On the number line shown, $AE=6$, $AB=1\frac{2}{3}$, $BC=1\frac{1}{4}$, and $DE=1\frac{1}{12}$. What is $CD$?

[asy]
unitsize(1cm);
draw((0,0)--(8,0),Arrows);
pair A,B,C,D,E;
A=(1,0); B=(8/3,0); C=(47/12,0);
D=(71/12,0); E=(7,0);
dot(A); dot(B); dot(C); dot(D); dot(E);
label("$A$",A,S);
label("$B$",B,S);
label("$C$",C,S);
label("$D$",D,S);
label("$E$",E,S);
[/asy]
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
On the number line shown, $AE=6$, $AB=1\frac{2}{3}$, $BC=1\frac{1}{4}$, and $DE=1\frac{1}{12}$. What is $CD$?

[asy]
unitsize(1cm);
draw((0,0)--(8,0),Arrows);
pair A,B,C,D,E;
A=(1,0); B=(8/3,0); C=(47/12,0);
D=(71/12,0); E=(7,0);
dot(A); dot(B); dot(C); dot(D); dot(E);
label("$A$",A,S);
label("$B$",B,S);
label("$C$",C,S);
label("$D$",D,S);
label("$E$",E,S);
[/asy]
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
2
On the number line shown, $AE=6$, $AB=1\frac{2}{3}$, $BC=1\frac{1}{4}$, and $DE=1\frac{1}{12}$. What is $CD$?

[asy]
unitsize(1cm);
draw((0,0)--(8,0),Arrows);
pair A,B,C,D,E;
A=(1,0); B=(8/3,0); C=(47/12,0);
D=(71/12,0); E=(7,0);
dot(A); dot(B); dot(C); dot(D); dot(E);
label("$A$",A,S);
label("$B$",B,S);
label("$C$",C,S);
label("$D$",D,S);
label("$E$",E,S);
[/asy]
train