Abe’s 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 to red apple trees
The correct answer and explanation is:
The problem states:
- Number of green apple trees = 18
- Number of red apple trees = 21
Find: The ratio of green apple trees to red apple trees.
Step 1: Write the ratio
The ratio of green apple trees to red apple trees is: Green:Red=18:21\text{Green} : \text{Red} = 18 : 21
Step 2: Simplify the ratio
To simplify, divide both numbers by their greatest common divisor (GCD).
- Factors of 18: 1, 2, 3, 6, 9, 18
- Factors of 21: 1, 3, 7, 21
- The greatest common factor is 3.
Divide both terms by 3: 183:213=6:7\frac{18}{3} : \frac{21}{3} = 6 : 7
Final answer:
The simplified ratio of green apple trees to red apple trees is: 6:7\boxed{6 : 7}
Explanation (300 words):
A ratio compares quantities of two different categories to express their relative sizes. Here, the problem involves two types of apple trees in Abe’s orchard: green apple trees and red apple trees.
The given numbers are 18 green apple trees and 21 red apple trees. When writing a ratio, the order matters and should match what is asked. Since the problem asks for the ratio of green apple trees to red apple trees, the first number in the ratio corresponds to green apple trees, and the second to red apple trees. Thus, the initial ratio is 18:2118 : 21.
Ratios can often be simplified to their lowest terms, just like fractions. Simplifying a ratio makes it easier to interpret and compare. To do this, you find the greatest common divisor (GCD) of the two numbers and divide both by that number.
Here, the GCD of 18 and 21 is 3 because 3 is the largest number that divides both 18 and 21 exactly.
Dividing both numbers by 3, we get: 18÷3=618 \div 3 = 6 21÷3=721 \div 3 = 7
So, the simplified ratio becomes 6:76 : 7.
This ratio means that for every 6 green apple trees, there are 7 red apple trees. It provides a clear and proportional way to compare the two types of trees in the orchard without listing actual numbers, which can be helpful for planning, resource allocation, or visualizing the orchard’s composition.
In summary, the ratio expresses the relative quantities of green to red apple trees in the orchard, and simplifying it makes the comparison more meaningful and easier to understand.