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Chapter 1: Problem 7

Use a graphing calculator to check each exercise. $$ 13-17 $$

Short Answer

Expert verified
The result of \(13 - 17\) is \(-4\).

Step by step solution

01

Interpret the Problem

The problem requires us to find the result of a simple subtraction: \(13 - 17\). This operation will yield a negative result because the subtrahend (17) is larger than the minuend (13).
02

Perform the Subtraction

Calculate the difference between 13 and 17. First, visualize or calculate \(17 - 13 = 4\). Since 17 is greater than 13, the result of \(13 - 17\) is \(-4\).
03

Use a Graphing Calculator

Enter the expression \(13 - 17\) in a graphing calculator. Confirm that the calculator also computes the result to be \(-4\). This acts as a verification for your manual calculation.

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Key Concepts

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

Understanding Negative Numbers
Negative numbers represent values below zero, often seen in situations like temperatures below freezing or negative balances in bank accounts. When subtracting a larger number from a smaller one, we enter the realm of negative numbers.
An example is the subtraction operation given by \(13 - 17\). Here, the minuend (number being subtracted from) is smaller than the subtrahend (number being subtracted), resulting in a negative outcome. This is because \(17\), the subtrahend, is greater than \(13\), leading to a deficit. Therefore, the result is \(-4\).
  • Negative numbers are indicated with a minus sign (\(-\)).
  • They are situated to the left on the number line, in contrast to positive numbers that lie on the right.
  • In our example, subtracting when the subtrahend is larger automatically shifts the result into the negative number zone.
Basics of Subtraction
Subtraction is a fundamental arithmetic operation that signifies taking away or finding the difference between numbers. It is not commutative, meaning \(a - b\) is not the same as \(b - a\). Careful attention to order is necessary.
When calculating \(13 - 17\), the operation reflects finding out how much smaller \(13\) is compared to \(17\). Here鈥檚 how you do it:
  • Find the difference of the numbers involved: \(17 - 13 = 4\).
  • Recognize that the subtraction order is reversed: \(13 - 17\) moves us from positive into negative territory.
  • This gives a final result of \(-4\), because \(13\) is \(4\) less than \(17\).
Manual Calculation Verification
To ensure accuracy in manual calculations, verify your work using tools like graphing calculators. These digital devices handle arithmetic operations reliably and swiftly.
Checking the subtraction \(13 - 17\) manually possibly leads to human errors. By inputting it into a graphing calculator, you gain confidence in your result:
  • Enter \(13 - 17\) directly into the calculator.
  • Observe the calculator output, which should read \(-4\).
  • The device's confirmation of your manual result highlights its precision.
This verification process not only reassures you but also teaches a good practice of double-checking calculations, paving the way for better mathematical proficiency.

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Most popular questions from this chapter

Simplify each expression. See Examples \(11,14,\) and \(15 .\) $$ \frac{1}{2}(10 x-2)-\frac{1}{6}(60 x-5 y) $$

Insert parentheses so that each expression simplifies to the given number. $$ 6-5 \cdot 2+2 ;-6 $$

Write each of the following as an algebraic expression. See Examples 12 and 13. The cost of \(x\) compact discs if each compact disc costs \(\$ 6.49\)

Use a calculator to approximate each square root. simplify the expression. Round answers to four decimal places. \(\sqrt{7.9}\)

Translating Write each phrase as an algebraic expression. Use the variable \(x\) to represent each unknown number. See Example 8 . Twice the sum of a number and three.
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