To solve this problem, we use the property of inverse proportion:

If $x$ and $y$ are inversely proportional, then $x \cdot y = k$, where $k$ is a constant.

Steps to Solve:

1. Use the provided values in the table to calculate $k$ using any complete pair.
2. Use $k$ to determine the missing values $a, b, c,$ and $d$.

Complete Pair: $x = 6$, $y = 1.5$

$k = x \cdot y = 6 \cdot 1.5 = 9$

Now, $k = 9$ for all pairs.

Finding $a$:

Given $y = 3$, $x \cdot y = k \implies a \cdot 3 = 9 \implies a = \frac{9}{3} = 3$

Finding $b$:

Given $x = 2.25$, $x \cdot y = k \implies 2.25 \cdot b = 9 \implies b = \frac{9}{2.25} = 4$

Finding $c$:

Given $y = 1$, $x \cdot y = k \implies c \cdot 1 = 9 \implies c = 9$

Finding $d$:

Given $x = 1.8$, $x \cdot y = k \implies 1.8 \cdot d = 9 \implies d = \frac{9}{1.8} = 5$

Final Values:

• $a = 3$
• $b = 4$
• $c = 9$
• $d = 5$

Would you like a detailed explanation of any step?

Related Questions:

1. What is the significance of the constant $k$ in inverse proportion?
2. How can inverse proportion be applied in real-life problems?
3. How would the calculations change if the table had more missing values?
4. Can you verify the solution using another method?
5. How can we generalize this concept to other types of proportionality?

Tip: Always cross-check your calculations when solving for unknowns using proportional relationships.