Question

Question
Drag the expressions to order them top to bottom from least to greatest.

Arrange responses in the correct order to answer the question. Select a response, navigate to the desired position and insert response at that position. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can be moved using the up and down arrow keys or by dragging with a mouse.


-4 3/7

-4 6/7

-5 3/7

4 2/7

5 1/5

Answer 1

the last one is supposed to be 5 1/7

Answer 2

To order the expressions from least to greatest, let's first convert them into improper fractions so we can easily compare them.

1. **-4 3/7** = -4 + (3/7) = -\(\frac{28}{7}\) - \(\frac{3}{7}\) = -\(\frac{31}{7}\)
2. **-4 6/7** = -4 + (6/7) = -\(\frac{28}{7}\) - \(\frac{6}{7}\) = -\(\frac{34}{7}\)
3. **-5 3/7** = -5 + (3/7) = -\(\frac{35}{7}\) - \(\frac{3}{7}\) = -\(\frac{38}{7}\)
4. **4 2/7** = 4 + (2/7) = \(\frac{28}{7}\) + \(\frac{2}{7}\) = \(\frac{30}{7}\)
5. **5 1/5** = 5 + (1/5) = \(\frac{25}{5}\) + \(\frac{1}{5}\) = \(\frac{26}{5}\) = \(\frac{78}{15}\) (this value is approximately 5.2)

Now, let's compare the values:

- **-5 3/7 (least)**: -\(\frac{38}{7}\) (approximately -5.43)
- **-4 6/7**: -\(\frac{34}{7}\) (approximately -4.86)
- **-4 3/7**: -\(\frac{31}{7}\) (approximately -4.43)
- **4 2/7**: \(\frac{30}{7}\) (approximately 4.29)
- **5 1/5 (greatest)**: \(\frac{26}{5}\) (approximately 5.2)

Now, let's arrange them from least to greatest:

1. **-5 3/7**
2. **-4 6/7**
3. **-4 3/7**
4. **4 2/7**
5. **5 1/5**

So the correct order from least to greatest is:

-5 3/7
-4 6/7
-4 3/7
4 2/7
5 1/5

Answer 3

Thank you for the correction. Let's redo the ordering with the updated expression \(5 \frac{1}{7}\).

1. **-4 \(\frac{3}{7}\)** = -4 + \(\frac{3}{7}\) = -\(\frac{28}{7}\) - \(\frac{3}{7}\) = -\(\frac{31}{7}\)

2. **-4 \(\frac{6}{7}\)** = -4 + \(\frac{6}{7}\) = -\(\frac{28}{7}\) - \(\frac{6}{7}\) = -\(\frac{34}{7}\)

3. **-5 \(\frac{3}{7}\)** = -5 + \(\frac{3}{7}\) = -\(\frac{35}{7}\) - \(\frac{3}{7}\) = -\(\frac{38}{7}\)

4. **4 \(\frac{2}{7}\)** = 4 + \(\frac{2}{7}\) = \(\frac{28}{7}\) + \(\frac{2}{7}\) = \(\frac{30}{7}\)

5. **5 \(\frac{1}{7}\)** = 5 + \(\frac{1}{7}\) = \(\frac{35}{7}\) + \(\frac{1}{7}\) = \(\frac{36}{7}\)

Now, let's compare the values:

- **-5 \(\frac{3}{7}\)** \(\approx -5.43\) (-\(\frac{38}{7}\))
- **-4 \(\frac{6}{7}\)** \(\approx -4.86\) (-\(\frac{34}{7}\))
- **-4 \(\frac{3}{7}\)** \(\approx -4.43\) (-\(\frac{31}{7}\))
- **4 \(\frac{2}{7}\)** \(\approx 4.29\) (\(\frac{30}{7}\))
- **5 \(\frac{1}{7}\)** \(\approx 5.14\) (\(\frac{36}{7}\))

Now we can arrange them from least to greatest:

1. **-5 \(\frac{3}{7}\)**
2. **-4 \(\frac{6}{7}\)**
3. **-4 \(\frac{3}{7}\)**
4. **4 \(\frac{2}{7}\)**
5. **5 \(\frac{1}{7}\)**

So the final order from least to greatest is:

-5 \(\frac{3}{7}\)
-4 \(\frac{6}{7}\)
-4 \(\frac{3}{7}\)
4 \(\frac{2}{7}\)
5 \(\frac{1}{7}\)