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Zorluk: OrtaFractions, Decimals, and Percentages

A community garden allocates space among three categories: vegetable beds, herb gardens, and flower borders. Vegetable beds take up 38\frac{3}{8} of the total area, herb gardens take up 0.250.25 of the total area, and flower borders occupy the remaining 1,800 square feet. What is the total area, in square feet, of the community garden?

  1. A
    2,700
  2. B
    2,880
  3. 4,800Cevap
  4. D
    675
  5. E
    7,200

Cevap

4,800 square feet
To find the total area, first convert 0.250.25 to 28\frac{2}{8}. Summing the vegetable portion (38\frac{3}{8}) and the herb portion (28\frac{2}{8}) gives 58\frac{5}{8} of the garden. The flower section takes up the remaining 1−58=381 - \frac{5}{8} = \frac{3}{8} of the area. Setting 38\frac{3}{8} of the total area equal to 1,800 square feet and dividing 1,800 by 38\frac{3}{8} gives 1,800×83=4,8001,800 \times \frac{8}{3} = 4,800 square feet.

Adım Adım Çözüm

1
Convert the decimal portion to a fraction with a common denominator.
0.25=14=280.25 = \frac{1}{4} = \frac{2}{8}
Converting all given portions into fractions with a common denominator allows direct addition.
2
Calculate the combined fraction for vegetable beds and herb gardens.
38+28=58\frac{3}{8} + \frac{2}{8} = \frac{5}{8}
Adding the two known fractions identifies the combined portion of the garden accounted for by vegetables and herbs.
3
Find the fraction representing the flower borders.
1−58=381 - \frac{5}{8} = \frac{3}{8}
Subtracting the combined fraction from the whole (1) yields the fractional part representing the remaining 1,800 square feet.
4
Solve for the total garden area.
\text{Total Area} = 1,800 \div \frac{3}{8} = 1,800 \times \frac{8}{3} = 4,800\text{ sq ft}
Dividing the part by its corresponding fractional portion calculates the whole quantity.

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Combining fractions and decimals to solve part-to-whole problems
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Fractions, Decimals, and Percentages

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