**Arranging the word 'ALGEBRA' without changing the order of the vowels**

To solve this problem, we need to consider the letters of the word 'ALGEBRA' and their respective positions. We have to find the number of ways we can arrange these letters without changing the order of the vowels (A, E, A).

**Step 1: Understanding the word 'ALGEBRA'**

The word 'ALGEBRA' consists of 7 letters: A, L, G, E, B, R, A. Out of these, the vowels are A, E, A. The consonants are L, G, B, R.

**Step 2: Identifying the restrictions**

The given problem restricts us from changing the order of the vowels (A, E, A). We can rearrange the consonants (L, G, B, R) and place them in different positions, but the vowels must remain in their original order.

**Step 3: Solving the problem**

To solve this problem, we can break it down into smaller steps.

1. Find the number of ways to arrange the consonants:
- We have 4 consonants (L, G, B, R).
- We can arrange these 4 consonants in 4! = 24 ways.

2. Find the number of ways to arrange the vowels:
- Since the vowels (A, E, A) must remain in their original order, we can consider them as a single entity.
- We can arrange this group of vowels in 1! = 1 way.

3. Multiply the number of ways from step 1 and step 2 to get the final answer:
- Number of ways = 24 * 1 = 24.

**Step 4: Conclusion**

Therefore, the letters of the word 'ALGEBRA' can be arranged in 24 different ways without changing the order of the vowels (A, E, A).