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Chapter 1: Problem 15

Add or subtract as indicated. $$-1-(-19)$$

Short Answer

Expert verified
The simplified expression is \( -1 - (-19) = -1 + 19 = 18 \).

Step by step solution

01

Identify the negative number and rewrite the expression

We notice that we are subtracting the negative number -19. We can rewrite the expression as an addition problem involving its positive counterpart: \( -1 + 19\).
02

Add the two numbers

Now we have the expression: \( -1 + 19 \). Adding -1 and 19 gives us: \( -1 + 19 = 18 \) So, \( -1 - (-19) = 18 \).

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Key Concepts

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

Integer Operations
Integer operations are fundamental to understanding algebra and involve performing mathematical tasks using whole numbers, including both positive and negative numbers. Operations can include addition, subtraction, multiplication, and division. However, dealing with integers, especially when they're negative, can sometimes be confusing.

When working with integers:
  • Remember that integers are whole numbers and can be positive, negative, or zero.
  • Positioning on a number line: Numbers to the right are positive, and those to the left are negative.
  • The operation rules change for negative numbers. For instance, subtracting a negative number is the same as adding its positive counterpart.
Understanding these rules helps in avoiding common mistakes and making calculations more straightforward.
Addition and Subtraction
Addition and subtraction are closely related operations, and working with negative numbers can make these tasks slightly more complex.

  • When Adding: Two positive numbers or two negative numbers easily add together. For two positives, you just add their values. For two negatives, add their absolute values, and keep the negative sign.
  • When Subtracting: Subtracting a negative is a special case. It involves switching the sign of the number being subtracted, effectively turning the operation into addition. For example, subtracting \(-(-19)\) becomes simply adding \(+19\).
  • Always look for opportunities to simplify expressions by reorganizing them into more familiar forms. This approach can turn potentially complicated arithmetic into more straightforward operations.
Mastering these principles ensures accurate and efficient problem-solving.
Negative Numbers
Negative numbers are a unique kind of integer that represent values less than zero. They are extremely useful in various real-world contexts such as temperatures below freezing or elevations below sea level.

  • When visualizing negative numbers on a number line, they're found to the left of zero.
  • In operations, they follow specific rules: adding a negative number is akin to subtraction, while subtracting a negative number is like addition.
  • Beyond calculations, grasp how negative numbers interact with positive ones and other negatives to shape your critical thinking in mathematical situations.
Embracing a comprehensive understanding of negative numbers enhances your overall mathematical literacy and problem-solving abilities.

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