write each time period as a mixed number and as an improper fraction
1. 2 h 45 min
2. 3h 30 min
3.7h 10 min
1. 2 hours 45 minutes can be written as a mixed number as 2 45/60 or as an improper fraction as 135/60.
2. 3 hours 30 minutes can be written as a mixed number as 3 30/60 or as an improper fraction as 210/60.
3. 7 hours 10 minutes can be written as a mixed number as 7 10/60 or as an improper fraction as 430/60.
But hey, who's keeping track of fractions when you can just say "a little over 2 hours," "around 3 and a half hours," and "almost 7 and a half hours"? Fractions are fun and all, but they're like the clowns of math. Always trying to sneak their way in and confuse you.
To write each time period as a mixed number and as an improper fraction, we will convert the minutes to a fraction of an hour and then add it to the whole number of hours.
1. 2 hours 45 minutes:
To convert 45 minutes to hours, we divide it by 60 since there are 60 minutes in an hour:
45 minutes ÷ 60 = 0.75 hours
Now, we add the whole number of hours and the fraction of an hour:
2 + 0.75 = 2.75
As a mixed number: 2 hours and 45 minutes, or 2 3/4 hours.
As an improper fraction: 2.75 hours.
2. 3 hours 30 minutes:
To convert 30 minutes to hours:
30 minutes ÷ 60 = 0.5 hours
Now, we add the whole number of hours and the fraction of an hour:
3 + 0.5 = 3.5
As a mixed number: 3 hours and 30 minutes, or 3 1/2 hours.
As an improper fraction: 3.5 hours.
3. 7 hours 10 minutes:
To convert 10 minutes to hours:
10 minutes ÷ 60 = 0.1667 hours (rounded to 4 decimal places)
Now, we add the whole number of hours and the fraction of an hour:
7 + 0.1667 = 7.1667
As a mixed number: 7 hours and 10 minutes, or 7 1/6 hours (rounded to the nearest fraction).
As an improper fraction: 7.1667 hours.
To convert each time period into a mixed number and an improper fraction, we need to understand the relationship between hours and minutes.
1. 2 hours 45 minutes:
- To convert 2 hours into minutes, multiply by 60: 2 hours x 60 = 120 minutes.
- Add the 45 minutes: 120 minutes + 45 minutes = 165 minutes.
- The mixed number representation is 2 hours 45 minutes.
- To convert to an improper fraction, we use the formula: (hours x 60 + minutes) / 60. In this case, (2 x 60 + 45) / 60 = 165 / 60, which simplifies to 2 3/4.
2. 3 hours 30 minutes:
- Convert 3 hours into minutes: 3 hours x 60 = 180 minutes.
- Add the 30 minutes: 180 minutes + 30 minutes = 210 minutes.
- The mixed number representation is 3 hours 30 minutes.
- To convert to an improper fraction: (3 x 60 + 30) / 60 = 210 / 60, which simplifies to 3 1/2.
3. 7 hours 10 minutes:
- Convert 7 hours into minutes: 7 hours x 60 = 420 minutes.
- Add the 10 minutes: 420 minutes + 10 minutes = 430 minutes.
- The mixed number representation is 7 hours 10 minutes.
- To convert to an improper fraction: (7 x 60 + 10) / 60 = 430 / 60, which simplifies to 7 1/6.
So, the time periods expressed as mixed numbers and improper fractions are:
1. 2 hours 45 minutes or 2 3/4
2. 3 hours 30 minutes or 3 1/2
3. 7 hours 10 minutes or 7 1/6
2h 45 min = 2 45/60 hr = 2 3/4 hr = 11/4 hr
and so on