1. Bell Work: Simplify 3 – 2.94

2. Answer: 0.06

3. Lesson 25: Multiplying and Dividing Decimal Numbers

4. To multiply decimal numbers with pencil and paper we do not need to align the decimal points. We instead multiply to find the product and then count all the decimal places in the factors to locate the proper position for the decimal point in the product.

5. Example: Simplify 0.3 x 0.12

6. Answer: 3/10 x 12/100 = 36/1000 = .036

7. Example: Simplify (1.5) 2

8. Answer: 1.5 x

9. Example: Simplify 4.25 x 10

10. Answer: Multiplying a decimal number by 10 simply shifts the decimal point one place to the right. = 42.5

11. What is 4.25 x 10,000? How many places is the decimal shifted to the right?

12. Answer: 42,500 4 places

13. Example: What is the cost of 0.86 pounds of cheese at $3.90 per pound? Explain why your answer is reasonable.

14. Answer: $3.90 x 0.86 = $ = $3.35 The answer is reasonable because 0.86 pounds is a little less than one pound and $3.35 is a little less than $3.90, which is the price per pound.

15. When dividing by a whole number the decimal point in the quotient is placed above the decimal point of the dividend. In this example the quotient and dividend have the same number of decimal places. We fill empty places with zero if necessary ÷ 6 = 0.07

16. Example: Simplify 0.48 ÷ 8

17. Answer: 0.06

18. Example: Simplify 4.8 ÷ 5

19. Answer: 0.96

20. Example: Simplify 4.8 ÷ 10 2

21. Answer: 4.8 ÷ 100 = 0.048

22. When dividing by a decimal number we take an extra step to make an equivalent problem in which the divisor is a whole number. Multiplying the dividend and the divisor by 10 shifts the decimal points one place without changing the quotient. Instead of showing the multiplication we can shift both decimal points the same number of places before we divide.

23. Example: Simplify 3.6 ÷ 0.6

24. Answer: 36 ÷ 6 = 6

25. Example: Simplify 3 ÷ 0.06

26. Answer: 300 ÷ 6 = 50

27. Example: Chloe drover her car 236. 4 miles on 9. 6 gallons of gas
Example: Chloe drover her car miles on 9.6 gallons of gas. Find the number of miles per gallon the car averaged to the nearest mile per gallon.

28. Answer: Miles/gallon 236.4/9.6  10/10 = 2364.000/96 = 24.625

29. Decimal Arithmetic Reminders
Operation
+ or - x
÷ by whole (W)
÷ by decimal (D)
Memory Cue
Line up decimals
Multiply, then count decimal places
Move decimal place value over
You may need to…
Place a decimal point to the right of a whole number
Fill empty places with zeros

30. HW: Lesson 25 #1-30 Due Tomorrow