## Thinking Mathematically (6th Edition)

$\dfrac{-71}{150}$
Factor each denominator completely to obtain: $15=3(5) \\50=2(25) = 2(5)(5)$ Thus, the least common multiple of the two numbers is: $2(3)(5)(5)=150$ This means that the LCD is also $150$. The fractions are not similar since they have different fractions. Make the fractions similar using their LCD of $150$. $\dfrac{1}{15} - \dfrac{27}{50} \\= \dfrac{1\color{blue}{(10)}}{15\color{blue}{(10)}}-\dfrac{27\color{blue}{(3)}}{50\color{blue}{(3)}} \\=\dfrac{10}{150}-\dfrac{81}{150}$ Now that the fractions are similar, subtract the numerators and copy the denominator to obtain: $=\dfrac{10-81}{150} \\=\dfrac{-71}{150}$