1/2 of a rectangle is painted red. 2/3 of the remainder is painted blue and the rest of the rectangle is painted yellow. What fraction of the rectangle is painted blue? What fraction of the rectangle is painted yellow?
1/2 = red
2/3 * 1/2 = 1/3 = blue
1/2 + 1/3 = 5/6, so 1/6 = yellow
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To solve this problem, we'll break it down step by step.
Step 1: Start with the whole rectangle.
Step 2: If 1/2 of the rectangle is painted red, then the remaining unpainted portion is 1/2 as well.
Step 3: From the remaining 1/2 of the rectangle, 2/3 is painted blue.
Step 4: To find the fraction of the rectangle that is painted blue, we find 2/3 of 1/2. This can be done by multiplying the numerators and denominators: (2 * 1) / (3 * 2) = 2/6.
Step 5: Simplifying 2/6 to its lowest terms, we get 1/3. Therefore, 1/3 of the rectangle is painted blue.
Step 6: To find the fraction of the rectangle that is painted yellow, we subtract the fractions of the rectangle that are painted red and blue from the whole rectangle.
Step 7: 1/2 (painted red) + 1/3 (painted blue) = 3/6 + 2/6 = 5/6.
Step 8: Subtracting 5/6 from 1 (the whole rectangle) gives us: 1 - 5/6 = 6/6 - 5/6 = 1/6.
Therefore, 1/6 of the rectangle is painted yellow.
To solve this problem, we'll need to find the fractions step by step.
Let's assume the whole rectangle is represented by a unit fraction, which we'll call "1."
First, we know that 1/2 of the rectangle is painted red. Therefore, the red portion is 1/2.
Next, we're given that 2/3 of the remaining unpainted portion is painted blue. To find this, we need to subtract the red portion (1/2) from the whole (1), giving us 1 - 1/2 = 1/2. So, we have 1/2 left.
Now, we need to find 2/3 of this 1/2. Multiplying 1/2 by 2/3 gives us (1/2) * (2/3) = 2/6 simplified to 1/3. Therefore, 1/3 of the remaining rectangle is painted blue.
Finally, to find the yellow portion, we subtract the red and blue portions from the whole. This can be done by subtracting 1/2 (red) and 1/3 (blue) from 1. Calculating it gives us 1 - 1/2 - 1/3 = 3/6 - 2/6 - 1/6 = 0/6 = 0. Therefore, no part of the rectangle is painted yellow.
In summary:
- The fraction of the rectangle that is painted blue is 1/3.
- The fraction of the rectangle that is painted yellow is 0.