Fill in the blanks using `gt` or `lt`:
`8/45 - 16/89`

Answer

To solve the problem of comparing the two fractions \( \frac{8}{45} \) and \( \frac{16}{89} \), we can follow these steps:

### Step 1: Write down the fractions
We have two fractions to compare:
- First fraction: \( \frac{8}{45} \)
- Second fraction: \( \frac{16}{89} \)

### Step 2: Find a common basis for comparison
To compare the two fractions easily, we can convert \( \frac{8}{45} \) into a fraction with a similar numerator to \( \frac{16}{89} \). We can do this by multiplying both the numerator and the denominator of \( \frac{8}{45} \) by 2.

\[ \frac{8 \times 2}{45 \times 2} = \frac{16}{90} \]

### Step 3: Compare the new fraction with the second fraction
Now we have:
- \( \frac{16}{90} \) (which is equivalent to \( \frac{8}{45} \))
- \( \frac{16}{89} \)

### Step 4: Analyze the fractions
Now, both fractions have the same numerator (16). To determine which fraction is greater, we can compare their denominators:
- Denominator of \( \frac{16}{90} \) is 90
- Denominator of \( \frac{16}{89} \) is 89

### Step 5: Determine which fraction is greater
Since both fractions have the same numerator, the fraction with the smaller denominator is greater. Here, 89 is smaller than 90, so:

\[ \frac{16}{89} > \frac{16}{90} \]

Thus, we conclude that:

\[ \frac{16}{89} > \frac{8}{45} \]

### Final Answer
Therefore, we fill in the blank with `lt` (less than):

\[ \frac{8}{45} \lt \frac{16}{89} \]

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