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

<
less than

=
equals

>
greater than

≥

Answer 1

To evaluate the expression \( 6 - \frac{1}{4} \cdot 28 - 2 \frac{1}{4} \) and \( \frac{3}{4} + 4 \cdot 2 - 11 \), we need to simplify both sides.

1. **Simplifying the left side**:
\[
6 - \frac{1}{4} \cdot 28 - 2 \frac{1}{4}
\]
First, calculate \( \frac{1}{4} \cdot 28 \):
\[
\frac{1}{4} \cdot 28 = 7
\]
Then, we convert \( 2 \frac{1}{4} \) to an improper fraction:
\[
2 \frac{1}{4} = \frac{9}{4}
\]
Now, substituting these into the expression:
\[
6 - 7 - \frac{9}{4}
\]
First, calculate \( 6 - 7 \):
\[
6 - 7 = -1
\]
Now, converting \(-1\) to a fraction:
\[
-1 = \frac{-4}{4}
\]
Thus, we have:
\[
-1 - \frac{9}{4} = \frac{-4}{4} - \frac{9}{4} = \frac{-13}{4}
\]

2. **Simplifying the right side**:
\[
\frac{3}{4} + 4 \cdot 2 - 11
\]
First, calculate \( 4 \cdot 2 \):
\[
4 \cdot 2 = 8
\]
Now substitute:
\[
\frac{3}{4} + 8 - 11
\]
Calculate \( 8 - 11 \):
\[
8 - 11 = -3
\]
Again, converting \(-3\) to a fraction:
\[
-3 = \frac{-12}{4}
\]
Thus, we have:
\[
\frac{3}{4} - 3 = \frac{3}{4} + \frac{-12}{4} = \frac{3 - 12}{4} = \frac{-9}{4}
\]

3. **Now we can compare the two results**:
\[
\frac{-13}{4} \quad \text{and} \quad \frac{-9}{4}
\]

Since \(\frac{-13}{4} < \frac{-9}{4}\), we determine that the left side is less than the right side.

Therefore, the correct operator to use is:

\[
< \quad \text{(less than)}
\]