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Chapter 1: Problem 53

Find each difference. $$ 7-(-2) $$

Short Answer

Expert verified
7 - (-2) = 9

Step by step solution

01

Understand the Problem

The task asks to find the difference between 7 and -2. Specifically, subtract -2 from 7.
02

Rewrite the Expression

Rewrite the subtraction of a negative number as an addition. So, instead of 7 - (-2), write 7 + 2.
03

Perform the Addition

Add the numbers. Calculate 7 + 2.
04

State the Final Answer

The result of the addition is 9. Therefore, 7 - (-2) equals 9.

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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 a problem like 7 - (-2), it's essential to understand what subtracting a negative number means. Subtracting a negative number is the same as adding its absolute value. In other words, subtracting -2 is the same as adding 2.

This concept might seem tricky at first, but it's straightforward once you recognize the pattern:
  • If you have 7 - (-2), you can rewrite it as 7 + 2.
  • This makes the problem easier to solve.
By converting the subtraction of a negative number into an addition, you simplify the arithmetic.

Remember, subtracting a negative is essentially the same as saying, 'taking away a debt,' which results in an increase in value.
addition of integers
Addition of integers is one of the fundamental skills in arithmetic. In the case of our example problem, 7 + 2, we're dealing with positive integers.

When you add two numbers, the result is called the sum. For integers, follow these basic rules:
  • Add positive integers by simply summing their values.
  • When adding negative integers, add their absolute values and apply the negative sign to the result.
  • For mixed signs, find the difference between their absolute values and apply the sign of the number with the larger absolute value.
For our specific problem:

  • We add 7 and 2.
  • The sum is calculated as 9.
This confirms that 7 + 2 equals 9, providing a straightforward result of our rewritten expression.
basic arithmetic
Basic arithmetic includes operations like addition, subtraction, multiplication, and division. Mastering these operations is crucial for solving more complex math problems.

Let's break down some key points:
  • Addition: Combining two or more quantities.
  • Subtraction: Finding the difference between two quantities.
  • Multiplication: Repeated addition of the same number.
  • Division: Splitting a quantity into equal parts.

In our example, we initially had a subtraction problem, 7 - (-2). By understanding the rule of subtracting negative numbers, we converted it into an addition problem, 7 + 2.

These fundamental concepts ensure that you can approach and solve a wide range of mathematical problems confidently.

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Most popular questions from this chapter

Solve each problem. Nadine Blackwood enjoys playing Triominoes every Wednesday night. Last Wednesday, on four successive turns, her scores were \(-19,28,-5,\) and \(13 .\) What was her final score for the four turns?

Write each sentence as an equation, using \(x\) as the variable. Then find the solution from the set of integers between \(-12\) and \(12,\) inclusive. See Example \(9 .\) 7 less than a number is 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. \(18,12,0,-4,\) and \(-10\)

Perform each indicated operation. $$ |-5-6|+|9+2| $$

Find each difference. $$ -\frac{5}{6}-\frac{1}{2} $$
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