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Chapter 5: Problem 22

Find each sum. \(13+(-5)\)

Short Answer

Expert verified
The sum of \(13+(-5)\) is 8.

Step by step solution

01

Simplify the expression

We are asked to add 13 and -5. You should note that adding a negative number is equivalent to subtracting its absolute value. Hence, \(13 + (-5)\) can be rewritten as \(13 - 5\).
02

Perform the subtraction

Subtract 5 from 13, which equals 8.

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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 can sometimes be tricky, but they are just numbers less than zero. They are represented with a minus sign (-) before the number.
When you add a negative number, you're essentially subtracting. This is because adding a negative is like taking away the number. For example, when you see \(13 + (-5)\), you can think of it as \(13 - 5\).
Working with negative numbers is common, and understanding them can help with everything from simple arithmetic to solving algebra problems.
The Role of Absolute Value
Absolute value is a way of expressing the "distance" a number is from zero on a number line, without considering direction. It's always positive. For example, the absolute value of both -5 and 5 is 5, written as \(|-5| = 5\).
When you add a negative number, the absolute value helps you understand how much to subtract. If you see \(13 + (-5)\), you recognize that the absolute value of -5 is 5, so you subtract 5 from 13.
Understanding absolute values can simplify many math problems and make concepts like "negative numbers" easier to grasp.
Basics of Subtraction
Subtraction is one of the fundamental operations in mathematics. It means taking away one number from another. It's the opposite of addition.
For the expression \(13 + (-5)\), you perform subtraction by recognizing it as \(13 - 5\). Begin by aligning the numbers and subtracting digit by digit when necessary.
Subtracting 5 from 13 leaves you with 8. This subtraction step is crucial in solving many math problems where negative numbers are involved.
Simplification Techniques in Math
Simplification is about making expressions easier to work with. It's a valuable skill for solving math problems efficiently.
Consider the problem \(13 + (-5)\). By recognizing that adding -5 is the same as subtracting 5, you can rewrite this as a simpler expression: \(13 - 5\).
Simplification often involves identifying patterns or equivalences, combining like terms, and reworking complex problems into basic calculations. These techniques save time and minimize errors.

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Most popular questions from this chapter

Determine whether each sequence is arithmetic or geometric. Then find the next two terms. \(-7,-2,3,8, \ldots\)

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. A sequence that is not arithmetic must be geometric.

Find the indicated term for the geometric sequence with first term, \(a_{1}\), and common ratio, \(r\). Find \(a_{100}\), when \(a_{1}=50, r=1\).

Determine whether each sequence is arithmetic or geometric. Then find the next two terms. \(3, \frac{3}{2}, \frac{3}{4}, \frac{3}{8}, \ldots\)

Write the first six terms of the geometric sequence with the first term, \(a_{1}\), and common ratio, \(r\). \(a_{1}=-\frac{1}{16}, r=-4\)
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