Fundamental Operations on Fractions PDF

Lesson 1.1 Fundamental Operations on Fractions Business Mathematics Accountancy, Business, and Management 1 Do you want to edit this presentation? Make a copy and edit in Download an offline copy Google Slides....

Lesson 1.1 Fundamental Operations on Fractions Business Mathematics Accountancy, Business, and Management 1 Do you want to edit this presentation? Make a copy and edit in Download an offline copy Google Slides. and edit in Microsoft PowerPoint. 1. On the menu bar, click File and then Make a copy and Entire 1. On the menu bar, click File and then Presentation. Download as. 2. Type a name for the file. 2. Choose a file type. Select Microsoft 3. Choose where to save it on your PowerPoint (.pptx). Google Drive. 3. Wait for the file to be downloaded to 4. Click Ok. your local disk. 5. A new tab will open. Wait for the file 4. Once completely downloaded, open to be completely loaded on a new the file and edit it using Microsoft tab. PowerPoint or any offline presentation 6. Once the file has loaded, edit this program. presentation using Google Slides. 2 In a clothing business, it is essential to know your inventory — what portion of the supply is sold and what part is still on stock and on the shelves. 3 An easier way to present the inventory is to use a pie chart. This shows the fractions of each piece of information. 4 Fractions are useful in understanding and monitoring the current status and financial capacity of a business. 5 Quick Look Doing an Inventory Suppose you are doing an inventory to your clothing business. Based on your initial checking, three-fourths of all the items are already sold, and one-eighth is still on stock. If there are no missing items, what part of all the inventory is still in the stockroom? 6 Quick Look Solution What part of all the inventory is still in the stockroom? Step 1: Identify what is required in the problem. You are asked to determine what part of the inventory (i) is still in the stockroom (s). Step 2: Identify the given in the problem. 34(i) sold (t) 18(i) display (d) 7 Quick Look Solution What part of all the inventory is still in the stockroom? Step 3: Write the working equation. i = 1 - (t + d) Step 4: Substitute the given values. 8 Quick Look Solution What part of all the inventory is still in the stockroom? Step 5: Find the answer. One-eighth of the inventory is still in the stockroom. 9 Quick Look Questions to Ponder 1. What is a fraction? 2. What is the importance of understanding fractions? 3. How do we use fractions in real life? 10 Learning Competency This lesson aims to target the following DepEd competencies: Perform fundamental operations on fractions and decimals (ABM_BMFO-Ia-1) Give real-life situations to illustrate fractions, decimals, and percent. (ABM_BMFO-Ic-4) Solve problems involving fractions, decimals, and percent. (ABM_BMFO-Id-5) 11 Learning Objectives In this lesson, you should be able to do the following: Recall the definition of fraction and its kind. Perform fundamental operations on fractions. Solve problems involving fractions related to business. 12 How will the world of business be affected without the concept of fraction? 13  Fractions In a selling business, we can determine what part of the inventory is sold and what portion is left. This can be represented through a fraction. 14  Fractions Fraction the quotient between numerator two numbers, p and q, where q≠0. denominator 15  Kinds of Fractions Proper Fraction a fraction whose numerator is smaller numerator < denominator than the denominator 2 denominator than the denominator 15 > 4 18  Kinds of Fractions Mixed Number a fraction written as a sum of a counting combination of a whole number and a proper number and a fraction proper fraction 19  Kinds of Fractions Mixed Number Suppose the company's total sales for the month increased by twice and a half — this can be illustrated through a mixed number 20  Operations on Fractions Addition and Subtraction of Fractions The concept of adding and subtracting fractions is essential in the world of business. In business partnerships, the profit and loss agreement of the partners can be expressed through fractions. The shares of two or more partners can be added to determine their combined share in the partnership profit or loss. 21  Operations on Fractions Addition and Subtraction of Similar Fractions In adding or subtracting similar fractions, add or subtract their numerators and copy their common denominator. 22 Addition and Subtraction of Similar Fractions 23  Operations on Fractions Addition and Subtraction of Dissimilar Fractions In adding or subtracting dissimilar fractions, find the lowest common multiple (LCM) first. 24  Operations on Fractions Addition and Subtraction of Dissimilar Fractions Then, express the fractions into its equivalent with the LCM as the denominator. 25  Operations on Fractions Addition and Subtraction of Dissimilar Fractions Finally, add or subtract their numerators. 26 Addition and Subtraction of Dissimilar Fractions 27  Operations on Fractions Multiplication of Fractions Suppose you want to know how much is half of your inheritance, and all you know is that your inheritance is half of the original value. To solve this, we will use the concept of fraction multiplication. 