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**