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Chapter 1: Problem 56

Find each difference. $$ -7-(-5) $$

Short Answer

Expert verified
-2

Step by step solution

01

Understand the Problem

The problem requires finding the difference between -7 and -5. In mathematical terms, it asks for the result of subtracting -5 from -7.
02

Apply the Rule for Subtracting a Negative Number

When subtracting a negative number, the two negatives cancel out and turn into a positive. Therefore, -7 - (-5) is equivalent to -7 + 5.
03

Perform the Addition

Add the numbers: -7 + 5. Start from -7 on the number line and move 5 steps to the right, which results in -2.

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Key Concepts

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

Difference in Algebra
Finding the difference between two numbers is a common algebraic operation. In this exercise, we aim to find the result of \(-7 - (-5)\).

The term 'difference' in algebra simply means performing a subtraction operation. To determine the difference, you need to know how to manipulate negative numbers correctly.

The key rule to remember is: **Subtracting a negative number is the same as adding its positive counterpart**. Therefore, in our example, we convert \(-7 - (-5)\) into \(-7 + 5\). By understanding and applying this rule, you can simplify the expression and make the calculation straightforward.
Number Line Usage
A number line is an excellent tool to visualize arithmetic operations involving integers. Using a number line, you can easily see how and where to move.

When dealing with \(-7 + 5\):
  • Start at -7 on the number line.
  • Since you are adding a positive 5, move 5 steps to the right.

If you follow these steps, you will land on -2.

This visual method can make the process of subtracting negative numbers simpler and more intuitive. It reinforces the idea that moving to the right on a number line represents adding, and moving to the left represents subtracting.
Integer Arithmetic
Integer arithmetic involves working with whole numbers, both positive and negative.
Subtraction of integers, especially with negative numbers, can often be tricky.

Here's what you need to know:
  • When subtracting a positive number, move to the left on the number line.
  • When subtracting a negative number, move to the right on the number line because two negatives make a positive.

To compute \(-7 - (-5)\), recognize that subtracting -5 is the same as adding +5.

Therefore, the calculation becomes \(-7 + 5\), and the result is -2.

Integer arithmetic rules like this are crucial for solving more complex algebraic expressions and real-world mathematical problems.

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Most popular questions from this chapter

Perform each indicated operation. $$ -3+[(-5-8)-(-6+2)] $$

Solve each problem. Marcial Echenique owes \(\$ 679.00\) on his Visa account. He returns three items costing \(\$ 36.89, \$ 29.40,\) and \(\$ 113.55\) and receives credit for these on the account. Next, he makes purchases of \(\$ 135.78\) and \(\$ 412.88\) and two purchases of \(\$ 20.00\) each. He makes a payment of \(\$ 400 .\) He then incurs a finance charge of \(\$ 24.57 .\) How much does he still owe?

Find each difference. $$ -4.4-8.6 $$

Perform each indicated operation. $$ -8-[(-4-1)+(9-2)] $$

To find the average (mean) of a group of numbers, we add the numbers and then divide the sum by the number of terms added. For example, to find the average of \(14,8,3,9,\) and \(1,\) we add them and then divide by 5. $$ \frac{14+8+3+9+1}{5}=\frac{35}{5}=7 \leftarrow \text { Average } $$ Find the average of each group of numbers. All even integers between \(-18\) and \(4,\) inclusive
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