MATHEMATICS5 Q2 3 solve multi-step probl.pptx

Math 5 Quarter 2 Week 3

1. Mastering Multi-Step Fraction Division Problems

2. Introduction to Multi-Step Fraction Problems Welcome to our journey through multi-step fraction division problems! We'll learn how to tackle complex problems involving fractions You'll become a fraction division expert by the end of this presentation Are you ready to dive in?

3. Review: Basic Fraction Division Remember: To divide fractions, we multiply by the reciprocal Example: 3/4 ÷ 1/2 = 3/4 × 2/1 = 6/4 = 1 1/2 Why do we use this method? Can you explain it to a classmate?

4. What are Multi-Step Problems? Multi-step problems involve more than one operation They may include addition, subtraction, multiplication, and division These problems test your ability to apply multiple skills Can you think of a real-life situation where you might use multi-step fraction problems?

5. Key Strategies for Multi-Step Problems Read the problem carefully Identify the important information Break the problem into smaller steps Solve one step at a time Check your answer - does it make sense?

6. Order of Operations: PEMDAS PEMDAS: Parentheses, Exponents, Multiplication and Division, Addition and Subtraction This order helps us solve problems correctly Remember: Multiplication and division are done left to right Addition and subtraction are also done left to right

7. Example 1: Two-Step Problem Problem: (2/3 ÷ 1/6) + 1/4 Step 1: Solve the division first Step 2: Add the result to 1/4 Can you solve this? Try it now!

8. Solution to Example 1 Step 1: 2/3 ÷ 1/6 = 2/3 × 6/1 = 4 Step 2: 4 + 1/4 = 16/4 + 1/4 = 17/4 = 4 1/4 Final answer: 4 1/4 Did you get it right? If not, where did you make a mistake?

9. Example 2: Three-Step Problem Problem: (3/4 - 1/2) × (2/5 ÷ 1/10) Step 1: Solve the subtraction inside the first parentheses Step 2: Solve the division inside the second parentheses Step 3: Multiply the results Give it a try before we solve it together!

10. Solution to Example 2 Step 1: 3/4 - 1/2 = 1/4 Step 2: 2/5 ÷ 1/10 = 2/5 × 10/1 = 4 Step 3: 1/4 × 4 = 1 Final answer: 1 How did you do? What was the most challenging part?

11. Common Mistakes to Avoid Forgetting to follow the order of operations Incorrectly simplifying fractions Mixing up multiplication and division of fractions Not reading the problem carefully What other mistakes have you encountered?

12. Real-World Application: Cooking Recipe calls for 3/4 cup of flour, but you only have 1/3 cup measure How many 1/3 cups do you need? This is a division problem: 3/4 ÷ 1/3 Can you solve it?

13. Solution: Cooking Problem Problem: 3/4 ÷ 1/3 Step: 3/4 × 3/1 = 9/4 = 2 1/4 You need 2 1/4 of the 1/3 cup measures This means 2 full 1/3 cups plus 1/4 of another 1/3 cup Can you think of other real-life situations where you might use fraction division?

14. Practice Problem 1 Sarah has 5/8 of a pizza. She wants to share it equally among 4 friends. What fraction of the whole pizza will each friend get? Hint: This is a division problem Try solving this on your own!

15. Solution: Practice Problem 1 Problem: 5/8 ÷ 4 Step 1: Convert 4 to a fraction: 4/1 Step 2: 5/8 ÷ 4/1 = 5/8 × 1/4 = 5/32 Each friend will get 5/32 of the whole pizza Did you get it right? If not, what mistake did you make?

16. Practice Problem 2 John runs 2/3 of a mile every day for 5 days. On the 6th day, he runs 1/2 mile more than his daily average. How far does John run on the 6th day? Hint: This is a multi-step problem involving multiplication and addition Give it a try before we solve it together!

17. Solution: Practice Problem 2 Step 1: Calculate total distance for 5 days: 2/3 × 5 = 10/3 miles Step 2: Calculate daily average: 10/3 ÷ 5 = 2/3 miles Step 3: Add 1/2 mile to daily average: 2/3 + 1/2 = 4/6 + 3/6 = 7/6 miles John runs 7/6 or 1 1/6 miles on the 6th day How did you approach this problem? Did you follow these steps?

18. Challenge Problem A recipe requires 3/4 cup of sugar. You want to make 1 1/3 times the recipe, but you only have a 1/8 cup measure. How many 1/8 cups of sugar do you need? This problem involves multiplication and division of fractions Take your time and try to solve it step by step!

