Question

why is 2 3/4 less than 2
Answer
why is it less
Answer
why is 2 x 3/4 less than 2
Answer
what ratio is equal to 2:5
Answer
which ratio is equivalent to the ratio 2 : 5
Answer
avery drops a rock from an elevation of 2 1/4 meter above the surface of a body of water the rock lands at an elevation of -2 1/2 meters which value represents the distance the rock falls in meters
Answered by GPT-4o mini
The fraction \( 2 \frac{3}{4} \) (which is read as “two and three-fourths”) represents a value that is greater than 2. To understand this, let's break it down:

1. The whole number part is 2.
2. The fractional part is \( \frac{3}{4} \), which is equal to 0.75 as a decimal.

When you combine these two parts, \( 2 \frac{3}{4} = 2 + \frac{3}{4} = 2 + 0.75 = 2.75 \).

Since 2.75 is greater than 2, we can conclude that \( 2 \frac{3}{4} \) is actually greater than 2, not less than 2.

If you meant to compare \( 2 \frac{3}{4} \) with some other number, please clarify, and I can help with that!
Answered by GPT-4o mini
It seems there might be a misunderstanding or a miscommunication regarding the values being compared. To clarify:

- **\( 2 \frac{3}{4} \)** (two and three-quarters) is equal to \( 2.75 \) in decimal form.
- **2** is simply \( 2.00 \) in decimal form.

Comparing the two:

- \( 2.75 \) (or \( 2 \frac{3}{4} \)) is greater than \( 2 \).

So, \( 2 \frac{3}{4} \) is **not** less than 2; it is indeed greater than 2.

If you are referencing a different comparison, please provide more information or context, and I would be happy to assist!
Answered by GPT-4o mini
Let's evaluate the expression \(2 \times \frac{3}{4}\) and compare it to 2.

1. **Calculate \(2 \times \frac{3}{4}\)**:
\[
2 \times \frac{3}{4} = \frac{2 \times 3}{4} = \frac{6}{4} = \frac{3}{2} = 1.5
\]

So, \(2 \times \frac{3}{4} = 1.5\).

2. **Compare it to 2**:
- \(1.5\) is indeed less than \(2\).

Thus, \(2 \times \frac{3}{4}\) is less than 2 because \(1.5 < 2\).
Answered by GPT-4o mini
The ratio \( 2:5 \) can be expressed in several equivalent forms by scaling both parts of the ratio by the same factor. Here are some examples of ratios that are equal to \( 2:5 \):

1. **Scaling by 2**:
\[
2 \times 2 : 5 \times 2 = 4 : 10
\]

2. **Scaling by 3**:
\[
2 \times 3 : 5 \times 3 = 6 : 15
\]

3. **Scaling by 4**:
\[
2 \times 4 : 5 \times 4 = 8 : 20
\]

In general, any ratio of the form \( 2n : 5n \) where \( n \) is a non-zero number will be equal to \( 2:5 \).

You can also express the ratio as a fraction:
\[
\frac{2}{5}
\]

This fraction is also equivalent to the ratio \( 2:5 \).
Answered by GPT-4o mini
To find ratios that are equivalent to \(2:5\), you can multiply both parts of the ratio by the same non-zero number. Here are a few examples:

1. **Multiply by 2**:
\[
2 \times 2 : 5 \times 2 = 4:10
\]

2. **Multiply by 3**:
\[
2 \times 3 : 5 \times 3 = 6:15
\]

3. **Multiply by 4**:
\[
2 \times 4 : 5 \times 4 = 8:20
\]

4. **Multiply by 5**:
\[
2 \times 5 : 5 \times 5 = 10:25
\]

5. **Multiply by 10**:
\[
2 \times 10 : 5 \times 10 = 20:50
\]

In general, any ratio of the form \(2n : 5n\) (where \(n\) is a positive non-zero integer) will be equivalent to \(2:5\).

You can also represent this ratio as a fraction:
\[
\frac{2}{5}
\]

This fraction is equivalent to the ratio \(2:5\).
Answered by GPT-4o mini
To determine the distance the rock falls, we need to find the difference in elevation between the initial height from which the rock was dropped and the height at which it lands.

1. **Initial height**: \(2 \frac{1}{4}\) meters
2. **Final height**: \(-2 \frac{1}{2}\) meters

### Step 1: Convert the mixed numbers to improper fractions

- \(2 \frac{1}{4} = \frac{9}{4}\) (because \(2 \times 4 + 1 = 9\))
- \(-2 \frac{1}{2} = -\frac{5}{2}\) (because \(-2 \times 2 - 1 = -5\))

### Step 2: Find the distance fallen

The distance fallen can be calculated by finding the difference between the initial and final heights. To do this properly, you calculate the total distance as follows:

\[
\text{Distance} = \text{Initial height} - \text{Final height} = \frac{9}{4} - \left(-\frac{5}{2}\right)
\]

This is the same as adding since subtracting a negative is equivalent to addition.

### Step 3: Find a common denominator

The common denominator for \(4\) and \(2\) is \(4\). So we need to convert \(-\frac{5}{2}\) to have a denominator of \(4\):

\[
-\frac{5}{2} = -\frac{5 \times 2}{2 \times 2} = -\frac{10}{4}
\]

### Step 4: Add the two fractions

Now we can add:

\[
\text{Distance} = \frac{9}{4} + \frac{10}{4} = \frac{19}{4}
\]

### Step 5: Convert back to a mixed number (if needed)

To convert \(\frac{19}{4}\) back to a mixed number:

\[
\frac{19}{4} = 4 \frac{3}{4}
\]

Thus, the distance the rock falls is \(4 \frac{3}{4}\) meters or \(4.75\) meters in decimal.