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Chapter 1: Problem 234

Simplify each expression. $$ -19-46 $$

Short Answer

Expert verified
-65

Step by step solution

01

- Identify the Operation

First, observe the expression to determine the operation that needs to be performed. The given expression is -19 - 46. This involves subtraction of two numbers.
02

- Apply the Subtraction

Since we need to subtract 46 from -19, we can think of it as moving 46 more steps to the left on the number line from -19. This means you are effectively adding the two negative numbers.
03

- Add the Absolute Values

Add the absolute values of the numbers involved: 19 + 46 = 65.
04

- Determine the Sign

Since both numbers are negative, the result will also be negative. Therefore, the result of -19 - 46 is -65.

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Key Concepts

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

Subtraction of Integers
Subtraction can be tricky, especially when dealing with negative numbers. Let's break it down step by step. Subtraction tells us to find the difference between two numbers. Think about it this way: subtracting a number is the same as adding its opposite. To simplify -19 - 46, you can think of it as -19 + (-46). This way, you transform the problem into adding two negative numbers, making it easier to handle.
Absolute Values
Absolute values play an important role in simplifying expressions involving negative numbers. The absolute value of a number is its distance from zero, regardless of direction. When looking at -19 and 46, we consider the absolute values 19 and 46. Add these absolute values together: 19 + 46 = 65. This helps to simplify the addition process, focusing on the magnitude of the numbers instead of their signs.
Negative Numbers
Understanding negative numbers is key to solving these types of problems. Negative numbers represent values less than zero. When you have -19 and -46, both are on the negative side of the number line. Adding these together means you're moving further left on the number line. Thus, -19 - 46 equals -65. Always remember that combining negative numbers will result in a more negative number, reflecting a greater distance from zero in the negative direction.

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