I'm getting 2 different answers: diff. of 33 minutes 7 seconds & 6 minutes 50 seconds

Claire

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Jun 7, 2018
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I'm getting 2 different answers: diff. of 33 minutes 7 seconds & 6 minutes 50 seconds

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.
 
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.
You are misusing the "=" sign? I do not understand what do you mean by those?
 
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.
 
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.
What you have to the left of the equal sign must equal to what you have to the right of the equal sign.

I agree that 33 x 60 = 1980 BUT I do not agree that 33 x 60 = 1980 + 7
6 x 60 might equal 360 but 6 x 60 does not equal 360 + 50

Instead maybe write 33 x 60 + 7 = 1980 + 7 = 1987
6x 60 + 50= 360 + 50 = 410


30-6 = 24 +3 =27-50 = 26.10+7 = 26.17
: I do agree that 24 + 3 =27. Now here is where you are making your biggest mistake. You say that 27 - 50 (which I assume you mean 27 minutes - 50 seconds) = 26.10. THIS IS NOT TRUE. The .10 is .10minutes (ie one tenth of a minute which is 6 seconds!). You mean to write 26:10. This means 26 minutes and 10 seconds. On the other hand, 26.10 means 26 minutes and 6 seconds.

Since you are so confused I will show you how to do this problem. For the record the worst way to do this problem is with a calculator since it gives seconds as a decimal part of minutes.

33 minutes and 07 seconds
-6 minutes and 50 seconds. Now you can't subtract 50 seconds from 7 seconds SO YOU BORROW remembering that 1 minute = 60 seconds.

Now the problem looks like
32 minutes and 67 seconds
-6 minutes and 50 seconds
26 minutes and 17 seconds


Now 17 seconds is \(\displaystyle \frac{17}{60}\)minutes = .28minutes. This is the result from your calculator! So 26minutes and 17 seconds = 26.28minutes. 26.28minutes is NOT 26 minutes and 28 seconds. The .28minutes represents \(\displaystyle \frac{28}{100}\) of a minute NOT \(\displaystyle \frac{28}{60}\) of a minute which DOES equal 28 seconds.
 
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