Question
Which sign makes the statement true?
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Answers
GPT-4o mini
To determine which sign makes the statement true, let's first evaluate both sides of the equation:
We need to check:
\[
1 \, 2 + \text{?} \, 2 \, 6 = 1 \, 6 + \text{?} \, 1 \, 2
\]
Let's rewrite this with possible operations (we'll denote "?" with a placeholder for operators such as "+", "-", "*", or "/").
Since the context seems to involve basic arithmetic, I'll assume these represent numbers concatenated, so I interpret:
- \( 1 \, 2 \) as \( 12 \)
- \( 2 \, 6 \) as \( 26 \)
- \( 1 \, 6 \) as \( 16 \)
- \( 1 \, 2 \) as \( 12 \)
So we have:
\[
12 \pm 26 = 16 \pm 12
\]
Now, let’s evaluate the possible operations (where "±" indicates that we have two operations we can try).
1. **Addition on both sides:**
\[
12 + 26 = 38
\]
\[
16 + 12 = 28
\]
This is **not** true.
2. **Subtraction on both sides:**
\[
12 - 26 = -14
\]
\[
16 - 12 = 4
\]
This is **not** true.
3. **Addition on the left and subtraction on the right:**
\[
12 + 26 = 38
\]
\[
16 - 12 = 4
\]
This is **not** true.
4. **Subtraction on the left and addition on the right:**
\[
12 - 26 = -14
\]
\[
16 + 12 = 28
\]
This is **not** true.
5. **Multiplication on both sides:**
Let’s evaluate:
\[
12 \times 26 = 312
\]
\[
16 \times 12 = 192
\]
This is **not** true.
6. **Division on both sides:**
Assuming integers:
\[
12 / 26 < 1
\]
\[
16 / 12 \approx 1.33
\]
This is **not** true.
Given all combinations of simple arithmetic, it is likely we have misunderstood the historical notation or context.
Assuming there is a different kind of interpretation, please clarify or provide more context to make it clear what the statement is intending (such as if "?" could represent modulo or exponentiation or other mathematical concepts).
Let me know if there is any specific operation you want to try, or if you can give an example of intended operations!
We need to check:
\[
1 \, 2 + \text{?} \, 2 \, 6 = 1 \, 6 + \text{?} \, 1 \, 2
\]
Let's rewrite this with possible operations (we'll denote "?" with a placeholder for operators such as "+", "-", "*", or "/").
Since the context seems to involve basic arithmetic, I'll assume these represent numbers concatenated, so I interpret:
- \( 1 \, 2 \) as \( 12 \)
- \( 2 \, 6 \) as \( 26 \)
- \( 1 \, 6 \) as \( 16 \)
- \( 1 \, 2 \) as \( 12 \)
So we have:
\[
12 \pm 26 = 16 \pm 12
\]
Now, let’s evaluate the possible operations (where "±" indicates that we have two operations we can try).
1. **Addition on both sides:**
\[
12 + 26 = 38
\]
\[
16 + 12 = 28
\]
This is **not** true.
2. **Subtraction on both sides:**
\[
12 - 26 = -14
\]
\[
16 - 12 = 4
\]
This is **not** true.
3. **Addition on the left and subtraction on the right:**
\[
12 + 26 = 38
\]
\[
16 - 12 = 4
\]
This is **not** true.
4. **Subtraction on the left and addition on the right:**
\[
12 - 26 = -14
\]
\[
16 + 12 = 28
\]
This is **not** true.
5. **Multiplication on both sides:**
Let’s evaluate:
\[
12 \times 26 = 312
\]
\[
16 \times 12 = 192
\]
This is **not** true.
6. **Division on both sides:**
Assuming integers:
\[
12 / 26 < 1
\]
\[
16 / 12 \approx 1.33
\]
This is **not** true.
Given all combinations of simple arithmetic, it is likely we have misunderstood the historical notation or context.
Assuming there is a different kind of interpretation, please clarify or provide more context to make it clear what the statement is intending (such as if "?" could represent modulo or exponentiation or other mathematical concepts).
Let me know if there is any specific operation you want to try, or if you can give an example of intended operations!