bill spent 7 9/10 hours working on is reading and math homework. if he spent 5 3/6 hours on his reading homework, how much time did he spend on his math homework?
Get the same denominator;
7 27/30
5 15/30
Subtract
2 12/30
Simplified; 2 2/15
To find out how much time Bill spent on his math homework, we need to subtract the time he spent on his reading homework from the total time he spent on both subjects.
First, let's convert the mixed numbers to improper fractions for easier calculation:
7 9/10 hours = (7 * 10 + 9)/10 = 79/10 hours
5 3/6 hours = (5 * 6 + 3)/6 = 33/6 hours
Now, we can subtract the time spent on reading from the total time:
Total time - Time spent on reading = Time spent on math
79/10 - 33/6
To subtract fractions, we need to have a common denominator. In this case, the least common multiple (LCM) of 10 and 6 is 30. So, let's convert the fractions to have a denominator of 30:
(79/10) * (3/3) = 237/30
(33/6) * (5/5) = 165/30
Now, we can subtract the fractions:
237/30 - 165/30 = (237 - 165)/30 = 72/30
Since 72/30 can be simplified, let's reduce it:
72/30 = (2 * 36)/(2 * 15) = 36/15 = 12/5
After simplifying, we find that Bill spent 12/5 hours on his math homework.
Alternatively, this can be expressed as a mixed number:
12/5 = 2 2/5 hours
Therefore, Bill spent 2 2/5 hours on his math homework.