A Baby Mango Tree Stands 2.6 Meters Above The Ground. Its Roots Extend 7 5 \frac{7}{5} 5 7 ​ Meters Below The Ground.Which Two Of The Following Expressions Represent The Vertical Distance Between The Top Of The Mango Tree And The Tips Of Its

Introduction

In this discussion, we will explore the vertical distance between the top of a baby mango tree and the tips of its roots. The height of the tree is given as 2.6 meters, and the depth of its roots is $\frac{7}{5}$ meters. We will examine two expressions that represent the vertical distance between the top of the tree and the tips of its roots.

Understanding the Problem

To find the vertical distance between the top of the tree and the tips of its roots, we need to consider the height of the tree and the depth of its roots. The height of the tree is a positive value, while the depth of its roots is a negative value. When we add these two values together, we get the total vertical distance between the top of the tree and the tips of its roots.

Expression 1: Adding the Height and Depth

The first expression that represents the vertical distance between the top of the tree and the tips of its roots is:

2.6 + (-$\frac{7}{5}$)

To evaluate this expression, we need to add the height of the tree (2.6 meters) and the negative depth of its roots ($-\frac{7}{5}$ meters). We can simplify this expression by finding a common denominator for the two fractions.

2.6 + (-$\frac{7}{5}$) = 2.6 - $\frac{7}{5}$

To subtract the fractions, we need to have the same denominator. We can convert the decimal 2.6 to a fraction with a denominator of 5:

2.6 = $\frac{13}{5}$

Now we can subtract the fractions:

$\frac{13}{5}$ - $\frac{7}{5}$ = $\frac{6}{5}$

So, the first expression that represents the vertical distance between the top of the tree and the tips of its roots is $\frac{6}{5}$ meters.

Expression 2: Subtracting the Depth from the Height

The second expression that represents the vertical distance between the top of the tree and the tips of its roots is:

2.6 - (-$\frac{7}{5}$)

To evaluate this expression, we need to subtract the negative depth of the tree's roots from the height of the tree. When we subtract a negative value, we are essentially adding the positive value. So, we can rewrite this expression as:

2.6 + $\frac{7}{5}$

To add the fractions, we need to have the same denominator. We can convert the decimal 2.6 to a fraction with a denominator of 5:

2.6 = $\frac{13}{5}$

Now we can add the fractions:

$\frac{13}{5}$ + $\frac{7}{5}$ = $\frac{20}{5}$

So, the second expression that represents the vertical distance between the top of the tree and the tips of its roots is $\frac{20}{5}$ meters, which simplifies to 4 meters.

Conclusion

In this discussion, we explored the vertical distance between the top of a baby mango tree and the tips of its roots. We examined two expressions that represent this distance and found that both expressions evaluate to the same value: $\frac{6}{5}$ meters. This means that the vertical distance between the top of the tree and the tips of its roots is $\frac{6}{5}$ meters.

Key Takeaways

• The vertical distance between the top of a tree and the tips of its roots is the sum of the height of the tree and the depth of its roots.
• When adding a positive value and a negative value, we need to have the same denominator to simplify the expression.
• When subtracting a negative value, we are essentially adding the positive value.

Further Exploration

This problem can be extended to explore other aspects of the tree's growth and development. For example, we could consider the rate at which the tree grows and how this affects the vertical distance between the top of the tree and the tips of its roots. We could also explore the relationship between the tree's height and the depth of its roots in different environments.

Mathematical Concepts

This problem involves the following mathematical concepts:

• Fractions and decimals
• Addition and subtraction of fractions
• Simplifying expressions
• Understanding the concept of negative values and how they affect the result of an expression.

Real-World Applications

This problem has real-world applications in agriculture and horticulture. For example, farmers and gardeners need to consider the vertical distance between the top of a tree and the tips of its roots when planting and caring for trees. This information can help them make informed decisions about tree care and pruning.

References

• [1] "Tree Growth and Development." Encyclopedia of Agriculture and Food Systems, 2014.
• [2] "Horticulture: Principles and Practices." 4th ed., Pearson Education, 2013.

Glossary

• Vertical distance: The distance between two points in a vertical direction.
• Height: The distance between the top of an object and the ground.
• Depth: The distance between the bottom of an object and the ground.
• Fraction: A way of expressing a part of a whole as a ratio of two numbers.
• Decimal: A way of expressing a fraction as a number with a point separating the whole number part from the fractional part.
  A Baby Mango Tree's Vertical Distance: Q&A =============================================

Introduction

In our previous discussion, we explored the vertical distance between the top of a baby mango tree and the tips of its roots. We examined two expressions that represent this distance and found that both expressions evaluate to the same value: $\frac{6}{5}$ meters. In this Q&A article, we will answer some common questions related to this topic.

Q: What is the vertical distance between the top of the tree and the tips of its roots?

A: The vertical distance between the top of the tree and the tips of its roots is $\frac{6}{5}$ meters.

Q: How do you calculate the vertical distance between the top of the tree and the tips of its roots?

A: To calculate the vertical distance between the top of the tree and the tips of its roots, you need to add the height of the tree and the depth of its roots. If the depth of the roots is negative, you need to subtract it from the height of the tree.

Q: What is the difference between the height of the tree and the depth of its roots?

A: The height of the tree is the distance between the top of the tree and the ground, while the depth of its roots is the distance between the bottom of the roots and the ground. The depth of the roots is typically negative, as it is below the ground level.

Q: Can you provide an example of how to calculate the vertical distance between the top of the tree and the tips of its roots?

A: Let's say the height of the tree is 2.6 meters and the depth of its roots is -$\frac{7}{5}$ meters. To calculate the vertical distance between the top of the tree and the tips of its roots, you would add the height of the tree and the depth of its roots:

2.6 + (-$\frac{7}{5}$) = 2.6 - $\frac{7}{5}$

To subtract the fractions, you need to have the same denominator. You can convert the decimal 2.6 to a fraction with a denominator of 5:

2.6 = $\frac{13}{5}$

Now you can subtract the fractions:

$\frac{13}{5}$ - $\frac{7}{5}$ = $\frac{6}{5}$

So, the vertical distance between the top of the tree and the tips of its roots is $\frac{6}{5}$ meters.

Q: What are some real-world applications of calculating the vertical distance between the top of the tree and the tips of its roots?

A: Calculating the vertical distance between the top of the tree and the tips of its roots has several real-world applications in agriculture and horticulture. For example, farmers and gardeners need to consider the vertical distance between the top of a tree and the tips of its roots when planting and caring for trees. This information can help them make informed decisions about tree care and pruning.

Q: Can you provide some tips for calculating the vertical distance between the top of the tree and the tips of its roots?

A: Here are some tips for calculating the vertical distance between the top of the tree and the tips of its roots:

• Make sure to have the same denominator when adding or subtracting fractions.
• Convert decimals to fractions with a common denominator.
• Use a calculator to simplify fractions and calculate the vertical distance.

Q: What are some common mistakes to avoid when calculating the vertical distance between the top of the tree and the tips of its roots?

A: Here are some common mistakes to avoid when calculating the vertical distance between the top of the tree and the tips of its roots:

• Not having the same denominator when adding or subtracting fractions.
• Not converting decimals to fractions with a common denominator.
• Not using a calculator to simplify fractions and calculate the vertical distance.

Conclusion

In this Q&A article, we answered some common questions related to the vertical distance between the top of a baby mango tree and the tips of its roots. We provided examples and tips for calculating this distance and highlighted some real-world applications of this concept. We hope this article has been helpful in understanding the vertical distance between the top of the tree and the tips of its roots.