19. Solution: Challenge Problem Step 1: Calculate sugar needed for 1 1/3 recipe: 3/4 × 4/3 = 1 cup Step 2: Convert 1 cup to eighths: 1 ÷ 1/8 = 1 × 8/1 = 8 You need 8 of the 1/8 cup measures Was this problem challenging? What strategy did you use to solve it?

20. Recap and Final Thoughts We've learned to solve multi-step problems with fraction division Remember to read carefully, use PEMDAS, and solve one step at a time Practice is key to mastering these problems What was your biggest takeaway from this lesson?

21. Keep Practicing! Fraction division problems are everywhere in real life The more you practice, the better you'll become Don't be afraid to ask for help when you need it What other topics would you like to explore related to fractions?

22. Review: What We've Learned So Far We can divide fractions by multiplying by the reciprocal Multi-step problems involve more than one operation The order of operations (PEMDAS) is crucial Breaking problems into smaller steps helps solve them What's been your favorite part of learning about fractions so far?

23. Identifying Key Information in Word Problems Look for numbers and fractions in the problem Identify important words like "of", "times", or "divided by" Underline or circle the question being asked Cross out unnecessary information Can you think of other ways to identify important information?

24. Converting Mixed Numbers to Improper Fractions Step 1: Multiply the whole number by the denominator Step 2: Add the numerator to the result Step 3: Put this sum over the original denominator Example: 2 3/4 = (2 x 4) + 3 = 11/4 Why do you think we sometimes need to convert mixed numbers?

25. Practice: Converting Mixed Numbers Convert these mixed numbers to improper fractions: 3 1/2 1 3/4 2 2/3 4 1/5 Share your answers with a partner. Did you get the same results?

26. Simplifying Fractions in Multi-Step Problems Simplify fractions whenever possible Divide both numerator and denominator by their greatest common factor Example: 6/8 simplifies to 3/4 Simplifying can make calculations easier When do you think it's most helpful to simplify fractions?

27. Finding Common Denominators Needed when adding or subtracting fractions Find the least common multiple (LCM) of the denominators Multiply each fraction by the appropriate factor Example: 1/2 + 1/3 → LCM is 6, so 3/6 + 2/6 How does finding common denominators help in fraction problems?

28. Practice: Finding Common Denominators Find common denominators for these pairs: 1/4 and 1/6 2/3 and 3/5 1/2 and 3/8 1/3 and 2/9 Discuss with a classmate: Which pair was the most challenging?

29. Multi-Step Problem: Baking a Cake A recipe needs 2 3/4 cups of flour and 1 1/2 cups of sugar You only have a 1/3 cup measure How many 1/3 cups of each ingredient do you need? Try solving this problem step-by-step. What's your strategy?

30. Solution: Baking a Cake Problem For flour: 2 3/4 ÷ 1/3 = 11/4 ÷ 1/3 = 11/4 × 3/1 = 33/4 = 8 1/4 For sugar: 1 1/2 ÷ 1/3 = 3/2 ÷ 1/3 = 3/2 × 3/1 = 9/2 = 4 1/2 You need 8 1/4 of the 1/3 cup for flour and 4 1/2 for sugar Did you get the correct answer? What steps did you follow?

31. Working with Decimals and Fractions Sometimes problems mix decimals and fractions Convert decimals to fractions or vice versa Example: 0.5 = 1/2, 0.75 = 3/4 Choose the form that makes the problem easier When might it be helpful to convert between decimals and fractions?

32. Practice: Converting Decimals to Fractions Convert these decimals to fractions: 0.25 0.8 0.375 0.6 Share your answers. Which conversion was the trickiest?

33. Multi-Step Problem: Pizza Party You have 3 1/4 pizzas left after a party Each pizza was cut into 8 slices If you eat 2.5 slices per day, how many days will the pizza last? What information do you need to solve this problem?

34. Solution: Pizza Party Problem Step 1: Convert 3 1/4 pizzas to slices: 3 1/4 × 8 = 26 slices Step 2: Convert 2.5 slices to a fraction: 2 1/2 slices Step 3: 26 ÷ 2 1/2 = 26 ÷ 5/2 = 26 × 2/5 = 52/5 = 10 2/5 days The pizza will last for 10 full days, plus part of another day How did you approach this problem? What was challenging about it?

