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-or-equal-to

>
greater than

<
less than

=

Answer 1

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

Let's calculate the left side:

6 - 1/4 ⋅ 28 - 2 1/4.

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

2. Replace \(1/4 \cdot 28\) with 7 in the expression:
\[ 6 - 7 - 2 \frac{1}{4} \]

3. Combine \(6 - 7\):
\[ -1 - 2 \frac{1}{4} \]
First, convert \(2 \frac{1}{4}\) to an improper fraction:
\[ 2 \frac{1}{4} = \frac{9}{4} \]

4. Now we can combine:
\[ -1 - \frac{9}{4} = -\frac{4}{4} - \frac{9}{4} = -\frac{13}{4} \]

Now let's compute the right side:

3/4 + 4 ⋅ 2 - 11.

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

2. Replace \(4 \cdot 2\) with 8 in the expression:
\[ \frac{3}{4} + 8 - 11 \]

3. Combine \(8 - 11\):
\[ \frac{3}{4} - 3 \]
Convert 3 to a fraction:
\[ 3 = \frac{12}{4} \]

4. Now combine:
\[ \frac{3}{4} - \frac{12}{4} = -\frac{9}{4} \]

Now we have the two sides:

Left side: \(-\frac{13}{4}\)

Right side: \(-\frac{9}{4}\)

Now we check which operator can fit between the two:

- \(-\frac{13}{4} < -\frac{9}{4}\)

Thus, the appropriate operator to insert between the two sides is:

< (less than).

So the answer is **< (less than)**.