Problem 41 - Prealgebra

Question

Add the following numbers left to right. $$-201+(-143)+(-101)$$

Step-by-Step Solution

Answer

The sum is -445.

Step 1: Add the first two numbers

We start by adding the first two numbers: \(-201 + (-143)\).When adding two negative numbers, add their absolute values and keep the negative sign:\(201 + 143 = 344\).Thus, \(-201 + (-143) = -344\).

Step 2: Add the result to the next number

Now, add the result from Step 1 to the last number:\(-344 + (-101)\).Again, add the absolute values and keep the negative sign, as both numbers are negative:\(344 + 101 = 445\).So;\(-344 + (-101) = -445\).

Key Concepts

Negative Numbers

Negative numbers represent values that are less than zero. You can recognize them by the minus sign (-) in front of the number. In the context of mathematics, negative numbers often appear in real-world situations, such as temperatures dropping below zero or debts versus credits.When dealing with negative numbers in arithmetic operations, especially addition or subtraction, it's crucial to understand how they interact with positive numbers. For instance:

• Adding two negative numbers together results in a more negative number. This is because you're essentially moving further left on the number line. For example, \(-3 + (-5) = -8\).
• Subtracting a negative number is the same as adding a positive number. This happens because removing a negative is like gaining a positive, \(-3 - (-5) = -3 + 5 = 2\).

Negative numbers require careful attention in calculations to ensure positive and negative interactions are correctly understood and applied.

Absolute Values

The absolute value of a number is its distance from zero on a number line, regardless of direction. Thus, the absolute value is always non-negative. For instance, both 5 and -5 have the same absolute value of 5.In mathematical terms, the absolute value of a number \(x\) is represented as \(|x|\). It can be described as:

• \(|5| = 5\)
• \(|-5| = 5\)

Absolute values are particularly important when working with negative numbers. When adding or subtracting negative numbers, finding their absolute values helps to determine the magnitude of the sum or difference. In the exercise provided, adding \(-201 + (-143)\) involves taking the absolute values 201 and 143, adding them, and then applying the negative sign to ensure direction on the number line is preserved.

Step-by-Step Math Solutions

Step-by-step math solutions break down a complex problem into smaller, easier-to-manage parts. This approach is especially beneficial in dealing with operations involving negative numbers and absolute values.For example, consider the exercise: \(-201+(-143)+(-101)\).Here’s a detailed walkthrough of how to apply a step-by-step approach:1. **Add the first two numbers**: - Identify the numbers involved: \(-201\) and \(-143\). - Find the absolute values: \(201\) and \(143\). - Add these absolute values: \(201 + 143 = 344\). - Apply the negative sign: The result is \(-344\).
2. **Add the next number**: - Use the result from the previous step: \(-344\). - Add \(-101\). Again, find the absolute values of \(344\) and \(101\). - Add these values: \(344 + 101 = 445\). - Keep the negative sign: This gives a final result of \(-445\).
Using a step-by-step approach helps you keep track of operations and ensures accuracy, especially when dealing with both negative and positive elements in a problem.