Fill in the blanks:
(i) `frac(-9)(5)=frac(....)(20)=frac(27)(....)=frac(-45)(....)`
(ii) `frac(-6)(11)=frac(-18)(....)=frac(....)(44)`

Answer

To solve the problem step by step, we will fill in the blanks for the two parts of the question.

### Part (i):
We need to fill in the blanks for the expression:
\[ \frac{-9}{5} = \frac{...}{20} = \frac{27}{...} = \frac{-45}{...} \]

**Step 1: Find the first blank \(\frac{...}{20}\)**

We start with the equation:
\[ \frac{-9}{5} = \frac{x}{20} \]
Cross-multiplying gives:
\[ -9 \cdot 20 = 5 \cdot x \]
Calculating the left side:
\[ -180 = 5x \]
Now, divide both sides by 5:
\[ x = \frac{-180}{5} = -36 \]
So, the first blank is \(-36\).

**Step 2: Find the second blank \(\frac{27}{...}\)**

Next, we have:
\[ \frac{-36}{20} = \frac{27}{y} \]
Cross-multiplying gives:
\[ -36y = 27 \cdot 20 \]
Calculating the right side:
\[ -36y = 540 \]
Now, divide both sides by -36:
\[ y = \frac{540}{-36} = -15 \]
So, the second blank is \(-15\).

**Step 3: Find the third blank \(\frac{-45}{...}\)**

Now we have:
\[ \frac{27}{-15} = \frac{-45}{z} \]
Cross-multiplying gives:
\[ 27z = -45 \cdot -15 \]
Calculating the right side:
\[ 27z = 675 \]
Now, divide both sides by 27:
\[ z = \frac{675}{27} = 25 \]
So, the third blank is \(25\).

### Summary for Part (i):
The filled expression is:
\[ \frac{-9}{5} = \frac{-36}{20} = \frac{27}{-15} = \frac{-45}{25} \]

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### Part (ii):
We need to fill in the blanks for the expression:
\[ \frac{-6}{11} = \frac{-18}{...} = \frac{...}{44} \]

**Step 1: Find the first blank \(\frac{-18}{...}\)**

Starting with:
\[ \frac{-6}{11} = \frac{-18}{w} \]
Cross-multiplying gives:
\[ -6w = -18 \cdot 11 \]
Calculating the right side:
\[ -6w = -198 \]
Now, divide both sides by -6:
\[ w = \frac{-198}{-6} = 33 \]
So, the first blank is \(33\).

**Step 2: Find the second blank \(\frac{...}{44}\)**

Now we have:
\[ \frac{-18}{33} = \frac{v}{44} \]
Cross-multiplying gives:
\[ -18 \cdot 44 = 33v \]
Calculating the left side:
\[ -792 = 33v \]
Now, divide both sides by 33:
\[ v = \frac{-792}{33} = -24 \]
So, the second blank is \(-24\).

### Summary for Part (ii):
The filled expression is:
\[ \frac{-6}{11} = \frac{-18}{33} = \frac{-24}{44} \]

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### Final Answers:
- For part (i): \(-36\), \(-15\), \(25\)
- For part (ii): \(33\), \(-24\)

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