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Chapter 3: Problem 30

For the following exercises, perform the indicated operations. $$ -5-(-3) $$

Short Answer

Expert verified
Answer: The result of the expression $$-5-(-3)$$ is $$-2$$.

Step by step solution

01

Rewrite the expression using addition

Since we have a negative number minus another negative number, we can rewrite the expression as an addition problem using the rule: $$a - (-b) = a + b$$. Applying this rule to our expression, we get: $$ -5-(-3) = -5+3 $$
02

Evaluate the expression

Now that we have rewritten the expression as an addition problem, we simply add the numbers together. To add a negative and positive integer, we subtract the smaller absolute value from the larger absolute value and keep the sign of the integer with the larger absolute value: $$ -5+3 = -2 $$
03

State the final result

The result of the given expression is -2. So, $$-5-(-3) = -2$$.

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Key Concepts

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

Subtracting Negative Numbers
When you encounter the operation of subtracting a negative number, you can transform it into addition. This might sound confusing at first, but it's quite straightforward with a simple rule: subtracting a negative number is the same as adding its positive counterpart.

So, in mathematical terms:
  • \(a - (-b) = a + b\)
Consider the example \(-5 - (-3)\). According to our rule, this can be rewritten as \(-5 + 3\). You just change the sign of the number you are subtracting from negative to positive, and then change the operation from subtraction to addition.

Using this technique allows you to turn any complex-looking expression involving subtraction of negatives into a simpler addition problem.
Integer Operations
Working with integers involves understanding how numbers interact through operations like addition and subtraction. These operations follow specific rules that make calculations predictable and reliable.

Let's dive into how these operations work:
  • Addition: When you add two positive integers or two negative integers, you get a larger positive or a larger negative integer respectively. For example, \(3 + 5 = 8\) and \(-3 + (-5) = -8\).
  • Subtraction: When subtracting a smaller integer from a larger one, you simply subtract as you would with whole numbers. When the opposite is true, the result is negative. For instance, \(5 - 3 = 2\) and \(3 - 5 = -2\).

Remember that when you are operating with a positive and a negative integer, think in terms of adding the positive to the negative. This helps in resolving scenarios where subtraction from a negative or subtracting a negative is involved, just like turning \(-5 - (-3)\) into \(-5 + 3\).
Absolute Value in Addition
Absolute value is the distance a number is from zero on a number line, and it's always positive. Understanding this concept can greatly simplify adding integers. For two numbers with different signs (one positive, one negative), adding them involves combining their absolute values.

Here鈥檚 how it works:
  • Find the absolute values. The absolute value of \(-5\) is \(5\) and for \(3\), the absolute value remains \(3\).
  • Subtract the smaller absolute value from the larger absolute value. Thus, \(5 - 3 = 2\).
  • Apply the sign of the integer with the larger absolute value. Since \(-5\) has the greater absolute value, the sign from \(-5\) (negative) is used in the result: \(-2\).
This process ensures that you correctly resolve the problem \(-5 + 3\) and end up with the correct result, \(-2\). Keeping track of absolute values and signs is crucial, especially when dealing with a mix of positive and negative numbers.

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Most popular questions from this chapter

Find the value of each of the following expressions. $$ -8(4-12)+2 $$

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