Let's evaluate both expressions step by step.
Numerator: \[ 6 - \frac{1}{4} \cdot 28 - \frac{21}{4} \]
First, calculate \(\frac{1}{4} \cdot 28\): \[ \frac{1}{4} \cdot 28 = 7 \] Now substitute back into the numerator: \[ 6 - 7 - \frac{21}{4} \] Next, convert 6 into a fraction with a denominator of 4: \[ 6 = \frac{24}{4} \] Now, the expression becomes: \[ \frac{24}{4} - 7 - \frac{21}{4} \] Now, express 7 as a fraction: \[ 7 = \frac{28}{4} \] So now it is: \[ \frac{24}{4} - \frac{28}{4} - \frac{21}{4} = \frac{24 - 28 - 21}{4} = \frac{-25}{4} \]
Denominator: \[ 3/4 + 4 \cdot 2 - 11 \]
Calculate \(4 \cdot 2\): \[ 4 \cdot 2 = 8 \] Now substitute this back into the denominator: \[ \frac{3}{4} + 8 - 11 \] Convert 8 into a fraction with denominator 4: \[ 8 = \frac{32}{4} \] And 11 as: \[ 11 = \frac{44}{4} \] So, the denominator becomes: \[ \frac{3}{4} + \frac{32}{4} - \frac{44}{4} = \frac{3 + 32 - 44}{4} = \frac{-9}{4} \]
Now we have: Numerator: \(\frac{-25}{4}\) Denominator: \(\frac{-9}{4}\)
The overall expression is: \[ \frac{-25/4}{-9/4} = \frac{-25}{-9} = \frac{25}{9} \]
Now we can compare \( \frac{25}{9} \) with \( 1 \).
To convert \(1\) into a fraction with a common denominator, we can write: \[ 1 = \frac{9}{9} \]
Now compare: \[ \frac{25}{9} > \frac{9}{9} \]
So, the proper relation to place in the blank is: \[ \frac{25}{9} > 1 \]
Thus, the answer is: >