6 - 1/4 * 28 - 2(1/4) ___ 3/4 + 4 * 2 - 11

Question

Which operator can be inserted to make the statement true?
=
(>_)
>
<

Answer 1

Let's simplify the expression given:

Expression:
\[ 6 - \frac{1}{4} \times 28 - 2\left(\frac{1}{4}\right) \quad __ \quad \frac{3}{4} + 4 \times 2 - 11 \]

Step 1: Calculate the left side.

1. Calculate \( \frac{1}{4} \times 28 \): \[ \frac{1}{4} \times 28 = 7 \]

2. Now substitute: \[ 6 - 7 - 2\left(\frac{1}{4}\right) \]

3. Calculate \( 2\left(\frac{1}{4}\right) \): \[ 2 \times \frac{1}{4} = \frac{2}{4} = \frac{1}{2} \]

4. Now substitute: \[ 6 - 7 - \frac{1}{2} \] \[ = -1 - \frac{1}{2} \] \[ = -\frac{2}{2} - \frac{1}{2} = -\frac{3}{2} \]

Step 2: Calculate the right side.

1. Calculate \( 4 \times 2 \): \[ 4 \times 2 = 8 \]

2. Now substitute: \[ \frac{3}{4} + 8 - 11 \] \[ = \frac{3}{4} + 8 - 11 = \frac{3}{4} + 8 - 11 = \frac{3}{4} - 3 \] \[ = \frac{3}{4} - \frac{12}{4} = -\frac{9}{4} \]

Step 3: Compare both sides:

Now we compare:

• Left side: \( -\frac{3}{2} = -\frac{6}{4} \)
• Right side: \( -\frac{9}{4} \)

Step 4: Determining the operator:

Now we check:

• \( -\frac{6}{4} > -\frac{9}{4} \)
• \( -\frac{6}{4} < -\frac{9}{4} \)

Since \( -\frac{6}{4} \) is greater than \( -\frac{9}{4} \):

The operator that can be inserted to make the statement true is: \[ > \]

Therefore, the answer is >.