A box in a college bookstore contains books, and each book in the box is a history book, an English book or a science book. If one-third of these books are history books and one-sixth are English books, what fraction of the books are science books?

A. 1/3
B. 1/2
C. 2/3
D. 3/4

****please explain this problem to me because I'm sure to have similar ones like this on my real exam.

Thank you in advance

As per the probability rule

Total of all probability is 1

So,
P(History)+P( English)+P( Science) = 1

1/3 + 1/6 + P( Science) = 1

P( Science) = 1- (1/3 + 1/6) = 1 - 1/2

P( Science) = 1/2

1/3+1/6+ science = Find the LCM (lowest common Multiple).

the LCM for 1/3 is 2.
the LCM for 1/6 is 1.
Multiply both numerator and denominator, which gives you
2/6 + 1/6 = science
then add the 2 and 1
copy the 6 at the bottom which result 3/6 then simplify to lowest form which 1/2.

Thank You

To solve this problem, we need to use the information given to determine the fraction of books that are science books. Let's go step by step.

Step 1: Let's start by summarizing the given information:
- One-third of the books are history books.
- One-sixth of the books are English books.

Step 2: To calculate the fraction of books that are science books, we need to subtract the fraction of history books and English books from 1 (since all the books must fall into one of these categories).

Fraction of science books = 1 - (fraction of history books + fraction of English books)

Step 3: Let's calculate the fraction of history books and English books separately.

Fraction of history books = 1/3
Fraction of English books = 1/6

Step 4: Plug the calculated values into the formula from Step 2.

Fraction of science books = 1 - (1/3 + 1/6)

Step 5: Simplify the expression.

Fraction of science books = 1 - (2/6 + 1/6)
= 1 - (3/6)
= 1 - 1/2
= 1/2

So, the fraction of books that are science books is 1/2.

Therefore, the answer is B. 1/2.

In similar problems, follow the same steps:
1. Summarize the given information.
2. Identify the fractions of each category.
3. Calculate the fraction of the remaining category by subtracting the sum of the known categories from 1.

B-1/2

Let no. of books be x
No. of history books equal x into 1/3 I.e.x/3
No. Of English books equal x into 1/3 I.e. x/6
Rest books = no. Of science books
=total books -(history books+English books)
=×-(×/3 +×/6)
=x-(3x/6)
=x-x/2
=x/2 books are of science of total books I.e. x
No of science book is 1/2 of total books