To find the sum of \( p \) and \( Q \) with \( p = -\frac{5}{9} \) and \( Q = -2 \), we can break it down step by step:
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Convert -2 to a fraction: \[ Q = -2 = -\frac{18}{9} \]
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Add \( p \) and \( Q \): \[ p + Q = -\frac{5}{9} + -\frac{18}{9} = -\frac{5 + 18}{9} = -\frac{23}{9} \]
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Conclusion: The sum of \( p \) and \( Q \) is: \[ -\frac{23}{9} \]
Now, let's analyze the steps involving the number line to position the values correctly:
A. Finding -2 knots on the number line and counting five spaces to the left
- Start at -2 (equivalent to -2.0), as you're counting spaces left means you're going into the negatives.
- Move 1 space to reach -3, 2 spaces to -4, 3 spaces to -5, 4 spaces to -6, and finally 5 spaces to reach -7.
B. Finding -2 knots on the number line and counting five spaces to the right
- Start at -2. Moving to the right increases the value.
- Move 1 space to -1, 2 spaces to 0, 3 spaces to 1, 4 spaces to 2, and 5 spaces to reach 3.
C. Finding -5 knots on the number line and counting two spaces to the right
- Start at -5. Moving to the right to increase the value.
- Move 1 space to -4 and then 1 more space to -3.
D. Finding -5/9 on the number line and counting two spaces to the left
- Start at -\(\frac{5}{9}\) (which is approximately -0.556). Moving left means getting more negative.
- Move 1 space left to reach approximately -1.556 and then another space to reach approximately -2.556.
This completes your instructions, and thus you understand how to add the fractions and visualize it on the number line.
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