Let's solve this step by step:

Problem Breakdown:

• Tyler reads:
  • $\frac{2}{15}$ of the book on Monday.
  • $\frac{1}{3}$ of the book on Tuesday.
  • $\frac{2}{9}$ of the book on Wednesday.
  • $\frac{3}{4}$ of the remaining portion on Thursday.
• After all this, Tyler has 14 pages left to read on Friday.
• We need to find the total number of pages in the book.

Step 1: Represent the total pages in the book as $x$.

Step 2: Add fractions of the book read on Monday, Tuesday, and Wednesday.

The total fraction of the book read up to Wednesday is: $\text{Monday: } \frac{2}{15}, \quad \text{Tuesday: } \frac{1}{3}, \quad \text{Wednesday: } \frac{2}{9}.$ Finding a common denominator for $\frac{2}{15}, \frac{1}{3}, \frac{2}{9}$: The least common denominator (LCD) of 15, 3, and 9 is 45.

Rewriting the fractions with a denominator of 45: $\frac{2}{15} = \frac{6}{45}, \quad \frac{1}{3} = \frac{15}{45}, \quad \frac{2}{9} = \frac{10}{45}.$ Adding these: $\frac{6}{45} + \frac{15}{45} + \frac{10}{45} = \frac{31}{45}.$

Thus, by the end of Wednesday, Tyler has read $\frac{31}{45}$ of the book.

Step 3: Remaining fraction after Wednesday.

The fraction of the book remaining is: $1 - \frac{31}{45} = \frac{14}{45}.$

Step 4: Fraction read on Thursday.

Tyler reads $\frac{3}{4}$ of the remaining portion on Thursday. The remaining portion is $\frac{14}{45}$, so the amount read on Thursday is: $\frac{3}{4} \cdot \frac{14}{45} = \frac{42}{180} = \frac{7}{30}.$

Step 5: Fraction left after Thursday.

The fraction of the book left after Thursday is: $\frac{14}{45} - \frac{7}{30}.$ Finding a common denominator for 45 and 30, the LCD is 90: $\frac{14}{45} = \frac{28}{90}, \quad \frac{7}{30} = \frac{21}{90}.$ Subtracting: $\frac{28}{90} - \frac{21}{90} = \frac{7}{90}.$

Thus, after Thursday, $\frac{7}{90}$ of the book remains.

Step 6: Relating the remaining fraction to the 14 pages.

If $\frac{7}{90}$ of the book equals 14 pages, the total number of pages $x$ can be found by solving: $\frac{7}{90}x = 14.$ Multiply both sides by 90: $7x = 1260.$ Divide by 7: $x = 180.$

Final Answer:

The book has 180 pages.

Do you want further details or clarification? Here are related questions to explore:

1. How do you find a common denominator for fractions in similar problems?
2. What if Tyler read different fractions on the first three days?
3. How does multiplying fractions for partial amounts work in general?
4. Can you explain how the fractions add up to form the remaining portion of the book?
5. How can we verify the solution by checking each step?

Tip: Always double-check fraction operations (addition, subtraction) by simplifying results when possible!