Business Mathematics PS 11 Q1 0202.pptx

Business Mathematics

1. Proportions Lesson 2.2 ‹#› Business Mathematics Accountancy, Business, and Management

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3. “The result of your work is proportional to the amount of effort you put into it.” ‹#›

4. Proportion expresses that two things are equal. It is essential in deciding if things are fair. ‹#›

5. Disproportionate: when something is too small or too big compared to something else. ‹#›

6. ‹#› The sales of products x , y , and z in a month are ₱90,000, ₱67,500, and ₱112,500, respectively. The ratio of the sales of x to the sales of y is 4:3. Suppose that the sales of product x next month are forecast to be ₱81,000. What will be the sales of product y if the sales of the two products maintain the same ratio? Product Sales

7. ‹#› Step 1: Let the ratio of sales of x and y be 4:3. That is, ”x is to y, as 4 is to 3” Solution Step 2: Rewrite the expression in Step 1 in symbols equating them. x : y = 4 : 3 or

8. ‹#› Step 3: Substitute x = ₱81,000 and solve for y. Solution Step 4: Clear the fraction by using cross multiplication ₱81,000 ⋅ 3 = 4y ₱243,000 = 4y

9. ‹#› Step 5: Divide both sides of the equation by 4 to find the answer. The projected sales of product y next month is ₱60,750. Solution

10. In the given problem, what type of numbers and measurements were compared? What does proportion denote about the relationship between these numbers and measurements? What do operations on proportions aim to verify or calculate? ‹#› Questions to Ponder

11. This lesson aims to target the following DepEd competencies: Write proportions illustrating real-life situations (ABM_BM11RP-Ie-2) . Solve problems involving direct, inverse, and partitive proportion (ABM_BM11RP-Ie-4) . ‹#›

12. ‹#› At the end of this lesson , you should be able to do the following: Describe the difference of proportions from ratios. Demonstrate the properties of proportion. Solve problems involving proportions.

13. ‹#› How can proportion express fairness in business transactions?

14. In ratio, the numerator and denominator dependent on each other. when one variable changes, it affects the other This concept will help you understand the concept of proportion . Proportion ‹#›

15. compares two or more ratios expresses that these ratios are equal written using the symbols: :: or = compares two quantities with the same unit written in fraction or percentage when in proportion, it is written as fraction Ratio Proportion ‹#›

16. refers to a part, share, or number considered in correlative relation to a whole t wo sets can be directly or inversely proportional Definition of Proportion ‹#›

17. Definition of Proportion Directly proportional if two sets of given numbers are increasing or decreasing in the same ratio y ∝ x Inversely proportional if one quantity increases, and the other quantity decreases in the same ratio y ∝ 1/x ‹#›

18. Means-Extremes Property or Cross-Product Property Property 1 Properties of Proportion ‹#›

19. Property 1 Properties of Proportion ‹#›

20. Means or Extremes Switching Property Property 2 Properties of Proportion ‹#›

21. Property 2 Properties of Proportion ‹#›

22. Upside down property Property 3 Properties of Proportion ‹#›

23. Property 3 Properties of Proportion ‹#›

24. Denominator Addition/Subtraction Property Property 4 Properties of Proportion ‹#›

25. Denominator Addition/Subtraction Property Property 4 Properties of Proportion ‹#›

26. Joem drinks 8 ounces of orange juice for every 5 tarts he eats. If he eats 20 tarts, how many ounces of orange juice does he drink? Let n be the unknown ounces of orange juice. ‹#› Illustrating the Properties of Proportion

27. By Cross-Product Property, If values are not equal to one another then Property 1 will produce a false statement. ‹#› Illustrating the Properties of Proportion

28. By Means or Extremes Switching Property, ‹#› Illustrating the Properties of Proportion

29. By Upside-Down Property, ‹#› Illustrating the Properties of Proportion

30. By Denominator Addition/Subtraction Property, ‹#› Illustrating the Properties of Proportion

31. A 2,205-pound seawater crocodile eats 25 pounds of meat per day. How many pounds of meat would you expect a 330-pound seawater crocodile to eat per day? Express your answer by presenting all the properties of proportion. ‹#› 1 Answer area

32. Problems Involving Proportion t o predict or project increase in revenue if more products are sold t o determine the total selling price if the quantity is increased ‹#›

33. t o determine if share in profit or expenses are proportional and fair ‹#› Problems Involving Proportion

34. Example 1: For every ₱1,500 Dania spends on her Mastercard, she earns 3 frequent flyer miles with ABC Airlines. If Dania spends ₱91,350 on her card, how many frequent flyer miles will she earn? ‹#› Problems Involving Proportion

