Abe’s apple orchard plans to plant both green apple trees. This planting will include 21 red apple trees and 18 green apple trees. What is the ratio of green apples to red apples?
The Correct Answer and Explanation is:
Correct Answer:
The ratio of green apple trees to red apple trees is 6:7.
Explanation:
Ratios are a way of comparing quantities of the same kind. In this case, we are comparing the number of green apple trees to the number of red apple trees in Abe’s orchard.
According to the problem, Abe is planting:
- 21 red apple trees
- 18 green apple trees
To find the ratio of green apple trees to red apple trees, we place the number of green apple trees first (since they are mentioned first in the question) and the number of red apple trees second. So, the ratio is written as: Ratio=Green Apple TreesRed Apple Trees=1821\text{Ratio} = \frac{\text{Green Apple Trees}}{\text{Red Apple Trees}} = \frac{18}{21}
This fraction can be simplified to its lowest terms by dividing both the numerator (top number) and the denominator (bottom number) by their greatest common divisor (GCD). The GCD of 18 and 21 is 3.
Now, divide both numbers by 3: 18÷321÷3=67\frac{18 \div 3}{21 \div 3} = \frac{6}{7}
So, the simplified ratio of green apple trees to red apple trees is: 6:7\boxed{6:7}
This means that for every 6 green apple trees Abe plants, he plants 7 red apple trees.
Understanding this ratio helps in planning, such as determining space allocation or visualizing the orchard layout. Ratios also support proportional reasoning—if Abe were to double the number of trees, for instance, the ratio would still hold as 6:7, even though the total numbers would be 36 green and 42 red apple trees.
In summary, the correct ratio of green apple trees to red apple trees is 6:7, and this expresses a proportional relationship between the two types of trees being planted.
