A piece of fabric is cut into three sections so that the first is three times as long as the second and the second is three times as long as the third. What part of the entire piece is the smallest section?
1/(9+3+1)
To find the answer, let's break down the information provided and solve step by step.
Let's say the length of the smallest section is x units.
According to the question, the first section is three times as long as the second section. So, the length of the first section is 3x units.
Similarly, the second section is three times as long as the third section. So, the length of the second section is 3 times the length of the smallest section, which is 3 * x = 3x units.
Now, we can add up the lengths of all three sections to represent the entire piece of fabric:
x + 3x + 3x = 7x units.
Since we know the entire piece of fabric is made up of three sections, the sum of their lengths must be equal to the length of the entire piece.
So, we can write the equation as follows:
x + 3x + 3x = length of entire piece
Simplifying the equation, we get:
7x = length of entire piece
Now, let's analyze the question: "What part of the entire piece is the smallest section?"
To find the answer, we need to determine the ratio of the smallest section to the entire piece. We can do this by dividing the length of the smallest section by the length of the entire piece.
Smallest section / Entire Piece = x / 7x
Canceling out the common factor of x, we get:
Smallest section / Entire Piece = 1 / 7
Therefore, the smallest section is 1/7th or 1/7 (approximately 0.1429) of the entire piece.
In conclusion, the smallest section represents approximately 1/7th of the entire piece of fabric.