Question

Consider the following expressions:

6−14⋅2/8−2 1/4 _______ 3/4+4⋅2−11 .

Which operator can be inserted to make the statement true?

(1 point)
Responses

≥
greater-than-or-equal-to

<
less than

>
greater than

=

Answer 1

To determine which operator can be inserted between the two expressions in the statement:

**Expression 1:**
\( 6 - 14 \cdot \frac{2}{8} - 2 \frac{1}{4} \)

**Expression 2:**
\( \frac{3}{4} + 4 \cdot 2 - 11 \)

Let's compute both expressions step by step.

### For Expression 1:

1. Calculate \( 14 \cdot \frac{2}{8} \):
\[
14 \cdot \frac{2}{8} = 14 \cdot \frac{1}{4} = \frac{14}{4} = 3.5
\]

2. Then compute the whole expression:
\[
6 - 3.5 - 2 \frac{1}{4}
\]
First convert \( 2 \frac{1}{4} \) to an improper fraction:
\[
2 \frac{1}{4} = 2.25
\]
Now we calculate:
\[
6 - 3.5 - 2.25 = 6 - 5.75 = 0.25
\]

So, Expression 1 evaluates to \( 0.25 \).

### For Expression 2:

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

2. Now compute the whole expression:
\[
\frac{3}{4} + 8 - 11
\]
First calculate \( 8 - 11 \):
\[
8 - 11 = -3
\]
Now add \( \frac{3}{4} \):
\[
-3 + \frac{3}{4} = -3 + (-\frac{12}{4}) + \frac{3}{4} = -\frac{12-3}{4} = -\frac{9}{4}
\]
This simplifies to:
\[
-2.25
\]

So, Expression 2 evaluates to \( -2.25 \).

### Comparing the Two Expressions:

Now we need to place the operators correctly:
- Expression 1 = \( 0.25 \)
- Expression 2 = \( -2.25 \)

Now we can compare the two results:

\[
0.25 \quad \text{vs} \quad -2.25
\]

Since \( 0.25 > -2.25 \), we can conclude:

The operator that fits is **> (greater than)**.

Thus, the correct operator to insert is:

\[
\text{>} \quad \text{(greater than)}
\]