- Calculate the ratio for Group 1: \(\frac{15}{45} = \frac{1}{3}\).
- Calculate the ratio for Group 2: \(\frac{30}{90} = \frac{1}{3}\).
- Observe that the ratios are equivalent.
- The correct proportion is \(\boxed{\frac{15}{45} = \frac{30}{90}}\).
Explanation
- Analysis of block ratios
To determine the correct proportion relating the relative amounts of red and green blocks in both groups, we first analyze the quantities provided. For the first group, there are 15 red blocks and 45 green blocks, giving a ratio of red blocks to green blocks of \(\frac{15}{45}\). For the second group, there are 30 red blocks and 90 green blocks, giving a ratio of red blocks to green blocks of \(\frac{30}{90}\).
- Simplifying and comparing the ratios
Next, we simplify these ratios to compare them. For the first group, we divide both the numerator and the denominator by their greatest common divisor, which is 15:
\[\frac{15}{45} = \frac{15 \div 15}{45 \div 15} = \frac{1}{3}.\]
For the second group, we divide both the numerator and the denominator by their greatest common divisor, which is 30:
\[\frac{30}{90} = \frac{30 \div 30}{90 \div 30} = \frac{1}{3}.\]
Since both simplified ratios are \(\frac{1}{3}\), we can conclude that the ratio of red to green blocks in the first group is equal to the ratio of red to green blocks in the second group. Therefore, the proportion that correctly describes this relationship is \(\frac{15}{45} = \frac{30}{90}\).
Examples
Proportions are very common in cooking and chemistry. For example, if a recipe calls for 2 cups of sugar for every 4 cups of flour, the ratio is \(\frac{2}{4} = \frac{1}{2}\). If you decide to double the batch, you will need 4 cups of sugar and 8 cups of flour, resulting in a ratio of \(\frac{4}{8} = \frac{1}{2}\). Understanding proportions helps ensure that you maintain the same relative amounts regardless of the total batch size.