To determine which operator can be inserted to make the statement true, we first need to simplify both sides of the expression.
Let's break it down step by step:
**Left Side:**
1. Start with the expression:
\[ 6 - \frac{1}{4} \times 28 - 2 \frac{1}{4} \]
2. Convert \( 2 \frac{1}{4} \) to an improper fraction:
\[ 2 \frac{1}{4} = 2 + \frac{1}{4} = \frac{8}{4} + \frac{1}{4} = \frac{9}{4} \]
3. Now the left side becomes:
\[ 6 - \frac{1}{4} \times 28 - \frac{9}{4} \]
4. Calculate \( \frac{1}{4} \times 28 \):
\[ \frac{1}{4} \times 28 = 7 \]
5. Substitute that back:
\[ 6 - 7 - \frac{9}{4} \]
6. Combine \( 6 - 7 = -1 \):
\[ -1 - \frac{9}{4} \]
7. To combine these, convert \(-1\) to a fraction:
\[ -1 = -\frac{4}{4} \]
8. Now combine:
\[ -\frac{4}{4} - \frac{9}{4} = -\frac{13}{4} \]
So, the left side equals:
\[ -\frac{13}{4} \]
**Right Side:**
1. Now simplify the right side:
\[ 3/4 + 4 \times 2 - 11 \]
2. Calculate \( 4 \times 2 = 8 \), so the right side becomes:
\[ 3/4 + 8 - 11 \]
3. Combine \( 8 - 11 = -3 \):
\[ 3/4 - 3 \]
4. Convert \(-3\) to a fraction:
\[ -3 = -\frac{12}{4} \]
5. Combine:
\[ 3/4 - \frac{12}{4} = \frac{3 - 12}{4} = \frac{-9}{4} \]
So, the right side equals:
\[ -\frac{9}{4} \]
**Final Comparison:**
Now we compare the two sides:
- Left side: \( -\frac{13}{4} \)
- Right side: \( -\frac{9}{4} \)
Now let's see which operator makes it true:
- \( -\frac{13}{4} < -\frac{9}{4} \)
Thus, the operator that can be inserted to make the statement true is:
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