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Simplify. Express your answer as a single fraction in simplest form. \newliner3−25\frac{r}{3} - \frac{2}{5}

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Full solution

Q. Simplify. Express your answer as a single fraction in simplest form. \newliner3−25\frac{r}{3} - \frac{2}{5}
  1. Find LCM of Denominators: Find the least common multiple (LCM) of the denominators 33 and 55. The LCM of 33 and 55 is 1515 because 33 and 55 are both prime numbers and their LCM is simply their product.
  2. Make Denominators Same: Make the denominators the same by multiplying the first fraction by 55 and the second fraction by 33. This gives us (r3)⋅(55)−(25)⋅(33)(\frac{r}{3}) \cdot (\frac{5}{5}) - (\frac{2}{5}) \cdot (\frac{3}{3}), which simplifies to (5r15)−(615)(\frac{5r}{15}) - (\frac{6}{15}).
  3. Simplify Expression: Simplify the expression by subtracting the numerators since the denominators are the same. The final simplified expression is (5r−6)/15(5r - 6)/15.

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