monica spent 8/13 hours listening to tapes of beethoven and brahms. she spent 2/5 hours listening to beethoven. how many hours were spent listenign to brahms
To find out how many hours Monica spent listening to Brahms, we need to subtract the time she spent listening to Beethoven from the total time she spent listening to both composers.
1. Let's start by finding the time Monica spent listening to Beethoven:
- Monica spent 2/5 hours listening to Beethoven.
2. Next, let's calculate the total time Monica spent listening to both composers:
- The total time Monica spent listening to both composers is 8/13 hours.
3. Now, let's subtract the time Monica spent listening to Beethoven from the total time:
Total time - Beethoven's time = Brahms's time
8/13 hours - 2/5 hours = ?
To subtract these fractions, we need to have a common denominator.
4. Let's find the common denominator for 13 and 5:
The first denominator (13) is a prime number, so we can't divide it evenly.
The second denominator (5) is a prime number, so we can't divide it evenly.
To find the least common multiple (LCM), we can multiply the denominators together since they don't share any common factors:
13 × 5 = 65
5. Now, let's rewrite the fractions with the common denominator of 65:
8/13 hours = (8/13) × (5/5) = 40/65 hours
2/5 hours = (2/5) × (13/13) = 26/65 hours
6. Finally, let's subtract the fractions:
40/65 hours - 26/65 hours = 14/65 hours
Therefore, Monica spent 14/65 hours listening to Brahms.
To find out how many hours Monica spent listening to Brahms, we can subtract the time she spent listening to Beethoven from the total time she spent listening to both Beethoven and Brahms.
Monica spent 8/13 hours listening to both Beethoven and Brahms.
Monica spent 2/5 hours listening to Beethoven.
To find out how many hours she spent listening to Brahms, we subtract the time spent on Beethoven from the total time.
Brahms' time = Total time - Beethoven's time
Brahms' time = 8/13 hours - 2/5 hours
To subtract fractions with different denominators, we need to find a common denominator. In this case, the common denominator is 65, which is the least common multiple of 13 and 5.
First, we'll convert both fractions to have a denominator of 65:
Beethoven's time = 2/5 hours * (13/13) = 26/65 hours
Total time = 8/13 hours * (5/5) = 40/65 hours
Next, we can subtract Beethoven's time from the total time:
Brahms' time = 40/65 hours - 26/65 hours
Brahms' time = (40 - 26)/65 hours
Brahms' time = 14/65 hours
Therefore, Monica spent 14/65 hours listening to Brahms.
8/13 = 40/65
2/5 = 26/65
40/65 - 26/65 = ?