CHAPTER 6
You will need
C
Rules of Signs for
Decimals
• number lines
• a calculator with a
sign change key
c GOAL
Apply the rules of signs for calculating with decimals.
Learn about the Math
Communication Tip
Positive and negative decimals can be represented on a
number line.
–2.0
–1.7
–1.0
–0.2
0
0.4
1.0
1.4
A decimal can be called a
decimal number.
2.0
can you add and subtract with negative
? How
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.
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–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
I added the decimals the same way as I add integers.
0.8
I subtracted to check.
0.8 (1.3)
0.8 1.3
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
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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
that relates to the division sentence.
2.4 (0.4) (0.4) 2.4
Determine the missing number.
6 (0.4) 2.4
2.4 (0.4) 6
Divide 2.4 0.4.
2.4 0.4 6
The rules of signs for dividing decimals
are the same as for dividing integers.
A negative number divided by a negative
number results in a positive number.
2.4 (0.4) 6
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6C Rules of Signs for Decimals
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A
Checking
11. Multiply.
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.
a)
(0.4) 0.12
b)
(0.4) 0.12
c)
0.4 0.12
d)
0.4 0.12
B. 0.12 (0.4) 12. Divide.
a) 4.2 (2)
b)
26
2 12
c) 0.48 (0.8)
d)
2 21.86
21.86
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)
b) 1.8 (4.5 5)
Practising
c) 7.42 0.7 (0.3) 1.1
7. Write the next three terms. Describe
the pattern in two ways.
4.2, 3.9, 3.6, …
9. Add.
c) 4 (2.72)
b) 5.42 (1.8) d) 2.6 0.9 (1.4)
10. Subtract.
c) 1.5 6.7
b) 1.39 (1.03) d) 4.8 0
Nelson Mathematics Elementary Year Two, Cycle One
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
8. Write a multiplication sentence for
the following.
(2.1) (2.1) (2.1) (2.1)
4
d) 2.5 0.5
a) [6.2 (3.1)] (1)
D. 0.12 0.4 a) 0.4 (7)
b) 0 (5.8)
14. Calculate.
C. 0.12 (0.4) a) 0.2 (0.1)
c) 1.4 (0.31)
13. Calculate.
A. 0.12 0.4 B
a) 7 (1.2)
a) Describe the error.
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?
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17. This table gives the maximum and
minimum temperature in Trois-Rivières
in a recent year.
a) 0
Minimum
Maximum
temperature temperature
(°C)
(°C)
Date
November 27
2.8
4.9
November 28
4.9
9.8
November 29
2.4
5.8
November 30
2.0
6.5
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
b) 9.1
19. Give two answers to complete each
equation.
1.3 6.8
(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.
9.1 0
c) 3.2
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0.8 4
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