There commercials are played in a row between songs on the radio. The three commercials fill exactly 3 minutes of time. If the first commercial uses 1 1/6 minutes, and the second uses 3/5 minute, how long is the third commercial?
A. 23/30 minute
B. 1 23/30 minutes
C. 1 7/30 minutes
D. 2 7/30 minutes
1 1/6 + 3/5 = 1 5/30 + 18/30 = 1 23/30
Answer is D
To find the length of the third commercial, we first need to determine the total time used by the first two commercials.
The first commercial uses 1 and 1/6 minutes, which is the same as 6/6 and 1/6 minutes.
The second commercial uses 3/5 minute.
To find the total time used by the first two commercials, we add the lengths together:
6/6 + 1/6 + 3/5
= 7/6 + 3/5
To add these fractions, we need to find a common denominator. In this case, the least common denominator (LCD) is 30.
Multiplying the fractions by the appropriate factors to get the LCD:
(7/6) * (5/5) + (3/5) * (6/6)
= 35/30 + 18/30
Adding the fractions:
35/30 + 18/30
= 53/30
Therefore, the total time used by the first two commercials is 53/30 minutes.
Since the total time used by the three commercials is 3 minutes, we can find the length of the third commercial by subtracting the total time used by the first two commercials from 3:
3 - 53/30
To subtract fractions, we need a common denominator. The LCD in this case is still 30.
(3/1) - (53/30)
= (90/30) - (53/30)
= 37/30
So the length of the third commercial is 37/30 minutes.
Therefore, the answer is D. 2 7/30 minutes.
To find out the length of the third commercial, we need to subtract the time taken by the first and second commercials from the total time of 3 minutes.
First, let's convert the time taken by the first commercial, which is 1 1/6 minutes, into an improper fraction. We know that 1 whole minute is equal to 6/6, so we can rewrite 1 as 6/6. Therefore, the first commercial takes (6/6 + 1/6) minutes, which simplifies to 7/6 minutes.
Next, let's convert the time taken by the second commercial, which is 3/5 minute, into a common denominator with the first commercial. The common denominator is 30, so we multiply both the numerator and denominator of 3/5 by 6 to get 18/30. Therefore, the second commercial takes 18/30 minutes.
Now, we can subtract the time taken by the first and second commercials from the total time of 3 minutes:
3 - (7/6 + 18/30)
To simplify this calculation, we need to find a common denominator between 6 and 30, which is 30.
Converting the fraction 7/6 to a fraction with a denominator of 30 gives us (35/30).
Now, we have:
3 - (35/30 + 18/30)
Combining the fractions inside the parentheses:
3 - (53/30)
To subtract fractions, we need to have a common denominator. In this case, it is 30. Let's bring 3 to a fraction with 30 as the denominator. 3 is equivalent to (90/30).
Therefore, we have:
(90/30) - (53/30)
Subtracting the fractions:
(90 - 53)/30 = 37/30
So, the length of the third commercial is 37/30 minutes.
In mixed number form, 37/30 can be written as 1 7/30.
Therefore, the answer is C. 1 7/30 minutes.