Question
-4/5 over -1/5
Which scenarios match the expression above?
Bruce's uncle is an oceanographer. He is in a submarine and is going to a depth of of a mile below sea level. So far, he has gone of a mile below sea level. How much deeper is he going to go?
Vince is writing an English paper that needs to be of a page long. He has written of a page. How much more of a page does he need to write?
A whale shark can dive to a depth of of a mile below zero. The record for a human diver is of a mile below zero. How many times deeper can the whale shark dive than a human?
Gina is measuring the distances of cities in South America from the equator and labeling distances above the equator positive and below the equator negative. On her map, Caracas is of a foot below the equator and Lima is of a foot below the equator. How many times farther below the equator is Caracas than Lima?
Gavin's golden retriever, Burt, is of a meter long. His Jack Russell terrier, Spot, is of a meter long. How many times longer is Burt than Spot?
Which scenarios match the expression above?
Bruce's uncle is an oceanographer. He is in a submarine and is going to a depth of of a mile below sea level. So far, he has gone of a mile below sea level. How much deeper is he going to go?
Vince is writing an English paper that needs to be of a page long. He has written of a page. How much more of a page does he need to write?
A whale shark can dive to a depth of of a mile below zero. The record for a human diver is of a mile below zero. How many times deeper can the whale shark dive than a human?
Gina is measuring the distances of cities in South America from the equator and labeling distances above the equator positive and below the equator negative. On her map, Caracas is of a foot below the equator and Lima is of a foot below the equator. How many times farther below the equator is Caracas than Lima?
Gavin's golden retriever, Burt, is of a meter long. His Jack Russell terrier, Spot, is of a meter long. How many times longer is Burt than Spot?
Answers
GPT-4o mini
The expression \(-\frac{4}{5}\) over \(-\frac{1}{5}\) can be simplified to find how many times one value fits into the other, which is essentially dividing two negative fractions:
\[
-\frac{4}{5} \div -\frac{1}{5} = \frac{-4}{5} \times \frac{-5}{1} = 4
\]
This indicates that the first value is 4 times the second value. Now, we can analyze each scenario to see which one matches this concept:
1. **Bruce's Uncle** - He is going to a depth of \(-\frac{4}{5}\) of a mile, and has already gone \(-\frac{1}{5}\) of a mile. To find how much deeper he is going:
\[
\text{Depth to go} = -\frac{4}{5} - (-\frac{1}{5}) = -\frac{4}{5} + \frac{1}{5} = -\frac{3}{5} \text{ miles}
\]
This doesn’t match the given expression.
2. **Vince's English Paper** - The length needed is \(-\frac{4}{5}\) of a page and he has written \(-\frac{1}{5}\) of a page:
\[
\text{Remaining length} = -\frac{4}{5} - (-\frac{1}{5}) = -\frac{4}{5} + \frac{1}{5} = -\frac{3}{5} \text{ pages}
\]
This also doesn’t match.
3. **Whale Shark Diving Depth** - The whale shark can dive to \(-\frac{4}{5}\) of a mile below zero, and the human diver goes to \(-\frac{1}{5}\) of a mile below zero. Calculating how many times deeper the whale shark can dive than the human:
\[
\frac{-\frac{4}{5}}{-\frac{1}{5}} = 4
\]
This matches the expression.
4. **Gina's Map** - Caracas is at \(-\frac{4}{5}\) feet and Lima is at \(-\frac{1}{5}\) feet. Calculating how many times farther below the equator Caracas is than Lima:
\[
\frac{-\frac{4}{5}}{-\frac{1}{5}} = 4
\]
This matches the expression too.
5. **Gavin's Dogs** - Burt is \(-\frac{4}{5}\) meters long and Spot is \(-\frac{1}{5}\) meters long. Calculating how many times longer Burt is than Spot:
\[
\frac{-\frac{4}{5}}{-\frac{1}{5}} = 4
\]
This also matches the expression.
Thus, the scenarios that match the expression \(-\frac{4}{5}\) over \(-\frac{1}{5}\) (or \(\frac{4}{1}\)) are:
- A whale shark can dive to a depth of \(-\frac{4}{5}\) of a mile below zero compared to a human diver at \(-\frac{1}{5}\) of a mile below zero. It can dive 4 times deeper.
- Gina's distances for Caracas at \(-\frac{4}{5}\) feet and Lima at \(-\frac{1}{5}\) feet gives that Caracas is 4 times farther below the equator than Lima.
- Gavin's dogs where Burt is 4 times longer than Spot.
So, the matching scenarios are the **whale shark diving depth**, **Gina measuring the distances**, and **Gavin's dogs**.
\[
-\frac{4}{5} \div -\frac{1}{5} = \frac{-4}{5} \times \frac{-5}{1} = 4
\]
This indicates that the first value is 4 times the second value. Now, we can analyze each scenario to see which one matches this concept:
1. **Bruce's Uncle** - He is going to a depth of \(-\frac{4}{5}\) of a mile, and has already gone \(-\frac{1}{5}\) of a mile. To find how much deeper he is going:
\[
\text{Depth to go} = -\frac{4}{5} - (-\frac{1}{5}) = -\frac{4}{5} + \frac{1}{5} = -\frac{3}{5} \text{ miles}
\]
This doesn’t match the given expression.
2. **Vince's English Paper** - The length needed is \(-\frac{4}{5}\) of a page and he has written \(-\frac{1}{5}\) of a page:
\[
\text{Remaining length} = -\frac{4}{5} - (-\frac{1}{5}) = -\frac{4}{5} + \frac{1}{5} = -\frac{3}{5} \text{ pages}
\]
This also doesn’t match.
3. **Whale Shark Diving Depth** - The whale shark can dive to \(-\frac{4}{5}\) of a mile below zero, and the human diver goes to \(-\frac{1}{5}\) of a mile below zero. Calculating how many times deeper the whale shark can dive than the human:
\[
\frac{-\frac{4}{5}}{-\frac{1}{5}} = 4
\]
This matches the expression.
4. **Gina's Map** - Caracas is at \(-\frac{4}{5}\) feet and Lima is at \(-\frac{1}{5}\) feet. Calculating how many times farther below the equator Caracas is than Lima:
\[
\frac{-\frac{4}{5}}{-\frac{1}{5}} = 4
\]
This matches the expression too.
5. **Gavin's Dogs** - Burt is \(-\frac{4}{5}\) meters long and Spot is \(-\frac{1}{5}\) meters long. Calculating how many times longer Burt is than Spot:
\[
\frac{-\frac{4}{5}}{-\frac{1}{5}} = 4
\]
This also matches the expression.
Thus, the scenarios that match the expression \(-\frac{4}{5}\) over \(-\frac{1}{5}\) (or \(\frac{4}{1}\)) are:
- A whale shark can dive to a depth of \(-\frac{4}{5}\) of a mile below zero compared to a human diver at \(-\frac{1}{5}\) of a mile below zero. It can dive 4 times deeper.
- Gina's distances for Caracas at \(-\frac{4}{5}\) feet and Lima at \(-\frac{1}{5}\) feet gives that Caracas is 4 times farther below the equator than Lima.
- Gavin's dogs where Burt is 4 times longer than Spot.
So, the matching scenarios are the **whale shark diving depth**, **Gina measuring the distances**, and **Gavin's dogs**.