After reading a book for English class, 100 students were asked whether or not they enjoyed it. Nine-twenty fifths of the class did not. How many students liked the book?
The correct answer and explanation is:
To find out how many students liked the book, let’s break it down:
- The total number of students surveyed is 100.
- Nine-twenty fifths of the students did not like the book. This fraction represents the portion of students who disliked the book.
- To find how many students didn’t like the book, we calculate 925\frac{9}{25} of 100: 925×100=36\frac{9}{25} \times 100 = 36 So, 36 students did not like the book.
- Since there are 100 students in total, the number of students who liked the book will be the total number of students minus the number who didn’t like it: 100−36=64100 – 36 = 64
Therefore, 64 students liked the book.
Explanation:
In this problem, you’re first asked to calculate how many students did not like the book. This involves multiplying the fraction of students who didn’t like the book, 925\frac{9}{25}, by the total number of students, which is 100. Once you know the number of students who didn’t enjoy the book, the rest of the students must have liked it. By subtracting the number of students who disliked the book from the total number of students, you determine how many students enjoyed the book.
This is an example of using basic fractions and subtraction to find an unknown quantity in a simple word problem.