week 3 ( ratio and proportion)

6. WEEK 3 AND 4: BUSINESS MATH

7. Learning Objectives: • MOST ESSENTIAL LEARNING COMPETENCY • Identify the different kinds of proportions and write examples of real-life situations for each. (ABM_BM11RP_Ie-3) • Solve problems involving direct, inverse and partitive proportion. (ABM_BM11RP-Ie-4)

8. Essential Question • How are the concepts of ratio and proportion being used in business?

9. How is the concept of ratio can be used in business? • Due to covid -19 pandemic, you thought of putting up an online business to have an additional income. You decided to try to bake banana cake at home. Based on the recipe you have searched online; recipe calls for 2 cups of flour and 1 cup of sugar. Then from this, you decided to double the recipe. First ratio of ingredients- 2cups of flour: 1 cup of sugar If doubled, it will become 4 cups of flour: 2 cups of sugar

10. 4 cups of flour: 2 cups of sugar

11. Ratio • Comparison of two or more quantities ( a: b) • To express ratio, use a. fraction b. colon c. to

12. Example: • Express the following ratio in similar unit and in lowest term. 50 minutes to 2 hours 1 hour= 60 mins. 50 mins: 120 mins. 5 mins.: 12 mins.

13. Example: • Express the following ratio in similar unit and in lowest term. 2000 g to 1.5 kg 1 kg=1000g 2000 g: 1500 g 4g: 3g

14. Use ratio to make decisions • In the dry goods market, one bakery sells pandesal at 6 pieces for Php 18, while the other bakery sells 10 pieces for Php 25. Which bakery sells pandesal at a cheaper price. 1. Php 18: 6 pcs. = Php 3/pc 2. Php 25: 10 pcs. = Php 2.5/pc

15. A banana cupcake recipe calls for 2 eggs for every 1.5 cups of flour

16. Rate • a special type of ratio used to compare quantities being compared that cannot be expressed in the same unit.

17. Other examples of rate • A taxi travels at an average speed of 70 kilometers per hour • An office secretary can type 120 words per unit • A painter consumes paint of one gallon of paint for every 50 sq.ft.of surface.

18. Sample problem using rate • As a proofreader, Eliza reads 3 pages of a manuscript in 15 minutes. At this rate, how many pages will she be able to read in 45 minutes. 3 pages:15 mins. 9 pages :45 mins.

19. How to use ratio • The ratio of boys and girls in the class is 12 to11. • This means, for every 12 boys you can find 11 girls to match. • There could be just 12 boys, 11 girls. • There could be 24 boys, 22 girls. • There could be 120 boys, 110 girls…a huge class

20. The ratio of length and width of this rectangle is 4 to 1. The ratio of cats and dogs at my home is 2 to 1. How many dogs and cats do I have? We don’t know, all we know is if they’d start a fight, each dog has to fight 2 cats.

21. How to simplify ratios? • The ratios we saw on last slide were all simplified. How was it done? • The ratio of boys and girls in the class is • The ratio of the rectangle is • The ratio of cats and dogs in my house is Ratios can be expressed in fraction form… This allows us to do math on them.

22. Now I tell you I have 12 cats and 6 dogs. Can you simplify the ratio of cats and dogs to 2 to 1? = = A person’s arm is 80cm, he is 2m tall. Find the ratio of the length of his arm to his total height • Let’s try cm first!

23. Two ratios and to be equal

24. Proportion • The equality of two ratios a:b= c:d

25. Proportion To find the missing term in a proportion, product of means=product of extremes ad=bc

26. Example: Find the missing term in the proportion. 9:3=126:a = =

27. Example: If a photocopying machine can make 40 copies in one minute, how many copies can it make in 8.4 minutes? 40:1=x:8.4 336=x 336 copies in 8.4 minutes

28. Kinds of Proportion • Direct Proportion • Inverse Proportion • Partitative Proportion

29. The more you eat, the more you grow. The lesser the number of items, the smaller the amount to pay. Direct Proportion • Two quantities are directly proportional if an increase in one quantity corresponds to a constant increase in the other quantity, or if a decrease in one quantity corresponds to a constant decrease in the other quantity.

30. Let us try looking at one word problem. Maita earns 450 pesos in selling sampaguita garlands on 4 Sundays. How many Sundays will it take her to earn 1,350 pesos? Is this a problem involving direct proportion? Why do you say so? Yes, it is, because the more Sundays Maita sells sampaguita, the more earnings she will have.

31. Maita earns 450 pesos in selling sampaguita garlands on 4 Sundays. How many Sundays will it take her to earn 1,350 pesos? . To solve this problem, after knowing what is asked, it’s better to list the given facts or numbers using a table Let n represent the number asked for in the problem

32. Maita earns 450 pesos in selling sampaguita garlands on 4 Sundays. How many Sundays will it take her to earn 1,350 pesos? Form two ratios given the numbers in the table. Equate the first ratio to the second ratio.

33. Solve for the value of n by using cross-multiplication. Indicate the proper label.

34. Maita earns 450 pesos in selling sampaguita garlands on 4 Sundays. How many Sundays will it take her to earn 1,350 pesos? Therefore, Maita should sell sampaguita garlands on 12 Sundays to earn 1,350 pesos.

35. Inverse Proportion Going up • When two quantities vary inversely an increase in one leads to the decrease in the other quantity and vice-versa, in inverse ratio. • a number is indirectly proportionate to another when as one value increases, the other decreases. Going down,

36. Example A supply of food lasts for a week for 20 families, how long would the supply last if 3 more families have to be supplied? Sol’n: (7days)(20 families)=(x days)(23 families) 140=23x about 6 days =x

37. Partitive Proportion • a whole is divided into several parts given a specified ratio.

38. Example: Abby and Jane were assigned to pay for their monthly house rental of P10,000 given the ratio 5:3. How much will abby pay for the house rental? Sol’n: 5+3=8, then = P1,250 Abby= 5(P1,250)=P6,250 Jane=3(P1,250)=P3,750 Therefore: abby will pay P6,250 for their house rental

39. Example A deceased person stated in his testament that his 30-hectare land be divided among his three children using 1:2:3 partition, the oldest getting the biggest share. How much will the second child receive? Sol’n: 1+2+3=6, then = 5 hectares Summarized: 1(5)=5 2(5)=10 3(5)=15 Therefore, the second child will receive 10 hectares

40. 1. Express in similar unit and in lowest term 16 pieces to 2.5 dozens. 2. If 5 oranges cost P60, how much will a dozen oranges cost? 3.Find the missing term in the proportion. 60:150= x:

41. Activity ( Group 1) • Solve the following problems. • When Mrs. Cruz went to abroad for an educational tour, she noticed that each guide goes along with three tourists. If there are 4 guides, how many tourists would they bring around? • The exchange rate of peso to a dollar in 2015 is P45.00 to $1. How much will you get for $6.50? • For every 3 metres of bamboo sticks, 5 frames of Christmas lanterns can be made. How many metres are needed to make 20 frames?

42. Activity ( Group 2) • Solve the following problems. • Three men can complete a project in 3 weeks. How many men will be needed if the project is to be completed in a week? • Twenty men can paint a building in 15 days. How many days will it take 30 men to paint the same building? • Five pipes can fill a tank in 2 hours. In how many hours can 1 pipe fill the same tank?

43. Activity ( Group 3) • Solve the following problems. • Divide 100 into parts 2:3:5. • Ruby, Rose and Ann are Business partners. They agreed to divide their profits in the ratio 1:2:3, How much should each receive if the total profit is P6000? • Divide a 72-m rope into 3 with the ratio 1:2:5. What is the measure of each rope?