sam spent a total of 5 2/3 hours doing homework. Julia spent 5 5/6 hours doing homework. who spent more time on homework this week?
5 2/3 = 5 4/6
To compare the time Sam and Julia spent on homework, we need to convert their mixed numbers into improper fractions. Let's start with Sam:
Sam spent a total of 5 2/3 hours doing homework. To convert 5 2/3 into an improper fraction, first, we multiply the whole number (5) by the denominator of the fraction (3) and add the numerator (2). This gives us:
5 * 3 = 15
15 + 2 = 17
So, Sam spent a total of 17/3 hours doing homework.
Now let's convert Julia's time:
Julia spent 5 5/6 hours doing homework. Following the same process, we multiply the whole number (5) by the denominator of the fraction (6) and add the numerator (5). This gives us:
5 * 6 = 30
30 + 5 = 35
Therefore, Julia spent a total of 35/6 hours doing homework.
To determine who spent more time on homework, we can compare the fractions:
17/3 vs. 35/6
To compare fractions, we need to find a common denominator. The least common multiple of 3 and 6 is 6. By multiplying 17/3 by 2/2 and 35/6 by 1/1, the fractions have a common denominator:
(17/3) * (2/2) = 34/6
(35/6) * (1/1) = 35/6
So, we can see that 34/6 is less than 35/6.
Thus, Julia spent more time on homework this week.