In the following numerical analogy 6 is related to −3. Using the same pattern, −18 will be related to which of the following numbers?

Introduction / Context:
This is a number analogy question involving both positive and negative numbers. The relation between 6 and minus 3 is used as a model, and you must apply the same arithmetic rule to minus 18 to determine the correct related number among the options.

Given Data / Assumptions:

• First pair: 6 : −3
• Second pair: −18 : ?
• Options include positive and negative values, so sign must be treated carefully.

Concept / Approach:
One direct way to connect 6 and minus 3 is to use multiplication by a constant factor. If 6 is multiplied by a certain number to produce minus 3, the same factor can then be applied to minus 18. Division gives the same information as multiplication by the reciprocal, so either viewpoint leads to the same factor and rule.

Step-by-Step Solution:

Verification / Alternative check:
Notice that the magnitude halves from 6 to 3 and from 18 to 9. The sign also flips once because multiplying a positive by a negative gives a negative, and then multiplying a negative by a negative returns a positive. This is consistent with basic sign rules and confirms the pattern. None of the other options produce such a neat and symmetric relation with both pairs.

Why Other Options Are Wrong:

• 3 would result from dividing minus 18 by minus 6, which does not match the original pair.
• Minus 9 corresponds to multiplying minus 18 by 0.5 without changing the sign, which contradicts the given transformation.
• Minus 6 would require multiplying minus 18 by one third, not by minus one half.
• 6 would represent a move from negative to positive with a different factor and does not keep the same proportional change.

Common Pitfalls:
Many students focus only on the sign reversal and ignore the magnitude change, or they notice the halving of magnitude but forget about the sign flip. Always consider both aspects. Check whether the chosen factor simultaneously explains both the numeric size and the sign change in the first pair before applying it to the second pair.

Final Answer:
Using the same pattern, minus 18 is related to 9.