Joseph and Shannon are trying to guess what fraction of the students in their school drama club have blue eyes.
Joseph guesses 5/6 and Shannon guesses 7/12.
a) What is the difference between their guesses?
Give your answer as a fraction in its simplest form.
2/3 of the students in their school drama club have blue eyes.
b) Whose guess is closer to the actual value?
a) To find the difference between their guesses, we need to subtract Shannon's guess from Joseph's guess:
5/6 - 7/12 = 10/12 - 7/12 = 3/12 = 1/4
So, the difference between their guesses is 1/4.
b) Since the actual value is 2/3, we need to find which guess is closer to 2/3.
First, let's find the difference between Joseph's guess and the actual value:
|2/3 - 5/6| = |4/6 - 5/6| = |-1/6| = 1/6
Now, let's find the difference between Shannon's guess and the actual value:
|2/3 - 7/12| = |8/12 - 7/12| = |1/12| = 1/12
Since 1/12 is smaller than 1/6, Shannon's guess is closer to the actual value of 2/3.