4. Solving problems involving fractions, decimals, and percent.pptx

Problems involving percent, fractions and decimals

1. Solving problems involving fractions, decimals, and percent LESSON 2

2. OBJECTIVES Give real-life situations involving fractions, decimals, and percent. Identify the base, portion, and rate in a given problem Solve problems involving fractions Solve problems involving decimals, and Solve problems involving percent

3. Divide the numerator by the denominator Determine the place value of the last digit of the decimal. Copy the digits of the decimal as the numerator and write the place value of the last digit as the denominator of the fraction. Simplify the fraction into its lowest or simplest form (if applicable) Express 3/5 as a decimal Divide 3 by 5 Express 0.75 to fraction. Hundredths (1/100) 75/100 3. 75/100 *divide by 25 to simplify Answer: 0.6 Answer: = ¾ Fraction to Decimal Decimal to Fraction

4. 1. Move the decimal point 2 places to the right and affix the percent sign % Move the decimal point 2 places to the left and remove the percent sign % Express 0.52 in percent form 0.52 = 52% Express 28% to decimal. 28% = 0.28 Answer: 52% Answer: 0.28 Percent to Decimal Decimal to Percent

5. Express the fraction to decimal Express the resulting decimal to percent. Express the percentage to decimal. Express the resulting decimal to fraction. Convert ¼ to percent % Express 50% to fraction. 50% = 0.50 = 50/100 Answer: ¼ = 0.25 = 25% Answer: 5/10 = ½ Percent to Fraction Fraction to Percent

6. Important terms to understand Base (B) – refers to the total amount, original amount or the whole part. Portion (P) – refers to the part or partial amount of the base. Rate (R) – refers to the quantity or amount or measure of the portion to the base. This is usually written in percent, but it may also be a decimal or fraction.

7. Identify the base, portion and rate Mauricio bought half a kilo of coconut oil from a nearby store. Since a kilo of coconut oil costs P68.00, he paid P34.00 Identify the base, portion and rate. B = P68 ( it is the cost of a kilo of coconut oil). P = P34 (it is the only amount that Mauricio has paid. R = ½ (since he only bought half a kilo of coconut).

8. Identify the base, portion and rate In a department store in certain mall in General Santos City, Sarah has seen a jacket which costs P1,099 with 15% discount. Now, since the jacket is on sale, its new price is P934.15. B = P1,099 – original cost of the product P = P934 – new price for the jacket R = 15% - % or discount ; portion of the base

9. Identify the base, portion and rate Because of the social distancing protocol, the number of passengers that can ride in a tricycle was cut into half. Before, it can accommodate 6 passengers. But now it can accommodate only 3. B = 6 – original number of passengers that can ride P = 3 – new number of passengers that can ride R = ½ - percent of new passengers that can ride

10. Identify the base, portion and rate If Marina earns P25,000 monthly and always saves 20% of it, then she saves P5000 in a month. Base = P25,000 – total earnings in a month Portion = P5000 – savings as portion left from the salary Rate = 20% - percent of savings from the salary

11. The three forms of portion formula To solve for the base , use the formula: Example: Base = = 25,000 Base = = 1,666.67 5000 0.20 ____ 0.30 ____ 500

12. To solve for Portion , use the formula: The three forms of portion formula Portion = 0.20 x 25,000 = 5,000 Portion = 0.35 x 60,000 = 21,000

13. The three forms of portion formula To solve for Rate , use the formula: Rate = 5,000 _____ 25,000 = 0.20 or 20% Rate = 18,000 ___ 120,000 = 0.15 or 15%

14. Let’s Practice! Before the lockdown, a certain restaurant in a mall in General Santos City has an average daily income of P120,000. However, due to the lockdown, its average daily income dropped to P20,000 which is only 1/6 of its regular daily income. Base Rate Portion

