you are creating a board game. you want to cut square game pieces that measure 1 1/4 on each side from a piece of paper that measures 8 1/2 inches by 11 inches... how many game pieces can you cut from the paper?

11 ÷ 1.25 = 8.8

So you make only 8 cuts along the length

8.5 ÷ 1.25 = 6.8
and only 6 cuts along the width

so you can make 6x8 or 48 complete squares.

notice that by taking the total area of
11 x 8.5 or 93.5 square units
and dividing that by the area of each square of
1.25x1.25 or 1.5625 square inches, we would get
59.84 , which of course is physically not possible.

To find out how many game pieces you can cut from the paper, you need to calculate the area of each game piece and then divide the total area of the paper by the area of each game piece.

First, let's calculate the area of each game piece:
The dimensions of each game piece are given as 1 1/4 inches on each side.
To convert the mixed number to a fraction, multiply the whole number (1) by the denominator (4), then add the numerator (1). This gives us (1 * 4) + 1 = 5.
So, the dimensions of each game piece are 5/4 inches by 5/4 inches.

Now, let's find the area of each game piece:
Area = length x width
Area = (5/4) inches x (5/4) inches

Next, let's find the area of the paper:
The dimensions of the paper are given as 8 1/2 inches by 11 inches.
To convert the mixed number to a fraction, multiply the whole number (8) by the denominator (2), then add the numerator (1). This gives us (8 * 2) + 1 = 17.
So, the dimensions of the paper are 17/2 inches by 11 inches.

Now, let's find the total area of the paper:
Total Area = length x width
Total Area = (17/2) inches x 11 inches

Finally, divide the total area of the paper by the area of each game piece to find out how many pieces you can cut from the paper:
Number of Game Pieces = Total Area of Paper / Area of each Game Piece

By substituting the values, you can calculate the exact number of game pieces that can be cut from the piece of paper.