To solve the problem of dividing a board that is [tex]\(\frac{3}{4}\)[/tex] yards long into 9 equal pieces, we need to determine the length of each smaller piece. Here is a detailed, step-by-step solution:
1. Understand the total length of the board:
The board has a total length of [tex]\(\frac{3}{4}\)[/tex] yards.
2. Determine the number of pieces:
The board is being divided into 9 equal pieces.
3. Set up the division to find the length of each piece:
To find the length of each piece, we need to divide the total length of the board by the number of pieces:
[tex]\[
\frac{\frac{3}{4} \text{ yards}}{9}
\][/tex]
4. Simplify the division:
When dividing a fraction by a whole number, it is helpful to multiply by the reciprocal of the whole number. This can be expressed as:
[tex]\[
\frac{3}{4} \div 9 = \frac{3}{4} \times \frac{1}{9} = \frac{3 \times 1}{4 \times 9} = \frac{3}{36}
\][/tex]
5. Reduce the fraction to its simplest form:
Simplify [tex]\(\frac{3}{36}\)[/tex] by finding the greatest common divisor (GCD) of 3 and 36, which is 3:
[tex]\[
\frac{3}{36} = \frac{3 \div 3}{36 \div 3} = \frac{1}{12}
\][/tex]
Therefore, the length of each piece is:
[tex]\[
\frac{1}{12} \text{ yards}
\][/tex]
So, each piece of the board will be [tex]\(\frac{1}{12}\)[/tex] yards long.
