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Chapter 1: Problem 70

Subtract. $$ 1-9 $$

Short Answer

Expert verified
-8

Step by step solution

01

Understand the problem

The exercise asks to subtract the number 9 from the number 1. This is a basic arithmetic operation of subtraction.
02

Set up the subtraction

Write the numbers in a format that clearly shows the subtraction operation: \(1 - 9\)
03

Perform the subtraction

Subtract 9 from 1. Since subtracting a larger number from a smaller number results in a negative number, the result will be negative. \(1 - 9 = -8\)
04

Verify the result

Double-check the subtraction by adding the result to the smaller number to see if it equals the larger number. \(-8 + 9 = 1\) The initial subtraction was performed correctly.

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Key Concepts

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

Subtraction
The concept of subtraction is one of the basic arithmetic operations. It allows you to find the difference between two numbers by taking one number away from the other. When we subtract, we often use the minus sign (-). In the example provided (1 - 9), we take 9 away from 1. Here's a simple approach to understand subtraction:
  • Identify the number you start with (the minuend)
  • Identify the number you are taking away (the subtrahend)
  • Subtract the subtrahend from the minuend
With these steps, subtraction can always be straightforward and easy to handle.
Negative Numbers
Negative numbers represent values less than zero. They are essential for understanding subtraction when the result is less than zero. In our given exercise (1 - 9), subtracting a larger number (9) from a smaller number (1) results in a negative number.

Negative numbers are usually represented with a minus sign (-) before the number, like this: -8. This means 8 less than 0. Understanding negative numbers can be further broken down:
  • Recognize that negative numbers are to the left of zero on a number line
  • Negative numbers decrease in value as you move left
  • Adding a negative number is the same as subtracting
Being comfortable with negative numbers is essential in many areas of mathematics, including algebra and calculus.
Verification of Results
Verification of results is an important step in any calculation. It ensures that the answer is correct, especially in subtraction where common mistakes can occur. In our exercise (1 - 9 = -8), we can verify the result by adding the difference back to the subtrahend:
  • The result of the subtraction is -8
  • We add -8 back to 9 to see if we get 1
  • -8 + 9 = 1, confirming our result
Using verification techniques like this helps build confidence in mathematical calculations and ensures accuracy in your work.

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Most popular questions from this chapter

To the student and the instructor: Writing exercises, denoted by \([\%,\) are meant to be answered using sentences. Because answers to many writing exercises will vary, solutions are not listed at the back of the book. Charlie insists that \(15-4+1 \div 2 \cdot 3\) is \(2 .\) What error is he making?

Find an equivalent expression by factoring. $$ 6 y-9 x-3 w $$

Write an equivalent expression without negative exponents and, if possible, simplify. $$ 9 x^{-4} $$

Find the opposite, or additive inverse. $$ 2.37 $$

Classify each statement as either true or false. The following sets are used: \(\mathrm{N}=\) the set of natural numbers; \(W=\) the set of whole numbers; \(\mathbb{Z}=\) the set of integers; \(\mathbb{C}=\) the set of rational numbers; \(\mathrm{H}=\) the set of irrational numbers; \(\mathrm{R}=\) the set of real numbers. $$ 196 \in \mathbb{N} $$
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