15. Let’s Practice! Before the lockdown, a certain restaurant in a mall in General Santos City has an average daily income of P120,000. However, due to the lockdown, its average daily income dropped to P20,000 which is only 1/6 of its regular daily income. Base Rate Portion P 120,000 16% P 20,000

16. Let’s Practice! If Marina earns P25,000 monthly and always saves 20% of it, then she saves P5,000 in a month. Base Rate Portion

17. Let’s Practice! If Marina earns P25,000 monthly and always saves 20% of it, then she saves P5,000 in a month. Base Rate Portion P 25,000 20% P 5,000

18. Let’s Practice! Peter’s age is 14 years old while his father is 42. This means that his age is 1/3 of his father’s age. Base Rate Portion

19. Let’s Practice! Peter’s age is 14 years old while his father is 42. This means that his age is 1/3 of his father’s age. Base Rate Portion 42 33% 14

20. HOW TO SOLVE PROBLEMS INVOLVING FRACTIONS, DECIMALS AND PERCENT? Identify the given: base, rate and portion. If rate is in percent, express it as decimal or fraction. Identify the right formula Substitute the values of the given to the formula. Perform the indicated operations Make your conclusion.

21. HOW TO SOLVE PROBLEMS INVOLVING FRACTIONS, DECIMALS AND PERCENT? Carla has P100. She has to spend 30% of her money to buy some snacks. What is the amount that she should spend? STEPS: How to Solve? 1. Identify the given . Since the rate is in percent form, express it as decimal. Base = P100 Rate = 0.30 Portion = ?

22. HOW TO SOLVE PROBLEMS INVOLVING FRACTIONS, DECIMALS AND PERCENT? Carla has P100. She has to spend 30% of her money to buy some snacks. What is the amount that she should spend? STEPS: How to Solve? 2. Identify the right formula to be used. Portion = Rate x Base

23. HOW TO SOLVE PROBLEMS INVOLVING FRACTIONS, DECIMALS AND PERCENT? Carla has P100. She has to spend 30% of her money to buy some snacks. What is the amount that she should spend? STEPS: How to Solve? 3. Substitute the values of the given to the formula. Portion = 0.30 x P100

24. HOW TO SOLVE PROBLEMS INVOLVING FRACTIONS, DECIMALS AND PERCENT? Carla has P100. She has to spend 30% of her money to buy some snacks. What is the amount that she should spend? STEPS: How to Solve? 4. Perform the indicated operations. Portion = P 30.00

25. HOW TO SOLVE PROBLEMS INVOLVING FRACTIONS, DECIMALS AND PERCENT? Carla has P100. She has to spend 30% of her money to buy some snacks. What is the amount that she should spend? STEPS: How to Solve? 5. Make your conclusion. Therefore, Carla should spend P30.00

26. HOW TO SOLVE PROBLEMS INVOLVING FRACTIONS, DECIMALS AND PERCENT? Joanna got 48 out of 60-item Business Math test. What percent was her score in the test? STEPS: How to Solve? 1. Identify the given. Base = 60 Portion = 48 Rate = ?

27. HOW TO SOLVE PROBLEMS INVOLVING FRACTIONS, DECIMALS AND PERCENT? Joanna got 48 out of 60-item Business Math test. What percent was her score in the test? STEPS: How to Solve? 2. Identify the right formula to be used. Rate = Portion / Base

28. HOW TO SOLVE PROBLEMS INVOLVING FRACTIONS, DECIMALS AND PERCENT? Joanna got 48 out of 60-item Business Math test. What percent was her score in the test? STEPS: How to Solve? 3. Substitute the values of the given to the formula Rate = 48/60

29. HOW TO SOLVE PROBLEMS INVOLVING FRACTIONS, DECIMALS AND PERCENT? Joanna got 48 out of 60-item Business Math test. What percent was her score in the test? STEPS: How to Solve? 4. Perform the indicated operations. Rate = 48/60 Rate = 0.8 or 80%

30. HOW TO SOLVE PROBLEMS INVOLVING FRACTIONS, DECIMALS AND PERCENT? Joanna got 48 out of 60-item Business Math test. What percent was her score in the test? STEPS: How to Solve? 5. Make your conclusion Therefore, Joanna got 80% in the test.

