Question 10 options:
Solve this problem.
A video tape will record 6 hours in the EP mode. Kyle has recorded 2 1 over 6 hours of a baseball game. He wants to record 3 3 over 4 hours more on the same tape. Can he do this?
To solve this problem, we need to determine if the remaining 3 3/4 hours can fit on the tape, given that 2 1/6 hours have already been recorded.
First, we need to find the total number of hours that have been recorded:
2 1/6 hours = (12 + 1) / 6 = 13/6 hours
Next, we add the total recorded hours to the additional hours Kyle wants to record:
13/6 + 3 3/4 = 13/6 + (12 + 3) / 4 = 13/6 + 15/4
To add these fractions, we need a common denominator:
In this case, the least common multiple of 6 and 4 is 12.
Converting 13/6 to a fraction with a denominator of 12:
13/6 = (13 * 2) / (6 * 2) = 26/12
Now we can add the fractions:
26/12 + 15/4 = (26 + 45) / 12 = 71/12
Therefore, a total of 71/12 hours have been recorded or are planned to be recorded.
Since the tape can record 6 hours in the EP mode, and 71/12 is less than 6, Kyle can still record the remaining 3 3/4 hours on the same tape.
To determine if Kyle can record 3 3/4 hours more on the same tape, we need to check if there is enough remaining space on the tape.
First, let's find the total amount of time Kyle has already recorded:
2 1/6 hours + 3 3/4 hours
To add these fractions, we need to find a common denominator:
The common denominator for 6 and 4 is 12.
Now let's convert the fractions to have a denominator of 12:
2 1/6 hours = (2 * 6 + 1) / 6 = 13/6 hours
3 3/4 hours = (3 * 4 + 3) / 4 = 15/4 hours
Adding these converted fractions:
13/6 hours + 15/4 hours
To add fractions with different denominators, we need a common denominator, which is 24 (the product of 6 and 4).
Now let's convert the fractions to have a denominator of 24:
13/6 hours = (13 * 4) / (6 * 4) = 52/24 hours
15/4 hours = (15 * 6) / (4 * 6) = 90/24 hours
Adding these converted fractions:
52/24 hours + 90/24 hours = (52 + 90) / 24 = 142/24 hours
Therefore, Kyle has already recorded 142/24 hours of the baseball game.
Now, we need to check if there is enough remaining space on the tape:
6 hours (total tape capacity) - 142/24 hours (time already recorded)
To subtract fractions, we also need a common denominator of 24:
6 hours = (6 * 24) / 24 = 144/24 hours
Subtracting:
144/24 hours - 142/24 hours = (144 - 142) / 24 = 2/24 hours
Simplifying the fraction:
2/24 hours = 1/12 hours
Therefore, Kyle has 1/12 hours (or 5 minutes) of space remaining on the tape. Since 3 3/4 hours is greater than 1/12 hours, Kyle can record 3 3/4 hours more on the same tape.
To solve this problem, we need to determine if the remaining recording time required (3 3/4 hours) is less than or equal to the available recording time on the tape (6 hours - 2 1/6 hours).
First, we need to convert the mixed numbers to improper fractions:
2 1/6 = (2 * 6 + 1)/6 = 13/6
3 3/4 = (3 * 4 + 3)/4 = 15/4
Next, we subtract the time already recorded from the available recording time:
6 hours - 13/6 hours = (6 * 6/6) - 13/6 = (36/6) - (13/6) = 23/6
Now, we compare the remaining recording time required (15/4 hours) to the available recording time (23/6 hours):
15/4 hours <= 23/6 hours
To compare fractions, we need to find a common denominator. The least common denominator (LCD) of 4 and 6 is 12:
15/4 = (15 * 3)/ (4*3) = 45/12
23/6 = (23 * 2) / (6 * 2) = 46/12
Now we can compare the fractions:
45/12 <= 46/12
Since the remaining recording time required (45/12 hours) is less than or equal to the available recording time (46/12 hours), Kyle can record 3 3/4 hours more on the same tape.