Paj is filling a 9-cubic-inch flower pot with soil from small bags. Each bag of soil contains 2 2/3cubic inches of soil. Exactly how many bags of soil are needed for Paj to fill the flower pot?
9/(2 2/3) = 9 / (8/3) = 9 * 3/8 = 27/8 = 3 3/8 bags
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To find out how many bags of soil Paj needs to fill the flower pot, we need to divide the volume of the flower pot by the volume of each bag of soil.
First, let's convert the mixed number 2 2/3 to an improper fraction. To do this, we multiply the whole number (2) by the denominator (3), then add the numerator (2) to get the new numerator. So, 2 × 3 + 2 = 6 + 2 = 8.
Therefore, 2 2/3 is equal to the improper fraction 8/3.
Now let's calculate the number of bags needed. We divide the volume of the flower pot (9 cubic inches) by the volume of each bag (2 2/3 cubic inches or 8/3 cubic inches).
9 cubic inches ÷ (8/3) cubic inches = 9 cubic inches × (3/8) cubic inches.
To divide by a fraction, we multiply by its reciprocal. Therefore, we multiply 9 by 3/8.
9 × (3/8) = (9 × 3) / 8 = 27/8.
So, Paj needs 27/8 bags of soil to fill the flower pot. However, we need to find a whole number answer, so we divide the numerator (27) by the denominator (8) and round it up to the nearest whole number.
27 ÷ 8 = 3 remainder 3.
So, Paj needs 3 whole bags of soil, with 3/8 of a bag remaining.
Therefore, Paj needs 3 bags of soil to fill the flower pot.