Jonathan spent 5 2/5 hours studying. He spent 1/3 of the time studying science, and 1/2 of the remaining time studying math. How long did he spend studying science and math?

5 2/5 * 2/3 = ?

To find out how long Jonathan spent studying science, we need to multiply the total time spent studying by the fraction representing the time spent on science.

Total time spent studying = 5 2/5 hours

Time spent on science = 1/3 of total time spent studying

Time spent on science = (1/3) * (5 2/5)

To multiply a whole number by a fraction, we convert the whole number to an improper fraction.

5 = 5/1

5 2/5 = (5/1) + (2/5) = (25/5) + (2/5) = 27/5

Time spent on science = (1/3) * (27/5)

To multiply fractions, we multiply the numerators and the denominators.

Time spent on science = (1 * 27) / (3 * 5) = 27/15

We can simplify the fraction.

27/15 = 9/5

Therefore, Jonathan spent 9/5 hours studying science.

To find out how long Jonathan spent studying math, we need to subtract the time spent on science from the total time spent studying.

Time spent on math = Total time spent studying - Time spent on science

Time spent on math = 5 2/5 hours - 9/5 hours

First, we need to convert the whole number to an improper fraction.

5 = 5/1

5 2/5 = (5/1) + (2/5) = (25/5) + (2/5) = 27/5

Time spent on math = (27/5) - (9/5)

To subtract fractions, we need to make sure that they have the same denominator.

Largest common denominator for 5 and 5 is 5.

Time spent on math = (27 - 9) / 5

Time spent on math = 18/5

Therefore, Jonathan spent 18/5 hours studying math.

In summary,

Jonathan spent 9/5 hours studying science and 18/5 hours studying math.

To find out how long Jonathan spent studying science and math, we need to follow a few steps:

Step 1: Convert the mixed number of hours to an improper fraction.
Jonathan spent 5 2/5 hours studying, which is equal to 5 + 2/5. To convert 5 to a fraction, we multiply it by the denominator of the fraction (5 x 5 = 25) and add the numerator (25 + 2 = 27). So, Jonathan spent a total of 27/5 hours studying.

Step 2: Calculate the time spent studying science.
Jonathan spent 1/3 of the total time studying science. To find the time spent on science, we multiply 27/5 by 1/3. Multiplying the numerators (27 x 1 = 27) and the denominators (5 x 3 = 15), we get 27/15. This can be simplified to 9/5.

Step 3: Calculate the time spent studying math.
We know that Jonathan spent 1/2 of the remaining time studying math. The remaining time is the total time (27/5) minus the time spent on science (9/5). So, we have:
27/5 - 9/5 = 18/5

Multiplying 18/5 by 1/2, we get (18 x 1) / (5 x 2) = 18/10 = 9/5.

Therefore, Jonathan spent 9/5 hours studying science and math.