Jim’s backyard is a rectangle that is 15 5/6 yards long and 10 2/5 yards wide. Jim buys sod in pieces that are 1 1/3 yards long and 1 1/3 yards wide how many pieces of sod will Jim need to buy to cover his backyard with sod

To get the result we have to find area of rectangle and area of each piece. Then we have to divide area of rectangle by area of piece.
Lets do this
A=\( 15\frac{5}{6}*10 \frac{2}{5} = \frac{95}{6}* \frac{52}{5} = \frac{4784}{30}=159.5 \)   - its area of rectangle
a=\( 1 \frac{1}{3}* 1\frac{1}{3}= \frac{4}{3}* \frac{4}{3} = \frac{16}{9}=1.8 \) - area of piece.  
Finally we can divide A by a to get the result
A: a====>  159.5:1.8=88.6
We have to round up this result because Jim have to buy 87 piece. (its imposible to buy 0.6 piece )

By definition, the area of a rectangle is given by:
 \( A = (w) * (l) \)
 Where,
 w: width of the rectangle
 l: length of the rectangle
 Substituting values we have:
 \( A = (10 \frac{2}{5} ) * (15 \frac{5}{6}) A = 164.7 \)
 Then, the area of each piece of sod is:
 \( A = (1 \frac{1}{3} ) * (1 \frac{1}{3}) A = 1.8 \)
 Thus, the number of pieces is given by the division of both areas:
 \( N = (164.7) / (1.8) N = 91.5 \)
 Rounding the nearest whole we have:
 \( N = 92 \)
 Answer:
 
Jim will need to buy 92 pieces of sod to cover his backyard


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