Answer:
[tex]-3\frac{2}{3}[/tex] equivalent to [tex]-3-\frac{2}{3}[/tex]
Step-by-step explanation:
Given: [tex]-3\frac{2}{3}[/tex]
We need to choose equivalent to given expression.
First we simplify the given expression mixed number to fraction.
[tex]\Rightarrow -3\frac{2}{3}[/tex]
[tex]\Rightarrow -\frac{3\cdot 3+2}{3}[/tex]
[tex]\Rightarrow -\frac{9+2}{3}[/tex]
[tex]\Rightarrow -\frac{11}{3}[/tex]
Option 1: [tex]-3+\frac{2}{3}[/tex]
[tex]\Rightarrow \dfrac{-9+2}{3}=-\dfrac{7}{3}\neq -\dfrac{11}{3}[/tex]
False
Option 2: [tex]-3-\frac{2}{3}[/tex]
[tex]\Rightarrow \dfrac{-9-2}{3}=-\dfrac{11}{3}= -\dfrac{11}{3}[/tex]
True
Option 3: [tex]3-\frac{2}{3}[/tex]
[tex]\Rightarrow \dfrac{9-2}{3}=\dfrac{7}{3}\neq -\dfrac{11}{3}[/tex]
False
Option 4: [tex]3+\frac{2}{3}[/tex]
[tex]\Rightarrow \dfrac{9+2}{3}=\dfrac{11}{3}\neq -\dfrac{11}{3}[/tex]
False
Hence, [tex]-3\frac{2}{3}[/tex] equivalent [tex]-3-\frac{2}{3}[/tex]
