Options A, B, and E are equivalent to [tex]\frac{p}{3} .[/tex]
Step-by-step explanation:
Step 1:
We must determine the values of all the expressions to determine which is equal to [tex]\frac{p}{3} .[/tex]
A. [tex]p - \frac{2}{3} p = \frac{3p-2p}{3} = \frac{1p}{3} = \frac{p}{3}.[/tex] So option A is equivalent to [tex]\frac{p}{3} .[/tex]
B. [tex]\frac{1}{3} p[/tex] can also be written as [tex]\frac{p}{3} .[/tex] So option B is also equivalent to [tex]\frac{p}{3} .[/tex]
Step 2:
C. [tex]p -3[/tex] cannot be simplified. So option C does not equal [tex]\frac{p}{3} .[/tex]
D. 3÷p [tex]= \frac{3}{p} .[/tex] This is the inverse of [tex]\frac{p}{3}[/tex] so option D does not equal [tex]\frac{p}{3} .[/tex]
E. [tex]\frac{3p}{9} = \frac{1p}{3} = \frac{p}{3} .[/tex] So option E equals [tex]\frac{p}{3} .[/tex]
F. [tex]\frac{1}{3} p + \frac{1}{3} p+\frac{1}{3} p = \frac{3}{3} p = p.[/tex] So option F does not equal [tex]\frac{p}{3} .[/tex]
So options A, B, and E are equivalent to [tex]\frac{p}{3} .[/tex]
