To determine the fraction of the book Sarah read on Tuesday, we need to consider the fractions she read on the previous days and subtract them from the whole book. Here is a detailed step-by-step solution:
1. Readings on Saturday, Sunday, and Monday:
- On Saturday, Sarah reads [tex]\(\frac{2}{15}\)[/tex] of the book.
- On Sunday, she reads [tex]\(\frac{1}{3}\)[/tex] of the book.
- On Monday, she reads [tex]\(\frac{1}{5}\)[/tex] of the book.
2. Converting all fractions to a common denominator:
- To add these fractions, we need a common denominator. The denominators are 15, 3, and 5. The least common multiple (LCM) of these numbers is 15.
- Convert [tex]\(\frac{1}{3}\)[/tex] to fifteenths:
[tex]\[
\frac{1}{3} = \frac{1 \times 5}{3 \times 5} = \frac{5}{15}
\][/tex]
- Convert [tex]\(\frac{1}{5}\)[/tex] to fifteenths:
[tex]\[
\frac{1}{5} = \frac{1 \times 3}{5 \times 3} = \frac{3}{15}
\][/tex]
3. Adding the fractions:
- Now, add the three fractions:
[tex]\[
\frac{2}{15} + \frac{5}{15} + \frac{3}{15} :
\][/tex]
- Since they have the same denominator, we can directly add the numerators:
[tex]\[
\frac{2 + 5 + 3}{15} = \frac{10}{15}
\][/tex]
4. Total read before Tuesday:
- Sarah has read [tex]\(\frac{10}{15}\)[/tex] of the book from Saturday to Monday.
5. Finding the fraction read on Tuesday:
- The whole book is considered 1 (or [tex]\(\frac{15}{15}\)[/tex] in fractional terms).
- Subtract the total fraction read before Tuesday from the whole book to find the fraction read on Tuesday:
[tex]\[
1 - \frac{10}{15} = \frac{15}{15} - \frac{10}{15} = \frac{5}{15}
\][/tex]
6. Simplifying the fraction:
- Simplify [tex]\(\frac{5}{15}\)[/tex] by dividing both the numerator and the denominator by their greatest common divisor, which is 5:
[tex]\[
\frac{5 \div 5}{15 \div 5} = \frac{1}{3}
\][/tex]
Therefore, the fraction of the book that Sarah read on Tuesday is [tex]\( \boxed{\frac{1}{3}} \)[/tex].
