Good Morning,
The question is simple.
Work out the difference between 33 minutes and 7 seconds and 6 minutes 50 seconds.
My working out for this is below:
1. with Calculator
33 x 60 = 1980 + 7 = 1987
6x 60 = 360 + 50 = 410
1987-410 = 1577
1577/60 = 26.28
2. without calculator
30-6 = 24 +3 =27-50 = 26.10+7 = 26.17
Why am I getting 2 different results, any help is appreciated.
The equal button on a calculator can be used in a way that is inconsistent with the meaning of an equal sign in mathematics. Moreover, decimal hours are not the same as hours and minutes.
Both your methods will work if done properly.
Method 1: Convert hours and minutes to minutes, subtract, and convert minutes to hours and minutes.
Convert 33 hours 7 minutes to minutes.
\(\displaystyle 33 \times 60 = 1980.\)
\(\displaystyle 1980 + 7 = 1987.\)
Convert 6 hours and 50 minutes to minutes.
\(\displaystyle 6 \times 60 = 360.\)
\(\displaystyle 360 + 50 = 410.\)
Subtract.
\(\displaystyle 1987 - 410 = 1577.\)
So far you were doing fine, and you showed the right sequence of keys for a calculator although it is not proper math notation.
You then calculated hours, which makes good sense, but a calculator will usually give you a decimal approximation rather than an exact fraction and will not break hours into hours and minutes.
\(\displaystyle \dfrac{1577}{60} = 26 + \dfrac{17}{60} \approx 26.28.\)
But that is an answer in hours only, not hours and minutes.
\(\displaystyle \dfrac{17}{60} \text { hours is } 17 \text { minutes.}\)
So the correct answer is 26 hours and 17 minutes, which is
approximately 26.28 hours.
Method 2: Work with hours and minutes separately.
Start with minutes. You can't subtract 50 from 7 within the non-negative numbers. So you must "borrow" some minutes from the hours. Subtracting 1 hour from the hours let's you add 60 to the minutes.
\(\displaystyle 33 \text { hours and } 7 \text { minutes is the same as } 32 \text { hours and } 67 \text { minutes.}\)
\(\displaystyle 67 \text { minutes } - 50 \text { minutes } = 17 \text { minutes.}\)
OK you are done with minutes. Now for hours, but remember you "borrowed" one hour.
\(\displaystyle 32 \text { hours } - 6 \text { hours } = 26 \text { hours.}\)
The correct answer is 26 hours and 17 minutes, which is
NOT 26.17 hours.