CHAPTER 6 C Rules of Signs for Decimals c GOAL Apply the rules of signs for calculating with decimals. You will need number lines a calculator with a sign change key Learn about the Math Positive and negative decimals can be represented on a number line. Communication Tip A decimal can be called a decimal number. 2.0 1.7 1.0 0.2 0 0.4 1.0 1.4 2.0? How can you add and subtract with negative decimals? Example 1: Using a number line Add 0.5 and 1.3 using a number line model. Raven s Solution I used an arrow going from 0 to 0.5 to represent 0.5. Then I used an arrow going left 1.3 spaces from 0.5 to represent adding 1.3 to 0.5. 1.0 0 1.0 I ended up at 0.8. 0.5 ( 1.3) 0.8 I subtracted 0.8 0.5 to check. I started at 0.5 and drew an arrow to 0.8. The arrow is 13 tenths or 1.3 long and goes left. The difference is 1.3. Copyright 2009 by Nelson Education Ltd. 1
1.0 0 1.0 0.8 0.5 1.3 so 0.5 ( 1.3) must equal 0.8. Example 2: Calculating as with integers Add 0.5 and 1.3 using an addition rule. Emilio s Solution 0.5 ( 1.3) 0.5 1.3 0.8 0.8 ( 1.3) 0.8 1.3 I added the decimals the same way as I add integers. I subtracted to check. I subtracted the decimals the same way I subtract integers. 0.5 To subtract 1.3, I added the opposite, 1.3. So, 0.5 ( 1.3) 0.8. Reflecting 1. How can you predict whether the sum of two decimals will be positive or negative, without calculating? 2. Explain why the sum for 2.1 ( 0.6) is between 2 and 3. 3. How is subtracting with positive and negative decimals the same as subtracting with integers? 4. Explain how to record ( 0.8) ( 0.8) ( 0.8) ( 0.8) as a multiplication sentence. 2 Nelson Mathematics Elementary Year Two, Cycle One Copyright 2009 by Nelson Education Ltd.
Example 3: Multiplying with negative decimals Calculate 1.1 ( 0.9). Solution A: Using the negative sign key Solution B: Using rules of sign 1.1 [ ] [( )] [.] 9 [Enter ] Multiply 1.1 and 0.9. 1.1 0.9 0.99 The calculator shows 0.99. The rules of signs for multiplying decimals are the same as for multiplying integers. A positive number multiplied with a negative number results in a negative number. 1.1 ( 0.9) 0.99 1.1 ( 0.9) 0.99 Example 4: Dividing with negative decimals Calculate 2.4 ( 0.4). Solution A: Using multiplication Solution B: Using rules of sign Write the multiplication sentence Divide 2.4 0.4. that relates to the division sentence. 2.4 0.4 6 2.4 ( 0.4) The rules of signs for dividing decimals ( 0.4) 2.4 are the same as for dividing integers. Determine the missing number. A negative number divided by a negative 6 ( 0.4) 2.4 number results in a positive number. 2.4 ( 0.4) 6 2.4 ( 0.4) 6 Copyright 2009 by Nelson Education Ltd. 3
A Checking 5. Subtract. Add to check. a) 0.3 ( 0.7) c) 1.64 1.3 b) 1.9 2 d) 2.4 ( 1.87) 6. Match each multiplication equation with the related division equation. Write the missing decimals. B a) ( 0.4) 0.12 b) ( 0.4) 0.12 c) 0.4 0.12 d) 0.4 0.12 A. 0.12 0.4 B. 0.12 ( 0.4) C. 0.12 ( 0.4) D. 0.12 0.4 Practising 7. Write the next three terms. Describe the pattern in two ways. 4.2, 3.9, 3.6, 8. Write a multiplication sentence for the following. ( 2.1) ( 2.1) ( 2.1) ( 2.1) 9. Add. a) 0.2 ( 0.1) c) 4 ( 2.72) b) 5.42 ( 1.8) d) 2.6 0.9 ( 1.4) 10. Subtract. a) 0.4 ( 7) c) 1.5 6.7 b) 1.39 ( 1.03) d) 4.8 0 11. Multiply. a) 7 ( 1.2) c) 1.4 ( 0.31) b) 0 ( 5.8) d) 2.5 0.5 12. Divide. a) 4.2 ( 2) c) 0.48 ( 0.8) 2 6 b) d) 2 12 13. Calculate. a) 9 ( 2.4) d) 2.8 ( 0.7) b) 1.1 ( 0.5) e) 7.18 0 c) 0 ( 0.3) f) 3.44 ( 1.9) ( 0.1) 14. Calculate. a) [6.2 ( 3.1)] ( 1) b) 1.8 ( 4.5 5) c) 7.42 0.7 ( 0.3) 1.1 d) 9 1.2 ( 0.6) e) [2.3 ( 5.0)] 2.6 15. There is an error in this solution. [ 4.2 ( 3.5)] ( 1) ( 7.7) ( 1) 7.7 a) Describe the error. 2 21.86 21.86 b) Determine the correct answer. 16. a) Evaluate with a calculator. 1.2 0.88 ( 0.5) b) Does your calculator follow the order of operations? How do you know? 4 Nelson Mathematics Elementary Year Two, Cycle One Copyright 2009 by Nelson Education Ltd.
17. This table gives the maximum and minimum temperature in Trois-Rivières in a recent year. Date Maximum temperature ( C) a) What was the difference between the maximum and minimum temperatures on November 28th? b) How much higher was the maximum temperature on November 27th than on November 30th? c) How much lower was the minimum temperature on November 30th than on November 29th? d) The mean temperature on November 27th was 1.1 C. Show the calculations. e) What was the mean temperature to the nearest tenth of a degree on November 30th? 18. Record the operation for each equation. a) 5.5 1.3 6.8 b) 9.1 9.1 0 Minimum temperature ( C) November 27 2.8 4.9 November 28 4.9 9.8 November 29 2.4 5.8 November 30 2.0 6.5 19. Give two answers to complete each equation. a) 0 ( 0.9) 0 b) 6.2 ( 1) 6.2 c) 4.6 0 4.6 20. How is dividing zero by a negative decimal the same as dividing zero by a positive integer? C Extending 21. Without calculating, determine which has a greater result. Explain how you know. a) A 6.2 ( 1.9) B 6.2 ( 1.8) b) A 5.75 ( 9.3) B 5.75 ( 8.3) 22. a) Use 2.6 ( 1.4) 1.2 to determine the result when 1.4 is increased by 2 tenths. Explain your strategy. b) Use 0.3 0.2 0.06 to determine the product when 0.2 is doubled. Explain your strategy. 23. On March 21th, the minimum temperature in Shawinigan was 16.2 C and the mean temperature was 8.8 C. What was the maximum temperature? 24. The product of two decimals is 2.8. What might the decimals be? Give three answers. c) 3.2 0.8 4 Copyright 2008 by Thomson Nelson 5