Question

Consider the following expressions:

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

>
greater than

<
less than

=
equals

≥

Answer 1

To solve the expression \( 6 - \frac{1}{4} \cdot 28 - 2 \frac{1}{4} \) and \( 3/4 + 4 \cdot 2 - 11 \), we first need to evaluate each side of the inequality separately.

1. Calculate \( 6 - \frac{1}{4} \cdot 28 - 2 \frac{1}{4} \):
- First, calculate \( \frac{1}{4} \cdot 28 = 7 \).
- Next, convert \( 2 \frac{1}{4} \) to an improper fraction: \( 2 \frac{1}{4} = \frac{9}{4} \).
- Now proceed with the computation:
\[
6 - 7 - \frac{9}{4} = -1 - \frac{9}{4} = -\frac{4}{4} - \frac{9}{4} = -\frac{13}{4}
\]

2. Calculate \( 3/4 + 4 \cdot 2 - 11 \):
- First, calculate \( 4 \cdot 2 = 8 \).
- Now perform the rest of the computation:
\[
\frac{3}{4} + 8 - 11 = \frac{3}{4} - 3 = \frac{3}{4} - \frac{12}{4} = -\frac{9}{4}
\]

Now, we compare the calculated values:
- The left side \( 6 - \frac{1}{4} \cdot 28 - 2 \frac{1}{4} \) equals \( -\frac{13}{4} \).
- The right side \( 3/4 + 4 \cdot 2 - 11 \) equals \( -\frac{9}{4} \).

Now we compare \( -\frac{13}{4} \) and \( -\frac{9}{4} \):

Since \( -\frac{13}{4} < -\frac{9}{4} \), the operator that can be inserted is:

< (less than)

So, the answer is:

< (less than)