Final answer:
The number of 1 1/4' by 4' pieces that can be cut from a 4' x 8' sheet of plywood is 6.
Step-by-step explanation:
To find out how many 1 1/4' by 4' pieces can be cut from a 4' x 8' sheet of plywood, we need to determine the number of pieces that can fit in the length and width of the sheet.
The length of the plywood sheet is 8', and each piece is 4' long. Therefore, the number of pieces that can fit in the length is 8 divided by 4, which is 2.
The width of the plywood sheet is 4', and each piece is 1 1/4' wide. To find the number of pieces that can fit in the width, we divide 4 by 1 1/4.
Dividing 4 by 1 1/4 can be done by converting 1 1/4 to an improper fraction: 1 1/4 = 5/4. Then, we can divide 4 by 5/4, which is the same as multiplying 4 by 4/5. The result is 16/5 or 3 1/5.
Therefore, the total number of pieces that can be cut from the plywood sheet is the product of the number of pieces in the length and width, which is 2 x (3 1/5) = 6 2/5. Since we cannot have a fraction of a piece, we round down to the nearest whole number, which is 6.