28  Operations on Fractions Multiplication of Fractions If a, b, and c are real numbers and b and c are not equal to zero, then 29 Multiplication of Fractions 30  Operations on Fractions Division of Fractions We use division in many areas of businesses. If you want to fairly divide a portion, we use the rule of division of fractions. 31 Division of Fractions 32  Operations on Fractions Division of Fractions If a, b, and c are real numbers and b and c are not equal to zero, then 33  Check Your Progress 1. Answer area 34  Check Your Progress 2. Answer area 35  Problems Involving Fractions We can use our knowledge about fractions to solve some problems. We can solve them by following these steps: Step 1: Identify what is required in the problem. Step 2: Identify the given in the problem. Step 3: Write the working equation. Step 4: Substitute the given values. Step 5: Find the answer. 36  Problems Involving Fractions Example 1 Athena bought 5 3/4 kg of chicken in the market. Of these, 2 1/2 kg of chicken was fried and 1 kg was used for adobo. How many kilograms of chicken were left? Solution: Step 1: Identify what is required in the problem. You are asked to calculate for the mass (m) of the chicken (c) left after some portions are cooked as fried (f) and adobo (a). 37  Problems Involving Fractions Step 2: Identify the given in the problem. 5 3/4 kg (c) chicken 2 1/2 kg (f) fried 1 kg (a) adobo Step 3: Write the working equation. m = c - (f + a) 38  Problems Involving Fractions Step 4: Substitute the given values. Step 5: Find the answer. 2 1/4 kg of chicken was left. 39  Problems Involving Fractions Example 2 Anthony bought 8 1/4 kg of macadamia nuts, 5 3/4 kg of pili nuts, and 5 5/6 kg of almonds for his cookies business. How many kilograms of ingredients does he have? Solution: Step 1: Identify what is required in the problem. You are asked to calculate for the mass (n) of the nuts Anthony has in total. 40  Problems Involving Fractions Step 2: Identify the given in the problem. 8 1/4 kg (m) macadamia 5 3/4 kg (p) pili 5 5/6 kg (a) almond Step 3: Write the working equation. n=m+p+a 41  Problems Involving Fractions Step 4: Substitute the given values. Step 5: Find the answer. Anthony has 19 5/6 kg of ingredients. 42  Check Your Progress Ulysses bought 6 ½ kg of beef, 3 ¾ kg of pork, and 5 ½ kg of 1 chicken. If 1kg of beef costs ₱400, 1 kg of pork costs ₱300, and 1kg of chicken costs ₱170, how much change is left if he gave ₱5,000 for his purchase? Answer area 43  Check Your Progress Loie spends 2 ¼ hours surfing the web. She uses 3/4 of 2 this time for research. How much time does she allot for research? Answer area 44  Make Sure Your Team’s Workload Is Divided Fairly Kyle, The Bulleit Group CEO, says that maintaining an even workload for his team is a challenge—even more so when it comes to managing the workloads of his high achievers and workhorses. While these bright individuals are frequently deserving of first-choice assignments, Kyle recognizes the importance of not overworking them and the importance of spreading projects around to promote other team members. Make Sure Your Team’s Workload Is Divided Fairly Rebecca Knight, “Case Study #2: Talk to your employees one-on-one about their share of the collective workload,” (Harvard Business Review, November 14 2016), https://hbr.org/amp/2016/11/make-sure-your-teams-workload-is-divided-fairly, last accessed on October 16 2021. 45  Make Sure Your Team’s Workload Is Divided Fairly Kyle previously managed a top performer named Janice while leading a team at Reuters. He recalls one particular instance when a high-profile and exciting task presented itself, and Kyle's instinct was to invite Janice to work on it. "I was aware of her work ethic," he explains. "She was never late for a deadline. Make Sure Your Team’s Workload Is Divided Fairly Rebecca Knight, “Case Study #2: Talk to your employees one-on-one about their share of the collective workload,” (Harvard Business Review, November 14 2016), https://hbr.org/amp/2016/11/make-sure-your-teams-workload-is-divided-fairly, last accessed on October 16 2021. 46  Make Sure Your Team’s Workload Is Divided Fairly And she was trustworthy." However, Kyle had an open conversation with Janice prior to making the request. "I spoke with her about what she was currently juggling. Additionally, I urged her to consult with her clients and team members to evaluate whether this additional work would fit into her calendar," he says. Make Sure Your Team’s Workload Is Divided Fairly Rebecca Knight, “Case Study #2: Talk to your employees one-on-one about their share of the collective workload,” (Harvard Business Review, November 14 2016), https://hbr.org/amp/2016/11/make-sure-your-teams-workload-is-divided-fairly, last accessed on October 16 2021. 47  Make Sure Your Team’s Workload Is Divided Fairly Janice was able to complete the project, but Kyle assisted her in being strategic with additional responsibilities that presented up. "At times, she purposely sat on the bench, waiting for a better moment to present itself," he recalls. "Because she was quite self- regulated, I assisted her in assessing opportunities." Janice currently manages corporate communications for a leading European consultancy. Make Sure Your Team’s Workload Is Divided Fairly Rebecca Knight, “Case Study #2: Talk to your employees one-on-one about their share of the collective workload,” (Harvard Business Review, November 14 2016), https://hbr.org/amp/2016/11/make-sure-your-teams-workload-is-divided-fairly, last accessed on October 16 2021. 