Associative Property of Multiplication Word Problems Math Center ... - Free Printable

Problem 1: Movie Theater Seats

Question: Last weekend, Sophia went to the movies. When she went into the movie theater, she saw three sections. Each section had 9 rows, and each row had 7 seats. How many seats are in the movie theater?

#### Step-by-Step Solution:
1. Identify the given information:
- There are 3 sections in the movie theater.
- Each section has 9 rows.
- Each row has 7 seats.

2. Understand the problem:
- We need to find the total number of seats in the movie theater.
- The total number of seats can be calculated using the formula:
\[
\text{Total seats} = (\text{Number of sections}) \times (\text{Rows per section}) \times (\text{Seats per row})
\]

3. Apply the associative property of multiplication:
- The associative property states that when multiplying three or more numbers, the grouping of the numbers does not affect the result. Mathematically:
\[
(a \times b) \times c = a \times (b \times c)
\]
- Here, we can group the numbers in any way:
\[
\text{Total seats} = (3 \times 9) \times 7 \quad \text{or} \quad 3 \times (9 \times 7)
\]

4. Calculate step-by-step:
- First, calculate the number of seats in one section:
\[
\text{Seats per section} = 9 \times 7 = 63
\]
- Then, calculate the total number of seats in all three sections:
\[
\text{Total seats} = 3 \times 63 = 189
\]

5. Final Answer:
- The total number of seats in the movie theater is 189.

#### Fill in the table:
| Equation | Answer | Model |
|-----------------------|------------|------------------------------------|
| \( (3 \times 9) \times 7 \) | 189 | Associative property: Grouping does not matter. |

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Problem 2: Farmer Joe's Garden

Question: Farmer Joe has a garden with two sections of vegetables. Each section of vegetables has 5 rows with 10 plants in each row. How many plants does Farmer Joe have planted in his garden?

#### Step-by-Step Solution:
1. Identify the given information:
- There are 2 sections in the garden.
- Each section has 5 rows.
- Each row has 10 plants.

2. Understand the problem:
- We need to find the total number of plants in the garden.
- The total number of plants can be calculated using the formula:
\[
\text{Total plants} = (\text{Number of sections}) \times (\text{Rows per section}) \times (\text{Plants per row})
\]

3. Apply the associative property of multiplication:
- Again, the associative property allows us to group the numbers in any way:
\[
\text{Total plants} = (2 \times 5) \times 10 \quad \text{or} \quad 2 \times (5 \times 10)
\]

4. Calculate step-by-step:
- First, calculate the number of plants in one section:
\[
\text{Plants per section} = 5 \times 10 = 50
\]
- Then, calculate the total number of plants in both sections:
\[
\text{Total plants} = 2 \times 50 = 100
\]

5. Final Answer:
- The total number of plants in the garden is 100.

#### Fill in the table:
| Equation | Answer | Model |
|-----------------------|------------|------------------------------------|
| \( (2 \times 5) \times 10 \) | 100 | Associative property: Grouping does not matter. |

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Final Answers:

1. Movie Theater Seats: \(\boxed{189}\)
2. Farmer Joe's Garden Plants: \(\boxed{100}\)