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Task 2 - Represent each of the negative rational numbers on the number line.

i. [tex]\(\frac{-5}{7}\)[/tex]

ii. [tex]\(\frac{-3}{12}\)[/tex]

iii. [tex]\(\frac{-2}{5}\)[/tex]

iv. [tex]\(\frac{-13}{32}\)[/tex]

v. [tex]\(\frac{-4}{5}\)[/tex]

vi. [tex]\(\frac{3}{8}\)[/tex]

vii. [tex]\( \frac{22}{-51}\)[/tex]

(Note: vi. [tex]\(\frac{3}{8}\)[/tex] is a positive rational number and should be omitted if only negative rational numbers are required.)



Answer :

GinnyAnswer
Sure, let's represent each of the given rational numbers on the number line. Here's a step-by-step breakdown of each number:

1. [tex]$(-5) / 7$[/tex]:
- [tex]$(-5) / 7$[/tex] is a negative rational number.
- Its decimal representation is approximately -0.7142857142857143.
- On the number line, this would be slightly to the left of -0.7.

2. [tex]$(-3) / 12$[/tex]:
- [tex]$(-3) / 12$[/tex] is a negative rational number.
- Simplifying this fraction gives us [tex]$(-1) / 4$[/tex] which is -0.25.
- On the number line, this would be positioned at -0.25.

3. [tex]$(-2) / 5$[/tex]:
- [tex]$(-2) / 5$[/tex] is a negative rational number.
- Its decimal representation is -0.4.
- On the number line, this would be positioned at -0.4.

4. [tex]$3 / 8$[/tex]:
- [tex]$3 / 8$[/tex] is a positive rational number.
- Its decimal representation is 0.375.
- On the number line, this would be positioned at 0.375.

5. [tex]$(-4) 5$[/tex] (seems to be an unclear or incorrect format):
- It appears there might be a typo here, as it doesn't represent a standard rational expression.
- Without an accurate representation, we cannot correctly place this on the number line.

6. [tex]$22(-51)$[/tex] (also seems to be an unclear or incorrect format):
- This seems to be another incorrectly formatted expression.
- It doesn't form a valid rational number or expression in its current state, so it cannot be correctly placed on the number line.

7. [tex]$(-13) / 32$[/tex]:
- [tex]$(-13) / 32$[/tex] is a negative rational number.
- Its decimal representation is approximately -0.40625.
- On the number line, this would be positioned at -0.40625.

### Summary on the Number Line:
- Negative numbers on the left side:
- -0.7142857142857143 (for [tex]$(-5) / 7$[/tex])
- -0.25 (for [tex]$(-3) / 12$[/tex])
- -0.4 (for [tex]$(-2) / 5$[/tex])
- -0.40625 (for [tex]$(-13) / 32$[/tex])

- Positive number on the right side:
- 0.375 (for [tex]$3 / 8$[/tex])

The potentially unclear or incorrect representations cannot be accurately placed on the number line without further clarification.

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