31. HOW TO SOLVE PROBLEMS INVOLVING FRACTIONS, DECIMALS AND PERCENT? P 250 is 20% of the original amount. What is the original amount? STEPS: How to Solve? 1. Identify the given. Portion = P 250.00 Rate = 20% = 0.20 Base = ?

32. HOW TO SOLVE PROBLEMS INVOLVING FRACTIONS, DECIMALS AND PERCENT? P 250 is 20% of the original amount. What is the original amount? STEPS: How to Solve? 2. Identify the right formula to be used. Base = Portion / Rate

33. HOW TO SOLVE PROBLEMS INVOLVING FRACTIONS, DECIMALS AND PERCENT? P 250 is 20% of the original amount. What is the original amount? STEPS: How to Solve? 3. Substitute the values of the given to the formula. Base = 250 / 0.20

34. HOW TO SOLVE PROBLEMS INVOLVING FRACTIONS, DECIMALS AND PERCENT? P 250 is 20% of the original amount. What is the original amount? STEPS: How to Solve? 4. Perform the indicated operations. Base = 1,250

35. HOW TO SOLVE PROBLEMS INVOLVING FRACTIONS, DECIMALS AND PERCENT? P 250 is 20% of the original amount. What is the original amount? STEPS: How to Solve? 5. Make your conclusion. Therefore, the amount is 1,250

36. Questions?

37. Exercises The Ramos family saved P720,000 which is 80% of what they need to buy a house and lot. How much more do they need? Identify the base, rate and portion. Show your solution. Carlo and Aaron decided to put up a bakeshop. If Carlo will invest 25,000 while Aaron will invest P15,000, what percent is Carlo’s investment to Aaron? Identify the base, rate and portion. Show your solution. Nikko a college student in a certain school in General Santos City, has P 200 daily allowance. If he saves ¼ of his allowance, how much does he save in a day? Identify the base, rate and portion. Show your solution.

38. Group activity Divide the class to into 4 groups. Pick 1 (one) problem. Show a creative visual representation on the assigned problem. Present it to the class. Material: any preferred materials or crafts Presentation: Next meeting

39. Group activity Divide the class to into 4 groups. Leader will pick a problem. Show a creative visual representation on the assigned problem. Present it to the class. Use any preferred materials or crafts Presentation: Next meeting

40. Scoring guide Content – 45% (accurate and correct information) Creativity – 30% (well-designed) Presentation skills – 25% (manner of delivery)

41. Problem # 1

42. Problem # 2

43. Problem # 3

44. Problem # 4

45. Finding the rate of increase / (decrease) Rate of Increase/(Decrease) = where = original quantity = new quantity The difference ( ) is positive if it is an increase , and a negative if it is a decrease  

46. Ms. Romero’s current salary is ₱3,600 a month. Her previous salary was ₱3,200. What is the rate of increase in her salary? Given: Current salary = ₱3,600 = Previous salary = ₱3,200 = R = = = = = 0.125 = 12.5%   Finding the rate of increase / (decrease)

47. Currently, 1 kilo of sugar cost ₱150.00, last year it only cost ₱ 120.00. What is the rate of increase in the price of sugar? Given: Current salary = ₱150 = Previous salary = ₱120 = R = = = = = 0.25 = 25%   Finding the rate of increase / (decrease)

48. Finding the rate of (increase / decrease) 24 oras reported that there will be a price rollback in gasoline products. Per liter it will now cost 40.00 comparing to its previous cost of 60/liter. What is the rate of rollback in the price of gasoline products? Given: Current salary = ₱40 = Previous salary = ₱60 = R = = = = - = - 0.33 = - 33%   Rate of decrease

49. Questions?

50. Thank You!