Question

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.

Answer 1

To find the fraction of the total area of the flag that is white, calculate the area of the white rectangles and the black square. The total area of the flag is 8 square feet. The fraction of the total area that is white is 1/6.

Step-by-step explanation:

To find the fraction of the total area of the flag that is white, we need to calculate the area of the white rectangles and the black square. The area of each white rectangle is 1' x 2' = 2 square feet. The area of the black square is 2' x 2' = 4 square feet. Since the white symbol covers one-third of the black square, its area is (1/3) x 4 = 4/3 square feet.

The total area of the flag is the sum of the areas of the white rectangles and the black square: 2 + 2 + 4 = 8 square feet.

To find the fraction of the total area that is white, we divide the area of the white symbol (4/3) by the total area of the flag (8): (4/3) / 8 = 4/24 = 1/6 of the total area is white.

Answer 2

Answer: 1/6

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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