Problem 26 - Prealgebra and Introductory Algebra

Question

Simplify. $$-4.9+3.27$$

Step-by-Step Solution

Answer

-1.63

Step 1: Identify the numbers

The numbers involved in this exercise are -4.9 and +3.27.

Step 2: Find the difference

Since you're adding a negative number to a positive one, you'll have to find the absolute difference between the two numbers. Absolute difference between 4.9 and 3.27 is 1.63.

Step 3: Assign the sign

Assign the sign of the larger number. Here, the larger number in absolute value is -4.9 so the result will be a negative number.

Key Concepts

Adding Negative Numbers

Adding negative numbers might seem tricky at first, but it's quite simple once you understand the rule behind it. When you add a negative number to a positive number, you're essentially subtracting the absolute value of the negative number from the positive number. Imagine you're standing on a number line at zero. Moving to positive numbers is like stepping forward, while moving to negative numbers is like stepping backward.

• Example: If you have 5 + (-3), it's the same as 5 - 3, which equals 2.
• In the exercise, you have -4.9 and 3.27. Adding -4.9 to 3.27 is like subtracting 4.9 from 3.27.

By thinking of adding negatives as a form of subtraction, you can simplify many expression problems easily.

Absolute Value

The concept of absolute value is crucial when working with negative numbers. Absolute value simply represents how far a number is from zero, without considering direction on the number line. It's always positive or zero.

• The absolute value of a number \( x \) is written as \( |x| \).
• For example, \( |-4.9| = 4.9 \) and \( |3.27| = 3.27 \).
• In our exercise, we needed to find the absolute difference between 4.9 and 3.27 to solve the problem. We ignored signs temporarily to compare their sizes.

Understanding absolute value helps us focus on the magnitude of numbers, which is critical when determining which number is larger or when assigning signs.

Simplifying Expressions

Simplifying expressions often involves a few clear steps, especially when negative numbers are involved. To simplify an expression like \(-4.9 + 3.27\), you must understand both the number operations and their properties.First, notice whether you're adding or subtracting numbers, and recall how to handle their signs. Here's a simple approach:

• Identify the numbers involved and note their signs.
• Use the absolute values to determine the difference between the numbers, as seen in our solution where the absolute difference was 1.63.
• Consider the sign of the larger number (in absolute terms) to assign the result's sign. In the exercise, since 4.9 is larger than 3.27, the result was negative.

Simplifying expressions this way allows you to deal systematically with both positive and negative numbers, turning seemingly complex problems into straightforward arithmetic.