Problem 74 - 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

2 is closest to 0.

Step 1: Understand the problem

We need to calculate the sum of 251 and -249 mentally, without pencil and paper or a calculator, and determine which of the given options the result is closest to.

Step 2: Calculate the Sum Mentally

Begin by calculating the sum of the two numbers: 251 and -249. Think of subtraction since adding a negative number is the same as subtraction: 251 - 249.

Step 3: Subtract the Numbers

Perform the subtraction: 251 - 249. Mentally, note that 251 is only 2 units above 249, so the result of 251 - 249 is 2.

Step 4: Compare Result with Options

Now compare the calculated result, 2, with the given options: 500, 0, and 500. Clearly, 2 is closest to 0.

Key Concepts

Addition and Subtraction

Addition and subtraction are two fundamental arithmetic operations that we often encounter in everyday life. They can be thought of as two sides of the same coin. When we talk about adding numbers, we're generally combining quantities or increasing a value. On the other hand, subtraction reduces the value or takes away some part from a total. When dealing with situations where a positive and a negative number are involved, such as in the problem "251 + (-249)", it helps to understand that adding a negative number is equivalent to performing subtraction. Here, the minus sign on 249 tells us that it's being subtracted from 251. This turns the problem into a straightforward subtraction: 251 minus 249. Simplifying problems in this way can help us solve them mentally and efficiently.

Integer Operations

Understanding integer operations is crucial when dealing with positive and negative numbers. Integers include all whole numbers and their negative counterparts. The main operations on integers are addition, subtraction, multiplication, and division. However, addition and subtraction are foundational and often used interchangeably with opposite signs to achieve the same effect. When you add a positive and a negative number, as in the exercise "251 + (-249)", you're essentially calculating the difference between their absolute values. Consider 251 and 249. The process involves understanding that since both are close in value, the negative sign in front of 249 effectively tells us to find how much more 251 is than 249. This way, we easily determine that 251 - 249 equals 2, showcasing how subtraction and addition of integers can interchangeably lead us to the solution.

Problem Solving Skills

Problem solving is not just about arriving at the right answer but also about applying the correct method efficiently. Tackling arithmetic problems mentally strengthens this skill by encouraging quick, logical reasoning and decision-making. In the exercise "251 + (-249)", the challenge lies in understanding the problem clearly without using any external tools. This means not just doing arithmetic in your head but also interpreting the problem and assessing the given choices effectively. In comparing the calculated answer of 2 with options like 500 and 0, you need to judge which number 2 is closest to. Improving problem-solving skills involves practicing mental math regularly, paying attention to details, and sharpening the ability to analyze and compare results. These skills are invaluable, forming the backbone of more complex problem-solving needed in advanced mathematics and real-world scenarios.