At boarding school, students spend 1/4 of their time eating and sleeping, 3/5 of their time in class, and 1'12 studying. The rest of the time is considered free time, which the student can spend doing activities of their own choosing. What fraction is considered free time?

1/15 of their time is free time.

Step-by-step explanation:

To find the answer to this 2-step problem, we have to add all the fractions up, then find how much of that time is not part of the fraction.

So to add all the fractions, you have the equation:

1/4 + 3/5 + 1/12

The first thing we have to do is to find a common denominator.

4, 5, and 12 are each able to multiply into 60.

So we can make the equation now with a common denominator.

15/60+36/60+5/60=56/60.

We now can simplfy this.

56/60=14/15

Now that we know how long it is to do all the other activities, it tells us that the rest of the time is free time. To find the rest of the time, we have to do:

1-14/15=1/15

So 1/15 of their time is free time.

(f - g)(x) = 5x^3 - 3

step-by-step explanation:

rearrange these functions vertically, with like terms in separate columns:

f(x) = 5x^3 - 2

g(x) =         +1

now subtract, column by column:

(f - g)(x) = 5x^3 - 3

n=9

step-by-step explanation:

7 times a number = 7n

decreased by 13 = 7n-13

same as is =

5 times the number = 5n

increased by 5 = 5n+5

7n-13 = 5n+5

2n=18

n=9