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?
blue=2/3(1-1/2)=1/3
yellow=1-1/3-1/2=1/6(6-2-3)=1/6
In a box of paper clips,3/8 of them are white,5/12 of them are red, and the rest are blue. There are 24 more red paper cilps than white paper clips. How many paper clips are there in the box?
1/3
Well, let me do some quick calculations here. If we start with a whole rectangle, and half of it is painted red, that means we have 1/2 left. Now, 2/3 of that remaining half is painted blue, leaving us with 1/3 of the original rectangle. So, the fraction of the rectangle that is painted blue is 1/3.
Now, the remaining fraction of the rectangle after the blue is painted is 2/3. If we say the rest of the rectangle is painted yellow, then the fraction of the rectangle that is painted yellow would be 2/3.
So, to summarize: 1/3 of the rectangle is painted blue, and 2/3 of the rectangle is painted yellow.
To find the fraction of the rectangle that is painted blue, we need to first calculate the fraction of the rectangle that is not painted red.
Since half of the rectangle is painted red, the remaining unpainted portion of the rectangle is 1 - 1/2 = 1/2.
Next, we need to find 2/3 of this remaining unpainted portion. Multiplying 1/2 by 2/3, we get (1/2) x (2/3) = 2/6.
So, 2/6 of the remainder is painted blue.
To find the fraction of the rectangle that is painted yellow, we know that half of the rectangle is painted red and 2/6 is painted blue. The remaining fraction of the rectangle that is not painted red or blue can be found by subtracting the sum of red and blue fractions from 1.
1 - 1/2 - 2/6 can be simplified by finding a common denominator:
1 - 3/6 - 2/6 = 1 - 5/6 = 6/6 - 5/6 = 1/6.
Therefore, 1/6 of the rectangle is painted yellow.
In summary, fraction of the rectangle that is painted blue is 2/6 and the fraction that is painted yellow is 1/6.