1. Math 5 Multiplying Decimals Instructor: Mrs. Tew Turner

2. In this lesson we will learn about multiplying decimals.

3. Math Warm-up Suppose school starts at 8:45 A.M. and is out at 2:30 P.M. How long is the school day?

4. Math Warm-up ANSWER Suppose school starts at 8:45 A.M. and is out at 2:30 P.M. How long is the school day? 5 hours 45 minutes

5. In this lesson we will answer the question: How can you multiply decimals?

6. Vocabulary Review estimation - to give an approximate value rather than an exact answer.

7. Vocabulary Review factors - numbers that are multiplied to get a product. 7 × 7 = 49 product - the number that is the result of multiplying two or more factors. 7 × 7 = 49

8. Vocabulary rectangular array - An arrangement of objects into rows and columns that form a rectangle. All rows and columns must be filled. Each row has the same number of objects and each column has the same number of objects. Ex.

9. In your Math Notebook Is this a rectangular array? Why or Why not?

10. In your Math Notebook ANSWER This is not a rectangular array because all of the spaces are not filled. This must be filled for it to be a rectangular array.

11. Connecting to Previous Learning In the previous unit you worked on multiplying larger numbers. What do you remember about multiplication? ×

12. Connecting to Previous Learning Multiplication is repeated addition. We use multiplication because it is faster than adding a number over and over again, especially when multiplying large numbers.

13. How do you multiply decimals? Let’s start by using estimation to help us. Remember you have used estimation to help you know if you calculated a reasonable product.

14. 32.84 x 4.6 = ? Find an estimate for this equation using compatible numbers. Think whole numbers!

15. 32.84 x 4.6 = ? Find an estimate for this equation using compatible numbers. Think whole numbers! 30 x 5 = 150 The actual product will be close to 150.

16. Estimate the following products 275 x 3.8 = 27.5 x 3.8 = 2.75 x 3.8 = Should the products be the same? Why or why not?

17. Estimate the following products 275 x 3.8 = 27.5 x 3.8 = 2.75 x 3.8 = The products should be different because the decimal point moved in the factors of each problem, making the factor a different value. This will make the products different.

18. Estimate the following products 275 x 3.8 = 300 x 4 = 1200 27.5 x 3.8 = 30 x 4 = 120 2.75 x 3.8 = 3 x 4 = 12 What do you notice about the products as the decimal point moves in the first factor?

19. Estimate the following products 275 x 3.8 = 300 x 4 = 1200 27.5 x 3.8 = 30 x 4 = 120 2.75 x 3.8 = 3 x 4 = 12 The decimal point moves to the left, which makes the value of the factor smaller. This makes the product smaller.

20. 3 x 0.4 In this course we will find the exact answer to problems like this one (multiplication with decimals) by using models.

21. Remember the models we used to represent decimals in unit one? ones tenths hundredthsthousandths

22. This is how you can draw these models in your math notebook. onestenths hundredths thousandths 

23. 3 x 0.4 Try to solve this in your math notebook using these models: onestenthshundredths

24. 3 x 0.4 You can use repeated addition to help you solve this problem. Start with 4 tenths.

25. 3 x 0.4 You can use repeated addition to help you solve this problem. Next, make 3 total groups of 4 tenths. You already have one.

26. 3 x 0.4 You can use repeated addition to help you solve this problem. Then, add all of the tenths to find the total. = 12 tenths

27. 3 x 0.4 You can use repeated addition to help you solve this problem. Finally, convert this to a number. = 12 tenths = 1 whole and 2 tenths 1.2

28. 3.2 x 2.4 For this type of problem, multiplying two decimals, you will use a rectangular array.

29. 3.2 x 2.4 Notice that I used our models to create the beginning of an array. The factors are used for the length and width of the array.

30. 3.2 x 2.4 Notice the use of partial products.

31. 3.2 x 2.4 How did the hundredths get there? Remember that the entire array must be filled in – the hundredths were needed to fill in the remainder of the array.

32. 3.2 x 2.4 2 10 4 10 8 100 x= You can also turn the decimals into fractions and multiply. You multiply the numerators (top), and the denominators (bottom).

33. Document Camera Get your notebook and pencil ready. Make sure you have the Lesson # and date on your page.

34. Guided Practice 2 x 4.8 1.6 x 3.7 5 x 1.2 4.1 x 1.81

35. Independent Practice A gumball costs $0.22. How much do 5 gumballs cost? Estimate the total, and then calculate. Was your estimate close?

36. Independent Practice ANSWER

37. Independent Practice ANSWER I estimate that the total cost will be a little more than a dollar. I know that 5- 20’s equal 100 and we have 5- 22’s. I have 10 whole columns shaded and 10 individual boxes shaded. The 10 columns equal 1 whole. The 10 individual boxes equal 10 hundredths or 1 tenth. My answer is $1.10. My estimate was a little more than a dollar, and my answer was $1.10. I was really close.

38. Lesson Review Use models to solve multiplication problems when one product is a whole number and the other contains a decimal. First, estimate the product.

39. Lesson Review Use models in a rectangular array to solve multiplication problems when both products contain a decimal. Use partial products to help solve the problems.

40. In your Math Notebook Quick Check Give an estimate and then solve. 1.A donut store uses 9.9 kilograms of sugar each hour. How many kilograms of sugar will the store use in 10 hours? 2.A bakery uses 4.4 kilograms of flour each hour. How many kilograms of flour will the bakery use in 2 hours?

41. In your Math Notebook Quick Check- ANSWERS 1. 9.9 x 10 = 99 kilograms 2.4.4 x 2 = 8.8 kilograms

42. Today you learned how to multiply decimals. Good Work with this lesson.