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Chapter 10: Problem 14

Add. Do not use the number line except as a check. $$ -15+15 $$

Short Answer

Expert verified
The sum of \(-15\) and \(15\) is zero.

Step by step solution

01

- Identify the Numbers

Identify the numbers involved in the addition problem: \(-15\) and \(15\).
02

- Recognize the Opposites

Recognize that \(-15\) and \(15\) are opposites. Opposite numbers are equidistant from zero but on different sides.
03

- Apply the Rule of Opposites

When you add a number to its opposite, the sum is always zero. Therefore, adding \(-15\) and \(15\) results in zero.
04

- Verify with Number Line (Check)

Check your result using a number line. Starting at \(-15\), moving 15 units to the right returns you to zero. This confirms that the sum is zero.

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Key Concepts

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

Opposite Numbers
In mathematics, every number has an opposite. Opposite numbers are those that are the same distance away from zero but in opposite directions on a number line.
For example, the opposite of 5 is -5, and the opposite of -7 is 7.
Key Points about Opposite Numbers:
  • They have the same value but different signs.
  • When added together, their sum is always zero.
  • On a number line, they are mirror images across zero.

Understanding opposite numbers helps in solving many addition problems quickly. For instance, adding \(-15\) and \(15\) results in \(0\) because these numbers are opposites.
Sum of Integers
Summing integers involves straightforward arithmetic, but recognizing patterns can make it even easier.
When opposite numbers are added, the result is always zero.
Example:
  • Take the integers \(-15\) and \(15\).
  • Since they are opposites, their sum is \(-15 + 15 = 0\).

Adding non-opposite integers requires considering both their signs and magnitudes. If the integers have the same sign, add their absolute values and keep the common sign.
If the integers have different signs, subtract the smaller absolute value from the larger one and keep the sign of the number with the larger absolute value.
Example:
  • \(-8 + 3 \) needs you to subtract 3 from 8 to get 5 and keep the sign of the bigger absolute value, giving \(-5\).
Practice and familiarize yourself with these rules to master integer addition.
Number Line
A number line is an essential tool in mathematics for visualizing numbers and operations on them. It extends infinitely in both directions with zero at the center.
Positive numbers are to the right of zero, and negative numbers are to the left.
How to Use a Number Line:
  • To add a positive number: move right from the starting point.
  • To add a negative number: move left from the starting point.
  • To check if numbers are opposites: see if they are equal distances from zero in opposite directions.
  • Use the number line to understand concepts of addition, subtraction, and the impact of opposites easily.
For example, if you start at \(-15\) and move 15 units right, you land on 0. This confirms that \(-15 + 15\) is indeed 0.
Using a number line can simplify and validate your calculations.

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Most popular questions from this chapter

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