# Displaying time in Improper fraction form

• Feb 6th 2010, 04:20 AM
saberteeth
Displaying time in Improper fraction form
Hi, (Hi)

How is 1 hr 40 mins and 48 secs written in improper fraction form?

This is what i did and turned out to be wrong:

1 hr 40 (48/60) = 1 hr 40 (4/5) = 1hr (204/5) = (209/5)
• Feb 6th 2010, 04:40 AM
earboth
Quote:

Originally Posted by saberteeth
Hi, (Hi)

How is 1 hr 40 mins and 48 secs written in improper fraction form?

This is what i did and turned out to be wrong:

1 hr 40 (48/60) = 1 hr 40 (4/5) = 1hr (204/5) = (209/5)

$\displaystyle 1+\frac{40}{60}+\frac{48}{3600} = 1+\frac{2448}{3600}$

Now simplify the fraction a little bit.
• Feb 6th 2010, 05:04 AM
saberteeth
Quote:

Originally Posted by earboth
$\displaystyle 1+\frac{40}{60}+\frac{48}{3600} = 1+\frac{2448}{3600}$

Now simplify the fraction a little bit.

Thanks for your reply. I simplified it and the answer is still incorrect. Im ending up with 59/50

The answer is 126/75 as per the book.
• Feb 6th 2010, 05:17 AM
Henryt999
Quote:

Originally Posted by saberteeth
Thanks for your reply. I simplified it and the answer is still incorrect. Im ending up with 59/50.

The solution is given as:

1 hr 40 4 min = 1 51 hrs = 126 hrs. 5 75 75

Dear saberteenth
How did you simplify?

$\displaystyle 1+\frac{2448}{3600}$
Can not be $\displaystyle \frac{59}{50}$
because that is equal to $\displaystyle 1 +\frac{9}{50}$
$\displaystyle \frac{2448}{3600}$ you can see that the fraction is larger then $\displaystyle \frac{1}{2}$
9/50 is not so there is an error somewhere.
• Feb 6th 2010, 10:49 AM
earboth
Quote:

Originally Posted by saberteeth
Thanks for your reply. I simplified it and the answer is still incorrect. Im ending up with 59/50

The answer is 126/75 as per the book.

$\displaystyle 1+\frac{2448}{3600} = 1+\frac{2^4 \cdot 3^2 \cdot 17}{2^4 \cdot 3^2 \cdot 5^2}$

Simplify the fraction:

$\displaystyle 1+\frac{17}{25} = \frac{42}{25}\ hours$

By the way: With $\displaystyle \frac{126}{75}$ you can divide numerator and denominator by 3 to get $\displaystyle \frac{42}{25}$ .
• Feb 6th 2010, 11:25 AM
Masterthief1324
Your request is ambiguous. Do you want to rewrite time in fraction in terms of minutes? Seconds? Nanoseconds?

I'm assumming that you want 1 hour, 40 minutes, 48 seconds written in terms of seconds:

1. In order to write a fraction in terms of a unit, you have to know a unit equivalent. Since you want to know the time in terms of seconds, you have to know the number of seconds in 1 unit of the highest unit.

The highest unit is hours. The unit you want to convert it to is seconds. So the question to ask (a.k.a unit equivalent) is "How many seconds are there in 1 hour?" 3600 seconds in an hour; this will be your denominator.

2. To rewrite the given time in terms of seconds, find out each component's equivalent in terms of seconds:

$\displaystyle \frac {1 hour, 40 minutes, 48 seconds} {3600 seconds}$

Written in terms of seconds is:

$\displaystyle \frac {3600 seconds + 40(60) seconds + 48 seconds} {3600 seconds}$

Because 3600 seconds is 1 hour; 40 minutes is 2400 seconds; 48 seconds is 48 seconds. The sum of the numbers will equal to 1 hour 40 minutes and 48 seconds.

3. Thus the fraction becomes:
$\displaystyle \frac {6048}{3600}$

Which simplifies to $\displaystyle \frac {126} {75}$
• Feb 6th 2010, 11:31 AM
Masterthief1324
Quote:

Originally Posted by saberteeth
Thanks for your reply. I simplified it and the answer is still incorrect. Im ending up with 59/50

The answer is 126/75 as per the book.

Review adding and subtracting fractions. Be sure to find a common denominator and correspond the numerator of the respective fraction correctly.
• Feb 6th 2010, 06:11 PM
saberteeth
Quote:

Originally Posted by Masterthief1324

Written in terms of seconds is:

$\displaystyle \frac {3600 seconds + 40(60) seconds + 48 seconds} {3600 seconds}$

Because 3600 seconds is 1 hour; 40 minutes is 2400 seconds; 48 seconds is 48 seconds. The sum of the numbers will equal to 1 hour 40 minutes and 48 seconds.

3. Thus the fraction becomes:
$\displaystyle \frac {6048}{3600}$

Which simplifies to $\displaystyle \frac {126} {75}$

This is where i goofed up. I didn't know im supposed to unify the unit type and then operate on it. Thanks everybody for helping. I appreciate it.
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