A student read the first 150 pages of a book that is 450 pages long. What fraction of the book does the student have left to read?

A. [tex]$\frac{1}{3}$[/tex]
B. [tex]$\frac{2}{3}$[/tex]
C. [tex]$\frac{2}{5}$[/tex]
D. [tex]$\frac{3}{5}$[/tex]



Answer :

Let's solve this problem step-by-step.

1. Identify the total number of pages in the book: The total number of pages in the book is 450.

2. Identify the number of pages the student has already read: The student has read 150 pages.

3. Calculate the number of pages left to read:
We subtract the number of pages read from the total number of pages to find the pages left.
[tex]\[ \text{Pages left} = 450 - 150 = 300 \][/tex]

4. Determine the fraction of the book that is left to read:
To find the fraction, we divide the number of pages left by the total number of pages.
[tex]\[ \text{Fraction left} = \frac{\text{Pages left}}{\text{Total pages}} = \frac{300}{450} \][/tex]

5. Simplify the fraction:
To simplify \(\frac{300}{450}\), we can divide both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 300 and 450 is 150.
[tex]\[ \frac{300 \div 150}{450 \div 150} = \frac{2}{3} \][/tex]

6. Conclusion:
The fraction of the book that the student has left to read is \(\frac{2}{3}\).

Thus, the correct choice is [tex]\(\boxed{\frac{2}{3}}\)[/tex].