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Chapter 10: Problem 28

Subtract. $$ -3-(-1) $$

Short Answer

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Step by step solution

01

Identify the problem

Given the expression -3-(-1), the task involves subtracting a negative number from another negative number.
02

Simplify double negatives

When subtracting a negative number, it is the same as adding its positive counterpart. Thus, -3-(-1) is equivalent to -3 + 1.
03

Basic subtraction

Perform the basic addition of the numbers: -3 + 1 = -2.

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Key Concepts

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

Basic Subtraction
Subtraction is a fundamental operation in mathematics. It involves finding the difference between two numbers. In our exercise, we are working with the expression \[ -3 - (-1) \].

Let's break it down:
  • The minus sign in front of 3 means the number is negative.
  • The subtraction symbol ( - ) indicates that we need to subtract.
  • The parentheses around -1 include another negative sign within them.
Remember, subtraction can also be thought of as adding the opposite. This is especially useful when we deal with negative numbers.
Simplifying Double Negatives
Double negatives can be tricky, but they essentially cancel each other out. When you have a double negative, it turns into a positive. In our exercise, we have the expression: \[ -3 - (-1) \].

Here's a key rule:
  • Subtracting a negative number is the same as adding a positive number.
Applying this rule to our expression: \[ -3 - (-1) = -3 + 1 \].

Why does this happen?
Subtracting a negative number means you are removing a negative, which is the same as adding a positive.
Addition of Integers
Now let's focus on adding integers. Integers include all whole numbers and their negatives. In our simplified expression, we have: \[ -3 + 1 \].

Here鈥檚 how you handle this:
  • Identify the two numbers: -3 and +1.
  • Think of it on a number line: Start at -3 and move 1 step to the right.
  • You end up at -2.
So, \[ -3 + 1 = -2 \]. This shows you that whenever you add a positive number to a negative number, you're essentially moving towards zero on the number line. The final result can be positive or negative, depending on the values.

Understanding these rules and steps makes working with integers much easier!

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