Problem 44 - Prealgebra

Question

Add the following numbers left to right. $$-571+437+(-502)$$

Step-by-Step Solution

Answer

The sum is \(-636\).

Step 1: Add the First Two Numbers

First, we need to add the first two numbers in the sequence: \(-571 + 437\)To do this, first subtract 437 from 571, treating the operation as subtraction since 571 is negative. Calculate: \(571 - 437 = 134\)Since the first number is negative, the result is \(-134\).

Step 2: Add the Result to the Next Number

Next, add the result from Step 1 to the next number in the sequence: \(-134 + (-502)\)This is the addition of two negative numbers. When adding two negative numbers, you add their absolute values and keep the result negative.Calculate:\(134 + 502 = 636\)Thus, the result is \(-636\).

Key Concepts

Understanding Negative Numbers

Negative numbers can be a bit tricky initially but are quite logical once you understand their behavior. A negative number is any number that is less than zero, and it is typically written with a minus (-) sign in front of it. For instance,

• -5, which indicates 5 units less than zero.
• -50 being 50 units less than zero.

When dealing with negative numbers in operations, like addition or subtraction, it's essential to pay attention to the signs:

• When you add a negative number, you're essentially subtracting its absolute value.
• If you see two negative numbers being added, you're essentially adding their absolute values together but keeping the negative sign.

Negative numbers are crucial in real-life scenarios like debts, temperatures below zero, or even time before a certain event.

The Absolute Value Concept

The absolute value of a number is like its distance from zero, regardless of direction on the number line. It's always a positive value or zero. Think of it as the "magnitude" of the number. For example:

• The absolute value of -7 is 7, because it is 7 units away from zero.
• The absolute value of 0 is 0, as it's already at zero.

Absolute values are pivotal when adding numbers since they help determine the sum's actual magnitude without regard to the original sign.

The Process of Sequential Addition

Sequential addition means adding numbers step-by-step, or one at a time, in sequence. This approach helps simplify complex addition problems by breaking them down into smaller, more manageable parts. For example, consider the set of numbers:

• When you add -571 and 437, the focus should be on aligning the numbers and handling the operation step-by-step. Convert any negative addition to subtraction if it helps simplify the process.
• Following that, add the result to the next number in line, with special care to manage negatives appropriately.

This method can be particularly useful when dealing with longer lists of numbers or mixed signs. It emphasizes the importance of careful calculations and consistently applying operations to maintain accuracy.