Abes apple orchard plans 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:
To find the ratio of green apple trees to red apple trees in Abe’s apple orchard, we need to compare the number of green apple trees to the number of red apple trees.
Abe plans to plant:
- Green apple trees: 18
- Red apple trees: 21
The ratio is expressed as:Ratio of green apple trees to red apple trees=Number of green apple treesNumber of red apple trees=1821\text{Ratio of green apple trees to red apple trees} = \frac{\text{Number of green apple trees}}{\text{Number of red apple trees}} = \frac{18}{21}Ratio of green apple trees to red apple trees=Number of red apple treesNumber of green apple trees=2118
To simplify this 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 greatest common factor between these two numbers is 3.
Now we can divide both the numerator and the denominator by 3:18÷321÷3=67\frac{18 \div 3}{21 \div 3} = \frac{6}{7}21÷318÷3=76
Thus, the simplified ratio of green apple trees to red apple trees is 6:7.
Explanation
In this context, ratios help us understand the relative amounts of different types of apple trees in Abe’s orchard. Ratios are a way to compare two quantities and can be expressed in various forms, including fractions, decimals, and proportions. They are essential in agricultural planning as they assist in visualizing the distribution of resources, such as land and water, across different crops.
When we simplified the ratio, we used the concept of finding the greatest common divisor. This mathematical technique is useful in reducing ratios to their simplest form, making it easier to comprehend and communicate the relationship between the quantities involved. In practical terms, a ratio of 6:7 indicates that for every 6 green apple trees, there are 7 red apple trees. This information can be crucial for decisions related to cultivation, maintenance, and expected yield, allowing Abe to effectively manage his orchard for optimal fruit production.