Answer: [tex]\bold{\dfrac{1}{70}}[/tex]
Step-by-step explanation:
PEMDAS states to do parentheses first, then multiplication and division, and lastly subtract.
[tex]\bigg(3\dfrac{1}{3}-1\dfrac{5}{6}\bigg)\div2\dfrac{1}{7}-1\dfrac{1}{3}\cdot2.4\\\\\\\text{Step 1: Subtract}\ 3\dfrac{1}{3}\ and\ 1\dfrac{5}{6}\quad \longrightarrow \quad \dfrac{10}{3}\bigg(\dfrac{2}{2}\bigg)-\dfrac{11}{6}\quad =\dfrac{9}{6}\quad =\dfrac{3}{2}\\\\\implies \quad \dfrac{3}{2}\div2\dfrac{1}{7}-1\dfrac{1}{3}\cdot2.4[/tex]
[tex]\text{Step 2: multiply}\ \dfrac{3}{2}\ and\ 2\dfrac{1}{7}\quad \longrightarrow \quad \dfrac{3}{2}\times \dfrac{15}{7}\quad =\dfrac{45}{14}\\\\\implies \dfrac{45}{14}-1\dfrac{1}{3}\cdot 2.4\\\\\\\\\text{Step 3: multiply}\ 1\dfrac{1}{3}\ and\ 2.4\quad \longrightarrow \quad \dfrac{4}{3}\times 2\dfrac{4}{10}\quad =\dfrac{4}{3}\times \dfrac{12}{5}\quad =\dfrac{16}{5}\\\\\implies \dfrac{45}{14}-\dfrac{16}{5}[/tex]
[tex]\text{Step 4: subtract}\ \dfrac{45}{14}\ and\ \dfrac{16}{5}\quad \longrightarrow \quad \dfrac{45}{14}\bigg(\dfrac{5}{5}\bigg)-\dfrac{16}{5}\bigg(\dfrac{14}{14}\bigg)\quad =\dfrac{1}{70}\\\\\implies \large\boxed{\dfrac{1}{70}}[/tex]