35. Estimating Answers in Multi-Step Problems Round fractions to nearest half or whole Perform a quick mental calculation Use estimation to check if your final answer makes sense Example: 7/8 ÷ 2/3 is about 1, because 7/8 is close to 1, and 2/3 is close to 1 Why is estimating useful in multi-step problems?

36. Practice: Estimating Fraction Division Estimate the answers to these problems: 5/6 ÷ 1/3 7/8 ÷ 3/4 11/12 ÷ 2/3 3/4 ÷ 1/5 Compare your estimates with a partner. How close were you to the actual answers?

37. Real-World Application: Recipe Scaling A recipe serves 6 people and uses 3/4 cup of milk You want to make it for 10 people How much milk do you need? What steps will you take to solve this problem?

38. Solution: Recipe Scaling Problem Step 1: Find out how much the recipe needs to be scaled up 10 ÷ 6 = 5/3 (we need 5/3 times the original recipe) Step 2: Multiply the amount of milk by 5/3 3/4 × 5/3 = 15/12 = 1 1/4 cups of milk Did you solve it correctly? What other ingredients might you need to scale?

39. Creating Your Own Multi-Step Problems Think of a real-life situation involving fractions Include at least two operations (e.g., multiplication and division) Write out the problem clearly Solve it yourself to make sure it works! What kind of problem will you create?

40. Wrap-Up: Key Takeaways Break complex problems into smaller steps Use the order of operations (PEMDAS) Practice converting between mixed numbers, improper fractions, and decimals Estimate to check if your answer makes sense Apply fraction division to real-world situations What's the most important thing you've learned about multi-step fraction problems?

41. Question 1 A recipe calls for 3/4 cup of flour. You want to make 1 1/2 times the recipe. How many cups of flour do you need? a) 1/2 cup b) 9/8 cup c) 1 1/8 cup d) 1 1/4 cup What steps will you take to solve this problem?

42. Question 2 John has 2 1/3 pizzas left after a party. Each pizza is cut into 8 slices. If he eats 3 slices per day, how many days will the pizza last? a) 5 days b) 6 days c) 6 1/4 days d) 7 days How will you convert the mixed number to slices?

43. Question 3 Sarah is making friendship bracelets. She has 5/6 of a spool of thread. Each bracelet requires 1/4 of a spool. How many complete bracelets can Sarah make? a) 2 b) 3 c) 3 1/3 d) 4 What operation will you use to solve this problem?

44. Question 4 A recipe needs 2 3/4 cups of sugar. You only have a 1/3 cup measure. How many 1/3 cups of sugar do you need? a) 7 b) 8 c) 8 1/4 d) 9 How will you approach this multi-step problem?

45. Question 5 Tom runs 3/5 of a mile every day for 4 days. On the 5th day, he runs 1/3 mile more than his daily average. How far does Tom run on the 5th day? a) 3/5 mile b) 7/9 mile c) 8/9 mile d) 11/15 mile What information do you need to calculate first?

46. Question 6 A piece of ribbon is 4 2/3 feet long. You want to cut it into pieces that are 1/6 of a foot each. How many pieces can you make? a) 25 b) 26 c) 27 d) 28 How will you convert the mixed number to an improper fraction?

47. Question 7 You have 3/4 of a gallon of paint. Each room requires 1/6 of a gallon. How many complete rooms can you paint? a) 3 b) 4 c) 4 1/2 d) 5 What division problem will you set up to solve this?

48. Question 8 A cake recipe serves 8 people and uses 1 1/4 cups of milk. You want to make it for 12 people. How much milk do you need? a) 1 5/8 cups b) 1 7/8 cups c) 2 cups d) 2 1/4 cups How will you scale up the recipe?

49. Question 9 You have 2 1/2 pounds of apples. Each serving is 3/8 of a pound. How many complete servings can you make? a) 5 b) 6 c) 6 2/3 d) 7 What's your first step in solving this problem?

50. Question 10 A water tank is 5/6 full. If 1/4 of the tank's capacity is used each day, how many full days will the water last? a) 2 days b) 3 days c) 3 1/3 days d) 4 days How will you set up the division problem?

51. Answer Key 1. c) 1 1/8 cup 2. c) 6 1/4 days 3. b) 3 4. c) 8 1/4 5. c) 8/9 mile 6. c) 27 7. b) 4 8. b) 1 7/8 cups 9. c) 6 2/3 10. b) 3 days How did you do? Which questions were most challenging for you?