Problem 36 - Beginning and Intermediate Algebra

Question

Perform the operation. See Example 3. Subtract 17 from 1

Step-by-Step Solution

Answer

The result is -16.

Step 1: Understand the Problem

In this exercise, you are asked to subtract two numbers: 17 from 1. This means you are subtracting 17 from 1, represented as \( 1 - 17 \).

Step 2: Set Up the Subtraction Equation

Write down the equation based on the problem statement: \( 1 - 17 \). This sets the stage for performing the subtraction operation.

Step 3: Perform the Subtraction

To subtract 17 from 1, you calculate \( 1 - 17 \). Since 1 is smaller than 17, the result will be a negative number. You perform the operation as follows: 1 minus 17 gives you \(-16\).

Step 4: Conclude the Answer

The result of the subtraction \( 1 - 17 \) is \(-16\). This means when you subtract 17 from 1, the answer is \(-16\).

Key Concepts

Understanding Negative Numbers

Negative numbers are numbers that are less than zero. They are represented with a minus sign (−) in front of the number. Understanding them is crucial because they frequently occur in real-world situations and algebraic calculations.
For instance:

• Temperatures below freezing are negative.
• An account balance below zero reflects negative values.

In mathematics, when you subtract a larger number from a smaller number, the result is negative. This is what happens in the exercise where you calculate \(1 - 17\). The outcome, \(-16\), is negative, indicating a position on the number line below zero.
By becoming comfortable with negative numbers, you can better understand various mathematical operations and real-world applications.

Mastering Step-by-Step Problem Solving

Tackling math problems often requires a methodical approach, where breaking down a problem into smaller steps can make it manageable. This approach ensures that you fully understand each part of the problem and the operations performed. Here's why it's helpful:

• It clarifies your thought process, reducing errors.
• Step-by-step methods highlight areas that need more explanation.
• They offer a clear path from problem to solution.

In our exercise, the problem-solving process involved:

• Understanding what subtraction is being asked for.
• Setting up the correct subtraction equation.
• Performing the operation using rules for negative numbers.
• Concluding by confirming the solution's correctness.

Following these steps consistently boosts confidence and skill, making complex problems seem simpler over time.

Effective Equation Setup

Setting up a correct equation is a pivotal step in solving mathematical problems. Without accurately setting up what operation needs to be solved, you could work out a wrong problem or arrive at an incorrect solution.
For subtraction, especially involving negative numbers, a well-structured equation is crucial to guide further steps.
To set up an equation correctly:

• Interpret the problem statement clearly. This involves recognizing the operation (e.g., subtraction) and the numbers involved.
• Translate the statement into a mathematical expression. For example, 'Subtract 17 from 1' becomes \(1 - 17\).
• Write it down plainly to avoid any confusion in your calculations.

This logical structuring forms the foundation upon which accurate calculations and understanding are built. Proper equation setup is your roadmap to solving the problem accurately and efficiently.