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To solve this problem, Mrs. Gracia needs to arrange 40 chairs into equal rows. The key here is to find all the divisors of 40, because each divisor represents a possible number of rows, with the corresponding quotient being the number of chairs per row.

Let's find the divisors of 40:

1. Divisors of 40 are the numbers that divide 40 without leaving a remainder.
   
   \( 40 \div 1 = 40 \)
   
   \( 40 \div 2 = 20 \)
   
   \( 40 \div 4 = 10 \)
   
   \( 40 \div 5 = 8 \)
   
   \( 40 \div 8 = 5 \)
   
   \( 40 \div 10 = 4 \)
   
   \( 40 \div 20 = 2 \)
   
   \( 40 \div 40 = 1 \)

So, the divisors of 40 are: 1, 2, 4, 5, 8, 10, 20, 40.

### Answer:
Mrs. Gracia can arrange the chairs equally into **8 different ways**, which are:

- 1 row of 40 chairs
- 2 rows of 20 chairs
- 4 rows of 10 chairs
- 5 rows of 8 chairs
- 8 rows of 5 chairs
- 10 rows of 4 chairs
- 20 rows of 2 chairs
- 40 rows of 1 chair

Would you like more details or any further clarifications?

Here are 5 related questions for further exploration:

1. What if Mrs. Gracia had 50 chairs instead of 40? How many ways could she arrange them equally into rows?
2. Can Mrs. Gracia arrange 60 chairs in a square formation (same number of rows and chairs per row)?
3. What is the greatest number of chairs she can arrange per row while keeping the number of rows less than 10?
4. How many ways could she arrange 45 chairs equally into rows?
5. How many different row arrangements would she have if she needed at least 4 rows?

**Tip:** When solving problems involving arrangements, always think in terms of factors or divisors of the total number of items.

Mrs. Gracia wants to arrange 40 chairs for the PTA meeting at the gym. She needs to arrange chairs equally into rows. How many ways can she arrange the chairs equally into rows?

Find out how Mrs. Gracia can arrange 40 chairs equally into rows for the PTA meeting. Explore the divisors of 40 to discover 8 possible ways to organize the seating arrangement. This problem introduces basic arithmetic concepts and is suitable for students in Grades 5-7.

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