Marcus has a wooden pole. Two-thirds of it is painted white. One-sixth of it is painted blue and the rest is painted yellow. What fraction of the pole is painted yellow?
2/3 = 4/6
6/6 - (4/6 + 1/6) = ________
To find the fraction of the pole that is painted yellow, we need to subtract the fractions painted white and blue from 1.
Let's solve it step by step:
Step 1: Find the fraction painted white.
We are given that two-thirds of the pole is painted white, which can be written as 2/3.
Step 2: Find the fraction painted blue.
We are given that one-sixth of the pole is painted blue, which can be written as 1/6.
Step 3: Calculate the fraction painted yellow.
To find the fraction painted yellow, we subtract the fractions painted white and blue from 1:
1 - (2/3 + 1/6)
Step 4: Simplify the expression.
First, let's find a common denominator for 2/3 and 1/6. The least common multiple of 3 and 6 is 6.
2/3 = 4/6
1/6 = 1/6
Now we can substitute the fractions back into the expression:
1 - (4/6 + 1/6)
Step 5: Perform the addition within the parentheses.
4/6 + 1/6 = 5/6
So the expression becomes:
1 - 5/6
Step 6: Subtract the fractions.
To subtract fractions, we need a common denominator. The denominator of 1 is already 6, so we don't need to change it.
1 - 5/6 = 6/6 - 5/6 = 1/6
Therefore, one-sixth (1/6) of the pole is painted yellow.