Question
A farmer sets up two corn mazes for a fall festival, as shown in this model.
Which equivalent expressions are represented by the model? Check the three that apply.
(3 points)
Responses
3(5+1)
3 times open paren 5 plus 1 close paren
(5)(3)+(5)(1)
5 times 3 plus 5 times 1
5(3+1)
5 times open paren 3 plus 1 close paren
15+5
15 plus 5
3+(5+1)
Which equivalent expressions are represented by the model? Check the three that apply.
(3 points)
Responses
3(5+1)
3 times open paren 5 plus 1 close paren
(5)(3)+(5)(1)
5 times 3 plus 5 times 1
5(3+1)
5 times open paren 3 plus 1 close paren
15+5
15 plus 5
3+(5+1)
Answers
GPT-4o mini
To determine which equivalent expressions are represented by the model, we need to analyze the structure of the expressions based on distributive properties and simplifications.
Let's explore the possible options:
1. **3(5+1)**: This is equivalent to \(3 \times (5 + 1) = 3 \times 6 = 18\). This matches the structure of one of the mazes and is equivalent to the overall calculation.
2. **(5)(3)+(5)(1)**: This represents the distribution of the addition, which is also equivalent to \((5 \times 3) + (5 \times 1) = 15 + 5 = 20\). This is another valid way to express the same value.
3. **5(3+1)**: This is equivalent to \(5 \times (3 + 1) = 5 \times 4 = 20\). This is also a proper way of structuring the multiplicative addition and matches the calculations made in the model.
4. **15+5**: This simply adds up to \(20\) as well, which again reflects the total area represented by the expressions so far.
5. **3+(5+1)**: This sums up to \(3 + (5 + 1) = 3 + 6 = 9\), which does not reflect the values coming from the multiplications displayed above.
Based on this analysis, the three equivalent expressions that apply are:
1. **3(5+1)**
2. **(5)(3)+(5)(1)**
3. **5(3+1)**
Thus, the correct responses are the first three options listed.
Let's explore the possible options:
1. **3(5+1)**: This is equivalent to \(3 \times (5 + 1) = 3 \times 6 = 18\). This matches the structure of one of the mazes and is equivalent to the overall calculation.
2. **(5)(3)+(5)(1)**: This represents the distribution of the addition, which is also equivalent to \((5 \times 3) + (5 \times 1) = 15 + 5 = 20\). This is another valid way to express the same value.
3. **5(3+1)**: This is equivalent to \(5 \times (3 + 1) = 5 \times 4 = 20\). This is also a proper way of structuring the multiplicative addition and matches the calculations made in the model.
4. **15+5**: This simply adds up to \(20\) as well, which again reflects the total area represented by the expressions so far.
5. **3+(5+1)**: This sums up to \(3 + (5 + 1) = 3 + 6 = 9\), which does not reflect the values coming from the multiplications displayed above.
Based on this analysis, the three equivalent expressions that apply are:
1. **3(5+1)**
2. **(5)(3)+(5)(1)**
3. **5(3+1)**
Thus, the correct responses are the first three options listed.