Marco wants to put soil in his garden shown below. If soil comes in bags that fill 2 square yards each, how many bags of soil should Marco buy? Hint: you may have some leftover soil.
A garden with a length of 10 yards and a width of two-thirds yards.
The area of the garden is 10 yards x (2/3) yards = 6.67 square yards.
To find out how many bags of soil Marco needs, we need to divide the total area of the garden by the area each bag of soil can cover:
6.67 square yards / 2 square yards per bag = 3.335 bags
Since you cannot buy a fraction of a bag, Marco should buy at least 4 bags of soil.
Find the area of the rectangle by multiplying the side lengths. 5/12 and 4/3
The area of the rectangle is:
(5/12) x (4/3) = (5 x 4) / (12 x 3) = 20/36
Now, we simplify this fraction. Both numerator and denominator can be divided by their greatest common factor, which is 4:
20/36 = (5 x 4) / (9 x 4) = 5/9
Therefore, the area of the rectangle is 5/9 square units.
To find out how many bags of soil Marco should buy, we need to calculate the area of his garden and divide it by the area covered by each bag of soil.
First, let's calculate the area of Marco's garden. The formula for finding the area of a rectangle is length multiplied by width. In this case, the length is 10 yards and the width is two-thirds of a yard.
Length = 10 yards
Width = two-thirds yards = 2/3 yards
Now, let's calculate the area:
Area = Length x Width
Area = 10 yards x (2/3) yards
To multiply fractions, multiply the numerators (top numbers) and multiply the denominators (bottom numbers). The result is:
Area = (10 x 2) / (3 x 1)
Area = 20 / 3 square yards
Now that we know the area of Marco's garden is 20/3 square yards, we can determine how many bags of soil he needs. Each bag fills 2 square yards.
Number of bags = Area of garden / Area covered by each bag
Number of bags = (20/3 square yards) / (2 square yards)
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction. In this case, the reciprocal of 2 is 1/2:
Number of bags = (20/3) x (1/2)
Number of bags = 20/6
Now, simplify the fraction:
Number of bags = 10/3
Based on the calculation, Marco should buy 10/3 bags of soil. Since we can't buy fractional bags, Marco should consider purchasing 4 bags of soil, with some leftover soil from the extra bag.