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Chapter 1: Problem 9

Subtract. \(-26-(-18)\)

Short Answer

Expert verified
The result of \(-26 - (-18)\) is \(-8\).

Step by step solution

01

Identify the expression

The expression to solve is \(-26 - (-18)\). We need to perform this subtraction.
02

Understand negative subtraction

When subtracting a negative number, it is equivalent to adding the positive of that number. For example, \(-a - (-b) = -a + b\). In this case, \(-26 - (-18)\) becomes \(-26 + 18\).
03

Perform the addition

Now we solve \(-26 + 18\). To do this, consider it as a comparison between negative and positive values: - Start at -26 and move 18 steps towards the positive on the number line.Ultimately, the calculation will be:- Find the difference between absolute values: \(26 - 18 = 8\).- The result takes the sign of the originally larger absolute value (26), which is negative.
04

Write the result

The result of the calculation \(-26 + 18\) is \(-8\), since the result of subtracting 18 from 26 (when seen as movement on the number line) keeps us in the negative zone.

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Key Concepts

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

Negative Numbers
Negative numbers are numbers less than zero, represented with a minus sign (e.g., -5, -26). They are the opposite of positive numbers and can be visualized on a number line to the left of zero. Negative numbers become essential when dealing with real-world contexts, such as temperatures below freezing or depths below sea level.
  • In arithmetic operations, handling negative numbers requires careful attention, especially in subtraction.
  • Subtracting a negative number can initially seem confusing but is straightforward once you understand it changes to addition.
For example, subtracting -18 from -26 can be translated to adding the opposite of -18, which is 18, i.e., \[-26 - (-18) = -26 + 18\]. This transformation is pivotal in easing the complexity from subtraction into a more familiar addition operation.
Absolute Value
The absolute value of a number refers to its distance from zero on a number line, regardless of direction. This concept is crucial when comparing magnitudes of numbers without considering their signs.
  • For instance, the absolute value of -26 is 26, and the absolute value of 18 is 18.
  • It transforms a negative number into its positive counterpart.
This property is particularly useful in our original exercise where we observe the difference between the absolute values. To calculate \(-26 + 18\), find:
  • The absolute value of -26: 26
  • The absolute value of 18: 18
  • Subtract these values: \(26 - 18 = 8\)
The actual result takes the sign of the number with the larger absolute value, resulting in \(-8\). Understanding absolute value helps simplify operations with negative numbers by temporarily ignoring their sign.
Number Line
A number line is a straight line with numbers placed at intervals along its length, which visually represents real numbers, including negative numbers and zero. It's a useful tool for visualizing operations like addition and subtraction.
  • Negative numbers are plotted on the left side of zero, while positive numbers are on the right.
  • Each position on the number line corresponds to a real number.
When subtracting as in \(-26 - (-18)\), thinking about moving along a number line can clarify the operation. Starting at -26, you move 18 steps to the right (since subtracting a negative is the same as adding).- This movement results in a position of -8 on the number line.Using a number line can be particularly helpful for students to visually comprehend how integers interact in addition and subtraction operations.

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Most popular questions from this chapter

Evaluate each expression when \(x=-5, y=4,\) and \(t=10\). \(\frac{|5 y-x|}{6 t}\)

Translate each phrase to an expression and simplify. Find the difference between -6 and -1 .

Each calculation below is incorrect. Find the error and correct it. $$ 9-(-7) \stackrel{?}{=} 2 $$

Simplify each expression. \(3^{3}-8 \cdot 9\)

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