Simplify \(\frac{\frac{17}{2}+\frac{18}{7}\text{ of…

Concept: In a compound fraction expression, apply the order of operations (BODMAS): treat “of” as multiplication and resolve every division or multiplication inside the numerator and the denominator before any addition or subtraction, then divide the simplified numerator by the simplified denominator.

1. Numerator — evaluate the “of” term first: \(\frac{18}{7}\text{ of }\frac{7}{2} = \frac{18}{7}\times\frac{7}{2} = \frac{18}{2} = 9\).

2. Numerator — add the remaining term: \(\frac{17}{2}+9 = \frac{17}{2}+\frac{18}{2} = \frac{35}{2}\).

3. Denominator — evaluate the division term first: \(\frac{15}{7}\div\frac{2}{7} = \frac{15}{7}\times\frac{7}{2} = \frac{15}{2}\).

4. Denominator — subtract from the remaining term: \(14-\frac{15}{2} = \frac{28}{2}-\frac{15}{2} = \frac{13}{2}\).

5. Divide the simplified numerator by the simplified denominator: \(\frac{35}{2}\div\frac{13}{2} = \frac{35}{2}\times\frac{2}{13} = \frac{35}{13}\).

Cross-check: \(\frac{35}{2}=17.5\) and \(\frac{13}{2}=6.5\), and \(17.5\div6.5\approx2.69\), matching \(\frac{35}{13}\approx2.69\).