Decide whether each proposed addition or subtraction of measurements is possible. If it is possible, write the result in the last column of the table. Be sure every answer you enter has the correct unit symbol.
| proposed addition or subtraction | Is this possible? | result |
|---|---|---|
| [tex]$61.0 ms-36.0 ms=?$[/tex] | yes no | |
| [tex]$21.000 s+44.000 ms=?$[/tex] | yes no | |
| [tex]$42.0 g+45.0 L=$[/tex] ? | yes no | |
Answer (2)
The first operation is possible with a result of 25.0 ms, the second operation is also possible yielding 21044 ms or 21.044 s, while the third operation is not possible due to different units measuring different physical quantities.
;
Subtract 61.0 ms and 36.0 ms to get 25.0 ms .
Convert 21.000 s to 21000 ms and add 44.000 ms to get 21044 ms or convert 44.000 ms to 0.044 s and add to 21.000 s to get 21.044 s .
Adding 42.0 g and 45.0 L is not possible due to different units and physical quantities.
The final answers are: 25.0 ms , 21044 ms or 21.044 s , and not possible.
Explanation
Understanding the Problem We are given three proposed additions or subtractions of measurements and we need to determine if they are possible and, if so, calculate the result.
First Calculation For the first case, 61.0 ms − 36.0 ms , the units are the same (ms), so the subtraction is possible. We perform the subtraction: 61.0 − 36.0 = 25.0 . The result is 25.0 ms .
Second Calculation For the second case, 21.000 s + 44.000 ms , the units are different (s and ms), so we need to convert them to the same unit before adding. We convert seconds to milliseconds: 21.000 s = 21.000 × 1000 ms = 21000 ms . Now we add: 21000 ms + 44.000 ms = 21044 ms . Alternatively, we convert milliseconds to seconds: 44.000 ms = 1000 44.000 s = 0.044 s . Now we add: 21.000 s + 0.044 s = 21.044 s .
Third Case Analysis For the third case, 42.0 g + 45.0 L , the units are different (g and L) and they measure different physical quantities (mass and volume), so the addition is not possible.
Final Results In summary:
61.0 ms − 36.0 ms = 25.0 ms , which is possible.
21.000 s + 44.000 ms = 21044 ms = 21.044 s , which is possible.
42.0 g + 45.0 L is not possible because we are adding mass and volume.
Examples
Imagine you're baking a cake. You need to add flour (measured in grams) and water (measured in milliliters or liters). You can't directly add these two measurements because they represent different physical quantities. However, if you needed to combine two time measurements, like the time it takes to mix the batter (in seconds) and the time it takes to preheat the oven (in minutes), you'd first need to convert them to the same unit (either both in seconds or both in minutes) before adding them together. This ensures that you're adding like quantities, giving you a meaningful total time.
