Consider the following expressions:

Question

6−1/4⋅28−2 1/4_______3/4+4⋅2−11.

Which operator can be inserted to make the statement true?
(1 point)
Responses

=
equals
≥
greater-than-or-equal-to
<
less than
>

Answer 1

To determine which operator can be inserted to make the statement true, we need to evaluate both sides of the expression.

First, let's calculate the left side:

\( 6 - 1/4 \cdot 28 - 2 \frac{1}{4} \)

Let's break it down step by step.

1. Calculate \( 1/4 \cdot 28 \): \[ 1/4 \cdot 28 = 7 \]

2. Then substitute this back into the expression: \[ 6 - 7 - 2 \frac{1}{4} \]

3. Convert \( 2 \frac{1}{4} \) into an improper fraction or decimal: \[ 2 \frac{1}{4} = 2.25 \]

4. Now plug it in: \[ 6 - 7 - 2.25 \]

5. Calculate \( 6 - 7 \): \[ 6 - 7 = -1 \]

6. Now calculate: \[ -1 - 2.25 = -3.25 \]

Thus, the left side equals \( -3.25 \).

Now let's calculate the right side:

\( 3/4 + 4 \cdot 2 - 11 \)

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

2. Substitute back into the expression: \[ 3/4 + 8 - 11 \]

3. Combine \( 8 - 11 \): \[ 8 - 11 = -3 \]

4. Now, add \( 3/4 \): \[ -3 + 3/4 = -3 + 0.75 = -2.25 \]

Now we have:

• Left side = -3.25
• Right side = -2.25

Now we will compare the two sides:

Since \( -3.25 < -2.25 \), the appropriate operator to insert between the expressions is:

< (less than).

Thus, the answer is: < (less than).