If she cuts 1 2/5 meters of ribbon, how many meters of ribbon is Alyssa left with?
   A. 2/5 m B. 4/5 m C. 2/5 m D. 1/5 m

   
   

7. Lita’s pitcher of water is 1/2 L full. If she adds 1/4 L, how many L of water does she have now?
   A. 2/4 B. 3/4 C. 2/6 D. 4/4

   
   

8. Alex ordered 10 kilograms of rice. Only 5 1/2 kilograms of rice were delivered. How many kilograms of rice were left undelivered?
   A. 3 1/2 kg B. 5 1/2 kg C. 3 1/2 kg D. 4 1/2 kg

   
   

9. Josie needs 3 1/4 cups of flour for the plain cake and 2 1/3 cups for the pineapple sponge cake. How many cups of flour does she need in all?
   A. 6 7/12 B. 5 7/12 C. 4 7/12 D. 3 7/12

   
   

10. Hanna used 1/4 kg ground meat for spaghetti and 2/3 kg for the hamburger. How much meat did she use?
    A. 9/12 kg B. 8/12 kg C. 1 11/12 kg D. 11/12 kg

    
    

Additional Activities

Directions: Choose the letter of the correct answer. Do this in your activity notebook.

1. Mrs. Zamora had 6 1/4 meters of red cloth. Carla asked 1 3/4 of it for her dress. How many meters of cloth were left?
   A. 4 1/8 B. 4 1/4 C. 4 1/2 D. 4 3/4

   
   

2. Geraldine gives 1/3 of a pan of brownies to Susan and 1/6 of the pan of brownies to Patrick. How much of the pan of brownies did Geraldine give away?
   A. 1/8 B. 1/4 C. 1/2 D. 3/4

   
   

3. Pam walks 3 7/8 miles to school. Paul walks 2 1/4 miles to school. How much farther does Pam walk than Paul?
   A. 1 1/4 B. 1 2/5 C. 1 4/7 D. 1 5/8

   
   

4. On Friday, In Mrs. Diaz’s class, many students were missing. 1/8 of the class went to a basketball tournament and 3/6 were sick. How many students are absent on that day?
   A. 5/8 B. 6/8 C. 7/8 D. 8/8

   
   

5. Marly made two types of cookies. She used 1 3/4 cup of sugar for one recipe and 3 4/7 cup for the other. How much sugar did she use in all?
   A. 5 8/28 B. 5 9/28 C. 5 10/28 D. 5 11/28

   
   

6. Mom bake 2 whole homemade cheesy pizza. She shared 1/2 slice to her friend and another 3/4 slice to her children. What is the remaining slice of pizza left for her?
   A. 5/4 B. 3/4 C. 1/2 D. 1/4

   
   

Answer Key

What’s New

1. a. Number of hours Raul work for the weekend
   b. 5 3/4 on Saturday and 2 2/3 on Sunday
   c. Addition
   d. 5 3/4 + 2 2/3 = N
   e. 5 3/4 + 2 2/3 = 5 9/12 + 2 8/12 = 7 17/12 = 8 5/12 hours

   
   

   [transcriber’s note: the scan is printed upside down and the fraction line in step e is partly scrambled; the reading above follows the printed numbers]

   
   

2. a. Number of miles Angelika hike in all
   b. 3/8 2 miles one day and 5/16 miles the next day
   c. Addition
   d. 3/8 2 + 5/16 = N
   e. 3/8 2 + 5/16 4 = 6/16 2 + 5/16 6 = 11/16 miles

   
   

   [transcriber’s note: the mixed numbers in this item are printed with the whole number out of order in the scan; the text is reproduced as printed]

   
   

What’s More

A.

1. 5 5/8 [?]
2. 1 7/24 [?]
3. 2 7/15 [?]
4. 31/40 [?]
5. 13/20 [?]

