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Chapter 5: Problem 90

What number is halfway between -22.4 and -22.5?

Short Answer

Expert verified
-22.45

Step by step solution

01

Verify the Range

Determine the two numbers between which the midpoint is sought: -22.4 and -22.5.
02

Identify the Formula

Use the midpoint formula: \[\frac{a + b}{2}\] where a and b are the given numbers.
03

Plug in the Values

Substitute \(a = -22.4\) and \(b = -22.5\) into the formula: \[\frac{-22.4 + (-22.5)}{2} = \frac{-22.4 - 22.5}{2}\]
04

Perform the Calculation

Calculate the sum within the numerator: \[-22.4 - 22.5 = -44.9\]. Then divide by 2: \[\frac{-44.9}{2} = -22.45\]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

midpoint formula
The midpoint formula is a fundamental concept in mathematics. It helps you find the number exactly halfway between two other numbers. The formula is: \(\frac{a + b}{2}\), where 'a' and 'b' are the numbers you are working with. This formula is straightforward: just add the two numbers together and divide by 2. Calculating midpoints can be useful in various math problems and real-life scenarios, like finding the middle of a journey or balancing accounts.
negative numbers
Negative numbers are numbers less than zero. They are written with a minus sign (e.g., -1, -5, -22.4). In the exercise, the numbers -22.4 and -22.5 are both negative. Adding or subtracting negative numbers can be tricky. When you add two negative numbers, you are essentially increasing the negativity (e.g., -22.4 + (-22.5) = -44.9). Understanding how negative numbers work is crucial for solving many math problems.
basic arithmetic
Basic arithmetic involves simple operations like addition, subtraction, multiplication, and division. These are the foundational skills needed for more complex math. In the exercise, we use:
  • Addition: -22.4 + (-22.5)
  • Subtraction: which is same as adding a negative number
  • Division: dividing by 2 to find the midpoint
. Mastering these basic operations is essential for solving problems quickly and accurately.
prealgebra
Prealgebra is an essential math subject that sets the stage for algebra. It typically covers topics like basic arithmetic, number lines, and the properties of numbers. Understanding prealgebra is crucial for tackling more advanced math concepts. The midpoint formula is one of the many tools you'll learn about in prealgebra. It's a simple yet powerful way to find the middle point between two numbers, which is a fundamental skill in math.

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