Jack spends 1 3/5 as long on his homework as Jill. Last week, Jill spent 7 1/4 hours doing homework. How long did Jack spend doing homework?
(29/4) * (8/5) = 232/20 = 11 3/5 hours
To find out how long Jack spent doing homework, you'll need to understand the relationship between Jack and Jill's homework time and use that to calculate Jack's time.
We're given that Jack spends 1 3/5 as long on his homework as Jill. This means that Jack's homework time is 1 3/5 times Jill's homework time.
Jill spent 7 1/4 hours doing homework last week. To calculate Jack's homework time, we need to multiply Jill's time by 1 3/5.
To multiply a whole number by a fraction, you can convert the whole number into a fraction by putting it over a denominator of 1. For example, 1 can be written as 1/1.
Let's convert 1 3/5 into an improper fraction. We multiply the whole number (1) by the denominator (5) and add the numerator (3). This gives us 5 + 3 = 8. So, 1 3/5 can be written as 8/5.
Now we can multiply Jill's time by 8/5 to find Jack's time:
7 1/4 hours = 29/4 hours (converting into improper fraction)
29/4 hours * 8/5 = (29 * 8) / (4 * 5) = 232/20
To simplify this fraction, we divide both the numerator and denominator by their greatest common divisor, which is 4.
232/20 = (232 ÷ 4) / (20 ÷ 4) = 58/5
Therefore, Jack spent 58/5 hours doing homework last week.