To determine which operation can be placed in the blank to make the statement true, we first need to simplify both sides of the equation.
Let's simplify the left side:
- Calculate \( 6 - \frac{1}{4} \times 28 - 2\frac{1}{4} \):
- \( \frac{1}{4} \times 28 = 7 \)
- Now substitute back: \( 6 - 7 - 2\frac{1}{4} \)
- Convert \( 2\frac{1}{4} \) to an improper fraction: \( 2\frac{1}{4} = \frac{9}{4} \).
- So we have \( 6 - 7 - \frac{9}{4} \).
To simplify further, convert 6 and 7 to fractions over 4:
- \( 6 = \frac{24}{4} \)
- \( 7 = \frac{28}{4} \)
Thus, the left side simplifies to: \[ \frac{24}{4} - \frac{28}{4} - \frac{9}{4} = \frac{24 - 28 - 9}{4} = \frac{-13}{4} \]
Next, simplify the right side: \[ \frac{3}{4} + 4 \times 2 - 11 \] Calculating \( 4 \times 2 = 8 \), so we substitute to get: \[ \frac{3}{4} + 8 - 11 = \frac{3}{4} + 8 - 11 = \frac{3}{4} - 3 \] Convert -3 to a fraction: \[ -3 = -\frac{12}{4} \] Thus, we have: \[ \frac{3}{4} - \frac{12}{4} = \frac{3 - 12}{4} = \frac{-9}{4} \]
Now we have the simplified left and right sides: Left side: \(\frac{-13}{4}\) \ Right side: \(\frac{-9}{4}\)
Now, we can fill in the blank: \[ \frac{-13}{4} __ \frac{-9}{4} \] To find the correct operation for the blank: \[ \frac{-13}{4} < \frac{-9}{4} \] This means that the operation that can be placed in the blank to make the statement true is <.
Thus, the complete statement is: \[ 6 - \frac{1}{4} \times 28 - 2\frac{1}{4} < \frac{3}{4} + 4 \times 2 - 11 \]