48 Keep in Mind Fraction is a numerical representation of the quotient of two numbers expressed as p/q, where q≠0. The three kinds of fractions are proper, improper, and mixed number. The fundamental operations of fractions are addition, subtraction, multiplication, and division. 49 Keep in Mind 50  Try This A. True or False. Write True on the blank if the statement is correct. Otherwise, write False. _______________1. Improper fractions are fractions whose values are greater than 1. _______________2. 3/4 is an example of a mixed number. _______________3. When adding or subtracting similar fractions, add or subtract their denominators and copy their common numerators. _______________4. When dividing fractions, get the reciprocal of both fractions then proceed to multiplication. _______________5. If a fraction’s value is less than 1, then it is a proper fraction. 51  Try This A. True or False. Write True on the blank if the statement is correct. Otherwise, write False. _______________6. In multiplying fractions, multiply the numerators of each fraction and also multiply their denominators. Simplify the fraction if needed. _______________7. Mixed number is also a fraction. _______________8. In adding or subtracting dissimilar fractions, add or subtract their numerators and copy the common denominator. _______________9. The denominator of fraction can be zero. _______________10. 11 3/5 is an example of a mixed number. 52  Try This B. Identify the kind of fraction indicated on each number. 1. 5/6 ___________________________ 2. 4/11 ___________________________ 3. 9/11 ___________________________ 4. 23/4 ___________________________ 5. 1 6/7 ___________________________ 53  Practice Your Skills Play with Fractions. Solve the following problems: 1. Suppose your monthly salary is already credited to your account. One-fourth of your salary goes to your rent. Two- fifths go to your water, electricity, and phone bills. If you earned ₱20,000 a month, how much money is left to be spent? Answer area 54  Practice Your Skills Play with Fractions. Solve the following problems: 2. Aling Lolita inherited 1/5 hectares (ha) of land from her parents. She wants to divide this lad equally among her 3 children. What is the area of the land that each child will get? Answer area 55  Practice Your Skills Play with Fractions. Solve the following problems: 3. Phoebe ordered 40 flowers. Two-fifths of the flowers are pink roses. How many are not pink roses? Answer area 56  Practice Your Skills Play with Fractions. Solve the following problems: 4. Mrs. Gerona’s monthly salary is ₱25,000. She spends 3/5 of her salary for her family’s food, 1/5 for the bills, and 1/10 for other expenses. How much is Mrs. Gerona’s total monthly expenses? Answer area 57  Practice Your Skills Play with Fractions. Solve the following problems: 5. Jesse has a plank of wood with a length of 2/3 meters (m). He cuts the plank wood into shorter pieces, each measuring 1/6 m. How many pieces of wood does Jesse have now? Answer area 58  Challenge Yourself Solve the following: 1. Suppose Laura and Phillip are among the partners of the same company. Profit is divided among themselves, with 1/6 going to Laura and 1/8 to Philip, while the remaining goes to other partners. At the end of the year, the company’s profit reached ₱1,260,000. 1.1 How much is Laura’s share in the company’s profit during the year? Answer area 59  Challenge Yourself Solve the following: 1. Suppose Laura and Phillip are among the partners of the same company. Profit is divided among themselves, with 1/6 going to Laura and 1/8 to Philip, while the remaining goes to other partners. At the end of the year, the company’s profit reached ₱1,260,000. 1.2 How much more is Laura’s share as compared to Phillip’s share? Answer area 60  Challenge Yourself Solve the following: 2. Jane has 5 1/4 yards of lace. If a handkerchief requires ¾ yards of lace and Jane will make 3 handkerchiefs, how many yards of lace will be left? Answer area 61  Challenge Yourself Solve the following: 3. Clarisa’s Siomai prepared 250 pieces of siomai. If 150 pieces were sold, what fraction of the total number of pieces of siomai was left? Answer area 62 Photo Credits Bibliography Slide 1: Business Planning by Creative Fractions. 2017. MathIsFun. Commons Zero - CC0 is licensed under CC0 https://www.mathsisfun.com/fractions- Public Domain via Public Domain Pictures. menu.html. Slide 3: Hangers, Clothing, Shopping, Market by Pixabay is licensed under Pixabay License. Lopez, B.C., Martin-Lundag, L.C. 2016. Business Slide 4: Parts Pieces Pie Chart Diagram Mathematics. Quezon City: Vibal Group Inc. Statistics by Creative Commons Zero - CC0 is licensed under CC0 Public Domain via Max Rebecca Knight, “Case Study #2: Talk to your Pixel. employees one-on-one about their share of the Slide 5: Business Analysis by Creative collective workload,” (Harvard Business Review, Commons Zero - CC0 is licensed under CC0 November 14 2016), Public Domain via Public Domain Pictures. https://hbr.org/amp/2016/11/make-sure-your- teams-workload-is-divided-fairly, last accessed on October 16 2021. Villanueva, T. T. 2017. Business Mathematics. Valenzuela City: Tru-Copy Publishing House, Inc. 63