Abes apples orchard plants both green apple trees and red apple trees this planting will include 21 red apple trees and 18 green apple trees what is the ratio of green apple trees and red apple trees
The Correct Answer and Explanation is:
The ratio of green apple trees to red apple trees in Abe’s orchard can be determined by comparing the number of green apple trees to the number of red apple trees.
Step-by-Step Calculation:
- Identify the number of each type of tree:
- Green apple trees: 18
- Red apple trees: 21
- Write the ratio:
The ratio of green apple trees to red apple trees is written as:
[
\text{Ratio} = \frac{\text{Green Apple Trees}}{\text{Red Apple Trees}} = \frac{18}{21}
] - Simplify the ratio:
To simplify the ratio, we need to find the greatest common divisor (GCD) of 18 and 21. The factors of 18 are 1, 2, 3, 6, 9, and 18, while the factors of 21 are 1, 3, 7, and 21. The largest common factor is 3. So, we divide both the numerator and the denominator of the ratio by 3:
[
\frac{18}{21} = \frac{18 \div 3}{21 \div 3} = \frac{6}{7}
]
Thus, the simplified ratio of green apple trees to red apple trees is 6:7.
Explanation of the Ratio:
A ratio is a way of comparing two quantities to show how many times one value contains or is contained within the other. In this case, the ratio 6:7 means that for every 6 green apple trees, there are 7 red apple trees. This provides a clear representation of the relative quantities of each type of tree in the orchard.
Ratios can also be expressed as fractions or in words. The fraction form of the ratio 6:7 is (\frac{6}{7}), which also shows the relationship between the two types of trees. Another way to describe the ratio would be, “For every 6 green apple trees, there are 7 red apple trees.”
This ratio helps to understand the distribution of trees in the orchard, giving a clearer picture of the variety of apples planted and can also aid in making decisions related to orchard management, such as harvesting or marketing the apples.