B. 1) 4-step plan a) Weight of Tony and Jun compared to Ben b) Ben weighs 44 1/2 kg, Tony weighs 41 5/8 kg and Jun weighs 22 1/4 kg c) Addition and Subtraction d) 41 5/8 + 22 1/4 – 44 1/2 = N e) difference of the weighs = 41 5/8 + 22 1/4 – 44 1/2 = 41 5/8 + 22 2/8 – 44 4/8 = 63 7/8 – 44 4/8 = 19 3/8 Thus, Tony and Jun weigh 19 3/8 kg more than Ben

2. Answer: 10 days

   
   

3. Answer:
   Allowed time to play by his mother = 1 1/10 hours
   VJ requested an additional 1 7/20 hours
   Total Time VJ is at the children’s play station if request is granted: 1 7/20 + 1 1/2 = 2 9/20 hours.

   
   

4. Answers may vary. One possible solution is:
   Box 1: 2/3, 1/3, 1 1/4
   Box 2: 5/8, 7/8, 3/4
   Box 3: 2/5, 3/5, 3/4, 1/2

   
   

What I Know

1. C
2. B
3. A
4. C
5. A
6. C
7. B
8. D
9. B
10. D

Assessment

1. C
2. B
3. A
4. C
5. A
6. C
7. B
8. D
9. B
10. D

What I Have Learned

Problem (1)

Understand the Problem: *Asked: Measure of the tablecloth after cutting the edge *How long is the tablecloth after cutting the stained part? *Given: Length tablecloth = 3 1/8 m; stained part = 3/8 m

Plan: *Subtraction

• 3 1/8 − 3/8 = N

Solve:

• 3 1/8 − 3/8 = 25/8 − 3/8 = 22/8 = 2 3/4

Check and look back:

• 22/8 + 3/8 = 25/8 = 3 1/8

Therefore, the new length of the tablecloth is 2 3/4 m.

Problem (1.1)

Given: New length of the table: 3 1/2 m

Answer: The length of the table is 3 1/2 m but the new table cloth is only 2 3/4 m.

[transcriber’s note: the printed answer line is out of order in the scan; the words are reproduced in the order printed]

Problem (1.2)

Given: 2 1/2 m – length of the table 3 1/8 m – length of the tablecloth

Task: find out if there is enough cloth that can cover the table after cutting the part of the cloth that got stained which is half of the measure of the table.

[transcriber’s note: the task sentence is scrambled in the scan; words are placed in reading order]

Answer:

• length of the cloth that got stained is half of the measure of the table: 1/2 of 2 1/2 m is 1 1/4 m
• length of the remaining tablecloth: 3 1/8 m – 1 1/4 m = ?
• The new length of the tablecloth is 1 7/8 m. Thus, it is not enough to cover the table since the table measures 2 1/2 m.

Problem 2

Asked: Find the distance (in km) Ronnie traveled by bus.

Given facts: 36 3/5 km – distance of his hometown from his house 1 1/4 km – distance traveled by walking 6 1/2 km – distance traveled by jeep 1/5 km – distance of the short walk

Solution: Find the sum of the distances walked and traveled by jeep: 1 1/4 + 6 1/2 + 1/5 = ? The sum is 7 19/20 km.

Problem 2 Con’t. Find the difference between the distance of Ronnie’s house to his hometown and the sum of the distances Ronnie walked and traveled by jeep to get the distance he traveled by bus: 36 3/5 – 7 19/20 = ? The difference is 28 13/20.

Therefore, Ronnie traveled 28 13/20 km by bus.

What I Can Do

1. 4 1/4 False
2. 1 1/12 True
3. 3/4 True
4. 23 2/3 True
5. 5 3/4 False
6. 4 1/4 False
7. Answers may vary. Possible answers are:
   a) 2/3 = 1/2 + 1/6
   b) 4/5 = 1/2 + 1/4 + 1/20
   c) 3/7 = 1/3 + 1/14 + 1/42

Additional Activities

1. C
2. C
3. D
4. A
5. B
6. B

References:

Department of Education. 2017. Regional Test Item Bank in Mathematics 5. Leyte: Department of Education.

MathCurious. n.d. Math Curious. Accessed July 28, 2021. https://app.mathcurious.com/puzzles.

Piere, Rod. 2020. About Math is Fun. October. Accessed July 2021. https://www.mathsisfun.com/citation.php.

University of Cambridge. 2021. Maths at Home. Accessed July 2021. https://nrich.maths.org/.

Ursua, A. C., and A.P. Lumbre. 2016. 21st Century Mathletes Textbook. Quezon: Vibal Group, Inc.

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