35. Set up the proportion By cross multiplication, ‹#› Problems Involving Proportion

36. Simplify ‹#› Problems Involving Proportion ✅ Check

37. Example 2: One movie house sold 324 tickets in 4 days. At the rate, find the number of tickets it can expect to sell in 14 days. ‹#› Problems Involving Proportion

38. 1,134 tickets are expected to be sold in 14 days. ‹#› Problems Involving Proportion

39. Georgina paid ₱5,805,000 for a 3-unit apartment house. Find the cost for a 12-unit apartment house. ‹#› 2 Answer area

40. The travel restrictions caused by the COVID-19 pandemic adversely affected the travel and tourism industry. One of the sectors severely hit was the airline sector, which had been experiencing massive losses since 2019. The airline sector looks forward to more favorable economic conditions to aid their recovery. The Effect of Oil Price Increase in Airline Recovery ‹#› Mercurio, Richmond, “Rising oil prices add to airlines,” The Philippine Star, January 26, 2022. https://www.philstar.com/business/2022/01/26/2156321/rising-oil-prices-add-airlines-woes, last accessed February 3, 2022.

41. However, the rising oil prices would prevent the airline sector’s full recovery. In January 2022, the price of oil hit a seven-year high. According to airline executives, this hike in oil price would further tighten their already tight margins. The Effect of Oil Price Increase in Airline Recovery ‹#› Mercurio, Richmond, “Rising oil prices add to airlines,” The Philippine Star, January 26, 2022. h ttps://www.philstar.com/business/2022/01/26/2156321/rising-oil-prices-add-airlines-woes, last accessed February 3, 2022.

42. Fuel accounts for a higher proportion in the operating costs of low-cost carriers. Fuel is estimated to consist of about 30-50% of total business cost. Considering this proportion, a 20% increase in oil price, would directly cause an increase in the cost of business operations, while adversely affecting revenues and profit. According to airline executives, this mathematical relationship already provides an unambiguous picture for the future of the sector. The Effect of Oil Price Increase in Airline Recovery ‹#› Mercurio, Richmond, “Rising oil prices add to airlines,” The Philippine Star, January 26, 2022. https://www.philstar.com/business/2022/01/26/2156321/rising-oil-prices-add-airlines-woes, last accessed February 3, 2022 .

43. In the Philippines, business operations and production are highly dependent on fuel. Thus, a tick in oil prices causes an increase in the prices of basic commodities and services. The Effect of Oil Price Increase in Airline Recovery ‹#› Mercurio, Richmond, “Rising oil prices add to airlines,” The Philippine Star, January 26, 2022. https://www.philstar.com/business/2022/01/26/2156321/rising-oil-prices-add-airlines-woes, last accessed February 3, 2022.

44. ‹#› Proportion compares two or more ratios, and expresses that these are equal. Proportions are useful when comparing one measure or magnitude to another. It is denoted by the symbol “::” or “=”.

45. Properties of Proportion Description Property 1 Means-Extremes Property, or Cross Product Property Property 2 Means or Extremes Switching Property ‹#›

46. Properties of Proportion Description Property 3 Upside-Down Property Property 4 Denominator Addition/Subtraction Property ‹#›

47. Fill in the blanks. Write your answer on the corresponding space. 1 . Proportion is denoted using _________________ symbols. ‹#› Answer area

48. Fill in the blanks. Write your answer on the corresponding space. 2 . Ratios and proportions can be written as _________________. ‹#› Answer area

49. Fill in the blanks. Write your answer on the corresponding space. 3 . The ___________Property states that if then, ‹#› Answer area

50. Fill in the blanks. Write your answer on the corresponding space. 4 . Inverse proportion can be expressed as ________________. ‹#› Answer area

51. Fill in the blanks. Write your answer on the corresponding space. 5 . __________describes two quantities that rise and fall in the same ratio to each other. ‹#› Answer area

52. Winny opened a bakery shop and had sales of ₱16740 during the first four days. At the rate, estimates sales for 52 days. Show your solution to present the following: Property 1 ‹#› Answer area

53. Winny opened a bakery shop and had sales of ₱16740 during the first four days. At the rate, estimates sales for 52 days. Show your solution to present the following: Property 2 ‹#› Answer area

54. Answer the following questions: John and Jay agree to be partners where their profits are shared in a ratio of 3:5, respectively. If Jay receives ₱45,500, how much profit goes to John ? ‹#› Answer area

55. Answer the following questions: Steve and his software developer friend, Ron, agreed to launch an online app. They agreed to split the development cost in a ratio of 6:4 (Steve to Ron). Steve paid ₱413,284.00 while Ron paid ₱305,523.00. Is the amount Ron paid fair in terms of their agreement? ‹#› Answer area

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