Question

The lowest level of the Willis Tower in Chicago is at an elevation of \(-43\) feet. The skydeck is at an elevation of 1353 feet. What is the distance between the lowest level and the skydeck?

Short answer

Answer: The distance between the lowest level and the skydeck in the Willis Tower is 1396 feet.

Step-by-step solution

Identify the given elevations

We are given the elevations as: - Lowest level: \(-43\) feet - Skydeck: 1353 feet

Find the difference in elevations

To find the distance between the lowest level and the skydeck, we need to subtract the elevation of the lowest level from the elevation of the skydeck. \(Distance = 1353 - (-43)\)

Evaluate the result

Now, we calculate the subtraction: \(Distance = 1353 + 43 = 1396\) The distance between the lowest level and the skydeck is \(1396\) feet.

Key concepts

Subtraction of Integers

When we talk about subtraction of integers, we're dealing with the arithmetic operation of finding the difference between two whole numbers that can be either positive or negative. It's a fundamental aspect of prealgebra and is essential for understanding how numbers interact with each other.

For instance, when you have two integers like 7 and -3, subtracting them involves considering the direction each number represents on the number line. Subtracting a negative number is the same as adding its positive counterpart. So, 7 - (-3) becomes 7 + 3, which equals 10. This rule often confuses students, but it's a key concept in understanding how integers work together mathematically.

Positive and Negative Numbers

The concept of positive and negative numbers is much more than a mathematical abstraction; it's a way to represent real-world quantities like debts or elevations relative to sea level. Positive numbers signify quantities greater than zero, usually representing something you have or gain. In contrast, negative numbers are less than zero and often depict something you owe or an amount below a standard reference point, such as sea level.

In our daily lives, we use positive numbers to express things like money earned, while negative numbers might represent money spent. If you imagine the number line, positive numbers are to the right of zero, and negative numbers are to the left. This helps us visualize arithmetic operations involving these integers, particularly when we're adding or subtracting them.

Real-world Math Application

Real-world math applications bring abstract concepts into practical use. In the case of the exercise with the Willis Tower, we're dealing with elevation levels, which are perfect examples of how mathematics helps us describe and understand the world around us. The question asks us to find the distance between two points of different elevations, showcasing how subtraction of integers applies to scenarios we might encounter, like measuring the height of buildings.

This practical application reinforces our understanding of math by providing tangible examples. It's essential for students to see these applications to relate to math not just as numbers on a page but as useful tools for solving everyday problems. Actions like budgeting, cooking, or even planning travel routes all use math as their foundation.

Prealgebra

Prealgebra serves as the groundwork for all higher-level mathematics, including algebra, geometry, and calculus. It introduces students to basic arithmetic operations and the fundamental properties of integers, fractions, and decimals. Grasping these concepts is crucial for developing mathematical literacy.

In the context of the exercise involving the Willis Tower, prealgebraic skills allow us to manipulate the numbers effectively to find the correct distance between elevations. Understanding how to add and subtract numbers, especially when dealing with negative integers, helps students to solve such practical problems accurately. Prealgebra paves the way for complex problem-solving by establishing a solid mathematical foundation.