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Chapter 1: Problem 41

Add. Do not use the number line except as a check. \(85+(-65)\)

Short Answer

Expert verified
The result is 20.

Step by step solution

01

- Identify the Numbers

Identify the numbers in the exercise. Here, the numbers are 85 and -65.
02

- Understand the Operation

Recognize that the operation required is addition, but one of the numbers is negative (85 + (-65)).
03

- Apply the Addition of a Negative Number

When adding a negative number, it is the same as subtraction: 85 + (-65) becomes 85 - 65.
04

- Perform the Subtraction

Subtract 65 from 85. To do this, calculate: 85 - 65.
05

- Calculate the Result

After performing the subtraction, the result is 20 (85 - 65 = 20).

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Key Concepts

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

negative numbers
Negative numbers are numbers less than zero. They are typically indicated with a minus sign (-) in front of the number. For example, -65 is a negative number. Negative numbers are used in everyday life, such as in temperatures below freezing, negative bank balances, or elevations below sea level. When you see a negative number in arithmetic, it means you are dealing with values less than zero. Understanding how to handle negative numbers is essential for performing various mathematical operations accurately.
subtraction as addition
In mathematics, subtraction can be viewed as adding a negative number. This perspective can simplify many calculations. For instance, the problem 85 + (-65) can be thought of as 85 - 65. This means you can convert subtraction problems into addition problems by reinterpreting the negative sign. This method helps avoid confusion by consistently reinforcing that subtracting a number is equivalent to adding its negative. Whenever you encounter an expression like 85 + (-65), remember that it simplifies to subtraction. This is because adding a negative is the same as taking away that number from the positive number.
arithmetic operations
Arithmetic operations are basic mathematical calculations involving numbers. These include addition, subtraction, multiplication, and division. They are the foundation of all math skills. Here's a quick review:
  • Addition: Combining two or more numbers to get a sum. Example: 5 + 3 = 8.
  • Subtraction: Finding the difference between two numbers by taking one away from another. Example: 10 - 6 = 4.
  • Multiplication: Adding a number to itself a certain number of times. Example: 4 脳 3 = 12.
  • Division: Splitting a number into equal parts. Example: 9 梅 3 = 3.
Understanding how to perform these operations, including the nuances of adding and subtracting negative numbers, is crucial for solving mathematical problems effectively. They are used in everyday tasks and advanced mathematical concepts, forming the cornerstone of mathematics.

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