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Chapter 2: Problem 115

use a calculator to perform the indicated operations. $$(-413)(871)$$

Short Answer

Expert verified
-359,423

Step by step solution

01

- Understand the Operation

The operation given is the multiplication of two numbers: (-413) and 871.
02

- Enter the Numbers

Using the calculator, first enter the number 413.
03

- Apply the Negation

Next, apply the negation to 413 to get -413.
04

- Perform the Multiplication

Now, multiply -413 by 871. Input -413 and then the multiplication symbol (*) followed by 871.
05

- Get the Result

The calculator will display the result of the operation.The multiplication of (-413) and 871 is -359,423.

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Key Concepts

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

Calculator Use
Using a calculator can make complex calculations easy and quick. First, ensure your calculator is on and functioning properly. For this exercise, you are multiplying two numbers, one of which is negative. Start by entering the number 413. Then, apply the negation function (often a button labeled 卤). This will convert 413 to -413. Next, enter the multiplication symbol (*). Finally, key in 871 and press the equals (=) button. The calculator will then display the result. Calculators are designed to handle such operations efficiently, reducing the risk of manual errors.
Multiplication of Integers
Multiplying integers is a fundamental skill in prealgebra. An integer is any whole number, either positive or negative. Multiplication involves combining certain numbers repeatedly. For instance, when you multiply 3 by 4, you're essentially adding 3 four times (3 + 3 + 3 + 3 = 12). In the same manner, multiplying -413 by 871 means you are adding -413, 871 times. Always follow these steps:
  • Identify the numbers you need to multiply.
  • Use a calculator for large numbers to avoid manual mistakes.
  • Ensure the correct integer (positive or negative) is used in each step.
This helps to manage larger numbers and operations accurately.
Negative Numbers in Multiplication
Understanding how to handle negative numbers in multiplication is essential. The key rule is:
  • Positive 脳 Positive = Positive
  • Positive 脳 Negative = Negative
  • Negative 脳 Positive = Negative
  • Negative 脳 Negative = Positive
For example, multiplying -413 by 871: The rule is Negative 脳 Positive = Negative, resulting in -359,423. This is because you're combining a negative number with a positive one. If both numbers were negative, the result would be positive due to the rule Negative 脳 Negative = Positive. Remember these rules to simplify working with negative numbers.

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