One group of children has 15 red blocks and 45 green blocks. Another group of children has 30 red blocks and 90 green blocks. Which proportion correctly describes the relative amounts of each color?
The first group has a ratio of red blocks to green blocks of 15:45. Simplifying this ratio, we get 1:3. The second group has a ratio of red blocks to green blocks of 30:90. Simplifying this ratio, we also get 1:3. Therefore, the correct proportion to describe the relative amounts of each color is 1:3.
To find the proportion that correctly describes the relative amounts of each color, we need to compare the number of red blocks to the number of green blocks in each group.
First, let's find the proportion for the first group:
Number of red blocks in the first group = 15
Number of green blocks in the first group = 45
Next, let's find the proportion for the second group:
Number of red blocks in the second group = 30
Number of green blocks in the second group = 90
To express the proportions, we divide the number of red blocks by the number of green blocks for each group:
Proportion for the first group = 15 red blocks / 45 green blocks
Proportion for the second group = 30 red blocks / 90 green blocks
To simplify the proportions, we divide both the numerator and the denominator by the greatest common divisor:
Proportion for the first group = 1/3 (divide both numerator and denominator by 15)
Proportion for the second group = 1/3 (divide both numerator and denominator by 30)
Therefore, the proportion 1/3 correctly describes the relative amounts of red and green blocks in both groups.
To find the proportion that correctly describes the relative amounts of each color, we need to compare the number of red blocks to the number of green blocks in both groups.
For the first group:
Number of red blocks = 15
Number of green blocks = 45
For the second group:
Number of red blocks = 30
Number of green blocks = 90
To create a proportion, we need to compare the corresponding ratios of red to green blocks in both groups.
Let's start with the first group. The ratio of red to green blocks in the first group is:
Red to green ratio in group 1 = Number of red blocks / Number of green blocks = 15 / 45
Similarly, for the second group, the ratio of red to green blocks is:
Red to green ratio in group 2 = Number of red blocks / Number of green blocks = 30 / 90
To simplify both ratios, we divide both the numerator and denominator by their greatest common divisor (GCD). In this case, the GCD of 15 and 45 is 15, and the GCD of 30 and 90 is 30. Dividing both ratios by their respective GCDs, we get:
Red to green ratio in group 1 = 1 / 3
Red to green ratio in group 2 = 1 / 3
Therefore, the proportion that correctly describes the relative amounts of each color in both groups is 1:3.