Problem 75 - Prealgebra

Question

Work mentally, without pencil and paper or a calculator. The answer to the problem -251+249 is closest to which of the following numbers? a. 500 b. 0 c. -500

Step-by-Step Solution

Answer

The answer is closest to 0.

Step 1: Understand the Problem

The problem asks for the sum of -251 and 249. We need to determine which of the provided options: 500, 0, or -500, this sum is closest to.

Step 2: Estimate the Sum

Since -251 and 249 are very close in magnitude but have opposite signs, their sum will be small or zero. Calculate \(-251 + 249 = -2.\)

Step 3: Compare to Given Choices

The result of the calculation is -2. We now compare this number to the options given: 500, 0, and -500. The number -2 is closest to 0.

Key Concepts

Mental Math

When solving problems mentally, you're using the power of your mind to perform calculations without any external aids. This skill is invaluable for quick estimations. In the given problem, you had to determine what

• -251 added to 249 equates to.
• Both numbers are conveniently close in value but differ in sign.

By recognizing the near equivalence of these numbers, you can deduce that their sum must be quite small, in one swift mental step, calculating

• -251 + 249 = -2,

bypasses unnecessary hassle.
Good mental math practice involves recognizing patterns and relationships, applying them to simplify your thought process, and deciding rationally without needing meticulous steps.

Integer Operations

Understanding and mastering integer operations is pivotal for mathematics in general. Integers include both positive and negative whole numbers, and knowing how to work with them strategically enhances your calculation agility.
The exercise involves adding negative and positive integers:

• -251 and 249.

A crucial aspect to note is that when adding two integers where one is negative and the other is positive, the operation becomes finding the difference between their absolute values.
In this case,

• |-251| and |249|

equate to 251 and 249, respectively.
The resulting difference is

• 2,

and since -251 is greater in magnitude, the sum is negative, resulting in -2.
Grasping these principles assists with quick decision-making, as shown in selecting the closest number to -2 from the given options.

Problem-solving

Effective problem-solving in mathematics is about understanding the problem, planning a strategy, executing it, and checking your work.
In this instance, the challenge was to determine which number -251 + 249 is closest to.
The steps in approaching such a problem are thorough yet straightforward:

• First, identify the nature of the numbers involved and their relationship, such as opposite signs but similar magnitudes.
• Next, swiftly estimate the outcome (an essential skill in exams where time is limited).
• Finally, review your result against the provided choices, ensuring that the estimation strategy used is reliable.

By fostering these problem-solving skills, you can bring efficiency and accuracy into many areas beyond just math exercises. By breaking the problem down into smaller parts, you're making it more manageable, taking pressure off yourself when dealing with more complex math problems in the future.