Robert cut
3
4 of a loaf of bread in half. Which equation can be used to determine the fraction of
the whole loaf represented by each piece n ?
What are your choices?
1/2 * 3/4 = ?
To determine the fraction of the whole loaf represented by each piece, we can use the equation:
n = (1/2)^x
where n represents the fraction of the whole loaf and x represents the number of times the bread was cut in half.
In this case, Robert cut the bread 3 times, resulting in 4 pieces. Each time the bread is cut in half, it doubles the number of pieces. So if we cut the bread 3 times, we get 2^3 = 8 pieces. However, we are given that there are only 4 pieces, suggesting that each piece was further divided in half. This means that each piece represents a fraction of the whole loaf.
Given that there are 4 pieces, we can rewrite the equation as:
n = (1/2)^x = 1/4
Simplifying the equation, we find that:
(1/2)^x = 1/4
To solve for x, we can take the logarithm of both sides of the equation:
log((1/2)^x) = log(1/4)
Using the property of logarithms (log(a^b) = b * log(a)), this simplifies to:
x * log(1/2) = log(1/4)
Using the fact that log(1/2) = -log(2), we can rewrite the equation as:
x * (-log(2)) = log(1/4)
Dividing both sides of the equation by -log(2), we get:
x = log(1/4) / -log(2)
This equation can be used to determine the fraction of the whole loaf represented by each piece n.