Jeff bought a pie and cut it into equal-sized pieces. Jeff ate 2 pieces, so 3 quarters of the pie is left.
What fraction of the pie is each piece?
Show your work!
AAAaannndd the bot gets it wrong yet again!
As the bot said,
the 2 pieces he ate must have been equal to 1 quarter (1/4) of the pie.
so each piece is 1/8 of the pie.
First, let's assume that the whole pie consists of "x" equal-sized pieces.
Since Jeff ate 2 pieces, we can subtract that from the total number of pieces to find the remaining pieces. So, the number of remaining pieces is x - 2.
Now, we know that 3 quarters (or 3/4) of the pie is left, which means that the remaining pieces (x-2) is equal to 3/4 of the whole pie (x).
We can now set up the equation:
(x-2) = (3/4) * x
To solve for x, we can distribute the 3/4 through the parentheses:
x - 2 = (3/4) * x
Next, we can multiply both sides of the equation by 4 to eliminate the fraction:
4(x - 2) = 4 * (3/4) * x
Expanding the equation gives us:
4x - 8 = 3x
Now, we can simplify the equation by subtracting 3x from both sides:
4x - 3x - 8 = 3x - 3x
x - 8 = 0
Finally, we can add 8 to both sides to isolate x:
x - 8 + 8 = 0 + 8
x = 8
Thus, the whole pie consists of 8 equal-sized pieces.
To find the fraction of the pie for each piece, we can divide the total pie (8 pieces) by the number of pieces:
Fraction per piece = 1 / 8
Therefore, each piece represents 1/8 of the whole pie.
To find out the fraction of the pie that each piece represents, we can follow these steps:
Step 1: Determine the total number of pieces before Jeff ate any.
Since Jeff ate 2 pieces, and there are 3 quarters of the pie left, we can conclude that there were 2 + 3 = 5 equal-sized pieces in total.
Step 2: Calculate the fraction of the pie that each piece represents.
To find the fraction, we divide the remaining 3 quarters equally among the 5 pieces.
Since there are 4 quarters in a whole pie, dividing the 3 quarters evenly among the 5 pieces means each piece represents 3/5 of a quarter or (3/5)*(1/4) = 3/20 of the whole pie.
Therefore, each piece represents 3/20 of the pie.
In summary, each piece represents 3/20 of the whole pie.
We know that 3 quarters (3/4) of the pie is left after Jeff ate 2 pieces. Therefore, the 2 pieces he ate must have been equal to 1 quarter (1/4) of the pie.
To find out what fraction of the pie each piece is, we can divide the remaining 3/4 of the pie by the number of pieces left. Since we know that Jeff ate 2 pieces, that means there are (1 + 1 + 2) = 4 pieces total.
So, we can calculate the fraction of the pie that each piece represents as:
3/4 remaining portions ÷ 4 total pieces = 3/4 ÷ 4 = 3/16
Therefore, each piece of the pie represents 3/16 of the total pie.