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Chapter 1: Problem 3

Use a graphing calculator to check each exercise. $$ -14+(-10) $$

Short Answer

Expert verified
-14 + (-10) is -24.

Step by step solution

01

Understand the operation

We are asked to add two negative numbers: -14 and -10.
02

Add Negative Numbers

When adding two negative numbers, you simply add the absolute values together and keep the negative sign. So, we take the absolute values of -14 and -10, which are 14 and 10 respectively, and add them: 14 + 10 = 24.
03

Apply Negative Sign

Since both numbers were negative, apply the negative sign to the result obtained in the previous step. Thus, the result is -24.
04

Verify with a Graphing Calculator

Enter -14 + (-10) into the graphing calculator. The calculator should output -24, confirming our manual calculation.

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Key Concepts

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

Using a Graphing Calculator
How can a graphing calculator assist us in verifying the addition of negative numbers? A graphing calculator can be a powerful tool in confirming your arithmetic calculations.
To use it for adding negative numbers, simply enter your expression:
  • Turn ON the graphing calculator.
  • Press the keys for '-14', the addition sign '+', the keys for '-10', and conclude with pressing the 'ENTER' or '=' key.
The display should show -24. This aligns with our manual calculation, providing an additional layer of assurance.
Working with Absolute Values
When adding negative numbers, the concept of absolute values can simplify the process. An absolute value represents the non-negative magnitude of a number, ignoring its sign.
This means:
  • The absolute value of -14 is 14.
  • The absolute value of -10 is 10.
Adding these gives you 24. Remember, when working with negative numbers, calculate the absolute values first and apply the negative sign to the sum afterward.
Verifying Calculations
Verification is an important part of ensuring your calculations are correct, especially when working with negative integers.
You can:
  • Perform a reverse calculation: Since we calculated -14 + (-10) to be -24, try subtracting -10 from -24. If you reach -14, it suggests your original calculation was accurate.
  • Recheck your calculations using different methods, like comparing with a graphing calculator.
  • Consult online calculators as an additional method of verification.
These strategies help reinforce the accuracy of your results.
Negative Integers
Understanding negative integers is crucial for efficient addition operations. Negative integers are numbers less than zero and are represented with a minus sign (-).
They behave differently in addition compared to positive integers:
  • Adding two negative integers results in a more negative number, as with -14 + (-10) yielding -24.
  • The further a negative integer from zero, the larger its absolute value.
Being comfortable with manipulating these can greatly enhance your math skills, especially in operations involving integers.

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Most popular questions from this chapter

Explain why \(-3^{2}\) and \((-3)^{2}\) simplify to different numbers.

In your own words, explain why every irrational number is a real number but not every real number is an irrational number.

Name the only real number that has no reciprocal, and explain why this is so.

Evaluate each expression when \(x=9\) and \(y=-2 .\) See Example 12 $$ \frac{y^{3}+\sqrt{x-5}}{|4 x-y|} $$

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