On the real number line, what is the midpoint of \(-5\) and 17\(?\) A. \(-11\) B. 6 C. 11 D. 12 E. 22

The real number line is a fundamental concept in mathematics that provides a visual representation of all real numbers. It is a straight line where each point corresponds to a unique real number. On this line, numbers to the right are greater, while those to the left are smaller. Learning to work with the real number line is essential in math problem solving as it helps students visualize and compare numbers.

When working out problems like finding the midpoint between two points, the real number line can serve as a handy tool. For instance, imagine plotting (-5) and 17 on this line: (-5) would appear to the left, and 17 to the right. The midpoint is the point directly in the middle of (-5) and 17 on this line. It's where you would balance a physical scale if (-5) and 17 were weights on either side. This spatial understanding enhances comprehension of the midpoint formula and contributes to more intuitive math problem solving.

Math problem solving involves understanding the question, identifying the data given, selecting the right method or formula, and meticulously working through the solution. A general approach to solving math problems efficiently includes several steps:

1. Comprehension: Read the problem several times and make sure you understand what is being asked.
2. Strategy: Decide the best way to approach the problem, which in the case of finding a midpoint would be to use the midpoint formula.
3. Execution: Carry out the strategy, such as by plugging numbers into the given formula.
4. Review: Ensure that the answer makes sense within the context of the problem.

Improving math problem-solving skills is not just about practicing countless problems; it's also about understanding the logic and theory behind the formulas used. For example, the midpoint formula (\(\frac{a + b}{2}\)) is founded on the concept of averages. Understanding that provides a deeper insight into why the solution works and allows for easier recall and application in different contexts.

Preparing for the ACT math section involves mastering topics such as algebra, geometry, and trigonometry. Moreover, it's about developing strategies for efficient problem solving. Here are some tips specifically tailored to mastering math problems for the ACT:

1. Understand the Concepts: Make sure you are familiar with the underlying concepts like the real number line, midpoint, and average values. Understanding the 'why' behind an approach can make memory retention easier.
2. Practice with Formulas: Know the common formulas, such as the midpoint formula, and practice using them in various problem scenarios.
3. Time Management: Become proficient at solving problems swiftly and accurately since the ACT is timed.
4. Take Practice Tests: Familiarize yourself with the ACT format and question types by taking practice tests.
5. Learn to Eliminate: On multiple-choice questions, as with the midpoint question, learn how to quickly eliminate implausible answers.

Regular practice, along with these strategies, will improve your ability not only to tackle the ACT math problems but also to feel more confident during the test.