A $4'$ by $2'$ rectangular flag is made of a $2'$ by $2'$ black square bordered by a $1'$ by $2'$ white rectangle on each of two opposite sides of the black square. A white symbol covers one-third of the area of the black square. What fraction of the total area of the front of the flag is white? Express your answer as a common fraction.

Work Shown:

A = area of black square

A = 2*2

A = 4

B = area of white symbol

B = (1/3)*A

B = (1/3)*4

B = 4/3

C = total area

C = 4*2

C = 8

Divide the values of B and C to find the fraction of the total area the white symbol covers up.

B/C = (4/3)/8

B/C = (4/3) / (8/1)

B/C = (4/3) divided by (8/1)

B/C = (4/3) times (1/8)

B/C = (4*1)/(3*8)

B/C = 4/24

B/C = 1/6

21/58.

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