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Chapter 1: Problem 39

Add. $$ -5.3+2.8 $$

Short Answer

Expert verified
-2.5

Step by step solution

01

Identify the Numbers

Identify the numbers involved in the addition problem. Here, the numbers are -5.3 and 2.8.
02

Understand the Operation

Understand that you are adding a negative number to a positive number. This means you will effectively be subtracting the smaller absolute value from the larger absolute value.
03

Perform the Subtraction

Subtract the smaller absolute value from the larger absolute value: 5.3 - 2.8 = 2.5 .
04

Determine the Sign

Since the larger absolute value was from -5.3, the result will have the same sign: -2.5 .

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Positive and Negative Numbers
Positive and negative numbers are fundamental concepts in math that describe values either above or below zero. Positive numbers are greater than zero, while negative numbers are less than zero. For example,
  • Positive numbers: 1, 2.5, 7
  • Negative numbers: -1, -2.5, -7
You can think of positive numbers like credits and negative numbers like debits. When you combine them, you either add to your total (with positive numbers) or subtract from it (with negative numbers). Adding a negative number is the same as subtracting its positive counterpart.
Absolute Value
The absolute value of a number is its distance from zero on the number line, regardless of direction. This means it is always a non-negative number. For example,
  • The absolute value of -5.3 is 5.3.
  • The absolute value of 2.8 is 2.8.
We denote absolute value with vertical bars. So, \(\left| -5.3 \right| = 5.3\) and \(\left| 2.8 \right| = 2.8\). Absolute value helps simplify expressions involving negative numbers by stripping the negative sign temporarily.
Subtraction Involving Negative Numbers
Subtraction can be tricky when involving negative numbers, but it gets easier with practice. Consider the operation step-by-step for clarity:
  • Identify the numbers: -5.3 and 2.8.
  • Note that you are adding a negative number (-5.3) to a positive number (2.8).
  • Convert the expression to a simple subtraction: 5.3 (absolute value of the larger number) - 2.8 (absolute value of the smaller number) = 2.5.
  • Determine the sign of the result: Since -5.3 has the larger absolute value, the result will inherit this sign.
Thus, -5.3 + 2.8 equals -2.5. Remember, combining different-signed numbers is often about their separation from zero, abstracted as distances.

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