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].
