Question

consider the following expressions:
6 - 1/4 cdot 28 - 2 1/4 _______ 3/4 + 4 cdot 2 - 11
which operation can be placed in the blank to make the statement true

Answer 1

no like is it less than more than equal to stuff like that what is it

Answer 2

Let's evaluate both sides of the expression step by step to find a suitable operation for the blank.

First, simplify the left side:

1. Start with \( 6 - \frac{1}{4} \cdot 28 - 2 \frac{1}{4} \).
- Calculate \( \frac{1}{4} \cdot 28 = 7 \).
- Convert \( 2 \frac{1}{4} \) to an improper fraction: \( 2 \frac{1}{4} = \frac{9}{4} \) (because \( 2 \cdot 4 + 1 = 9 \)).

Now we have:
\[
6 - 7 - \frac{9}{4}
\]

2. Convert \( 6 \) to a fraction with a denominator of 4:
\[
6 = \frac{24}{4}
\]

3. Now the expression becomes:
\[
\frac{24}{4} - 7 - \frac{9}{4} = \frac{24}{4} - \frac{28}{4} - \frac{9}{4}
\]

4. Combine the fractions:
\[
\frac{24 - 28 - 9}{4} = \frac{-13}{4}
\]

Now let's simplify the right side:

1. \( \frac{3}{4} + 4 \cdot 2 - 11 \).
- First calculate \( 4 \cdot 2 = 8 \).
- Therefore, it becomes:
\[
\frac{3}{4} + 8 - 11
\]

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

3. Now convert \( -3 \) to a fraction with a denominator of 4:
\[
-3 = \frac{-12}{4}
\]

4. Now the right side can be evaluated:
\[
\frac{3}{4} - \frac{12}{4}
\]
which becomes:
\[
\frac{3 - 12}{4} = \frac{-9}{4}
\]

Now we have:

- Left side: \( \frac{-13}{4} \)
- Right side: \( \frac{-9}{4} \)

So, we want to make \( \frac{-13}{4} \) equal to \( \frac{-9}{4} \) by placing some operation in the blank.

Now we can identify the operation.

To equate \(\frac{-13}{4}\) and \(\frac{-9}{4}\), we need:

\[
\frac{-13}{4} \; \_\_ \; \frac{-9}{4} = 0
\]

The operation to achieve that is:

\[
\frac{-13}{4} + \frac{4}{4} = \frac{-9}{4}
\]

Thus, we can place a **plus (+)** in the blank:

So the complete expression would be:

\( 6 - \frac{1}{4} \cdot 28 - 2 \frac{1}{4} \) **+** \( \frac{3}{4} + 4 \cdot 2 - 11 \)

Conclusively, the operation that fits the blank to make the statement true is: **+** (plus).

Answer 3

I apologize for the misunderstanding! Let's calculate both sides and determine the correct relation (greater than, less than, or equal to).

As we previously calculated:

1. **Left side:**
\[
6 - \frac{1}{4} \cdot 28 - 2 \frac{1}{4} = \frac{-13}{4} = -3.25
\]

2. **Right side:**
\[
\frac{3}{4} + 4 \cdot 2 - 11 = \frac{-9}{4} = -2.25
\]

Now we can compare the two results:

- Left side: \(-3.25\)
- Right side: \(-2.25\)

Here, \(-3.25 < -2.25\).

So, we can conclude:
\[
6 - \frac{1}{4} \cdot 28 - 2 \frac{1}{4} < \frac{3}{4} + 4 \cdot 2 - 11
\]

Thus, the operation that can be placed in the blank to make the statement true is: **<** (less than).