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Chapter 0: Problem 27

Find each sum or difference. $$ 8-(-13) $$

Short Answer

Expert verified
21

Step by step solution

01

Identify the Operation

Determine if you need to find a sum or a difference. In this case, you need to find the difference as indicated by the minus sign.
02

Understand the Subtraction of a Negative

Recognize that subtracting a negative number is equivalent to adding the absolute value of that number. This means that: subtracting -13 is the same as adding +13.
03

Perform the Calculation

Convert the expression: \(8 - (-13)\) becomes \(8 + 13\). Now, simply add the two values together: \(8 + 13 = 21\).

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Key Concepts

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

subtraction of negative numbers
Understanding the subtraction of negative numbers is fundamental in algebra. When you see a minus sign followed by a negative number, like in the expression 8 - (-13), it can be confusing at first. However, subtracting a negative number is the same as adding its absolute value.

Think of it as a double-negative scenario: the two negatives cancel each other out. So, -(-13) becomes +13. This is why we can rewrite the expression 8 - (-13) as 8 + 13.

It's helpful to remember this rule whenever you come across such operations.
absolute value
The absolute value of a number is its distance from zero on the number line, regardless of direction. In simpler terms, the absolute value is always a positive number.

For example, the absolute value of -13 is 13, written in mathematical notation as \(|-13| = 13\). This concept is crucial in algebra, particularly when dealing with subtraction of negative numbers.

In our exercise, recognizing that \(-\text{-}13\) essentially means adding the absolute value of -13 (which is +13) simplifies our calculations.
sum and difference
The sum and difference are basic mathematical operations. The sum is the result of adding two or more numbers, whereas the difference is the result of subtracting one number from another.

In our initial problem, we are dealing with a difference, but through our understanding of subtracting negative numbers, it converts into an addition problem.

This is why \(8 - (-13)\) converts to \(8 + 13\)\: the difference between two numbers can morph into the sum of one with the positive equivalent of the other, helping us easily find the solution of 21.

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Most popular questions from this chapter

The following problems provide more practice on operations with fractions and decimals. Perform the indicated operations. $$ -24.84 \div 6 $$

Choose the correct response. The additive inverse of \(a\) is A. \(-a\) B. 0 C. 1 D. \(\frac{1}{a}\).

Perform the indicated operations $$ -9-4-(-3)+6 $$

Sea level refers to the surface of the ocean. The depth of a body of water can be expressed as a negative number, representing average depth in feet below sea level. The altitude of a mountain can be expressed as a positive number, indicating its height in feet above sea level. The table gives selected depths and altitudes. $$ \begin{array}{|l|c|l|c|} \hline \text { Body of Water } & \begin{array}{c} \text { Average Depth in Feet } \\ \text { (as a negative number) } \end{array} & \text { Mountain } & \begin{array}{c} \text { Altitude in Feet } \\ \text { (as a positive number) } \end{array} \\ \hline \text { Pacific Ocean } & -14,040 & \text { Denali } & 20,310 \\ \text { South China Sea } & -4802 & \text { Point Success } & 14,164 \\ \text { Gulf of California } & -2375 & \text { Matlalcueyetl } & 14,636 \\ \text { Caribbean Sea } & -8448 & \text { Rainier } & 14,410 \\ \text { Indian Ocean } & -12,800 & \text { Steele } & 16,624 \\ \hline \end{array} $$ List the mountains in order, starting with the shortest and ending with the tallest.

Use an inequality symbol to write each statement. $$ -6 \text { is less than or equal to }-6 $$
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