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Chapter 1: Problem 7

In Exercises \(1-72\), compute the value of each expression. $$-8-(-2)$$

Short Answer

Expert verified
-6

Step by step solution

01

Understand the expression

The given expression is \[\begin{equation}-8-(-2)\end{equation}\]. You need to subtract \[\begin{equation}-2\end{equation}\] from \[\begin{equation}-8\end{equation}\].
02

Apply subtraction of negative numbers

Remember that subtracting a negative number is the same as adding its positive. Therefore, \[\begin{equation}-8 - (-2)\end{equation}\] is the same as \[\begin{equation}-8 + 2\end{equation}\].
03

Perform the addition

Now, solve the expression \[\begin{equation}-8 + 2\end{equation}\]. Adding 2 to -8 results in -6.

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Key Concepts

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

subtraction of negative numbers
When you see a subtraction of a negative number, like in the expression \(-8-(-2)\), it might feel confusing at first. However, there's a simple rule: subtracting a negative number is the same as adding the positive version of that number. Think of it as removing a debt 鈥� if you take away something negative, it's like gaining something positive. So, \(-8 - (-2)\) turns into \(-8 + 2\).
integer arithmetic
Integer arithmetic refers to the math involving whole numbers, both positive and negative. In our example, we deal with the integers -8 and -2.
When performing arithmetic operations with integers, remember the following rules:
  • Adding two positive numbers always results in a positive number.
  • Adding two negative numbers results in a more negative number.
  • Subtracting a positive number from a negative number results in a more negative number.
  • Subtracting a negative number from a negative number is the same as adding the corresponding positive number.
In the case of our example, you subtract -2 from -8, which by our rule of subtracting negative numbers, turns into an addition of 2 to -8.
basic algebra operations
Basic algebra operations include addition, subtraction, multiplication, and division. Understanding these can simplify expressions and help in solving algebraic problems.
When dealing with basic algebra operations:
  • Addition is straightforward: combine the values.
  • Subtraction involves taking one value away from another.
  • Multiplication increases the value by repeated addition.
  • Division splits the value into equal parts.
In algebra, these operations can be performed with both positive and negative numbers. For example, in \(-8-(-2)\), by converting the double negative into a positive, we simplify it to \(-8 + 2\). Performing the addition next, \(-8 + 2 = -6\). So, the solution to the expression is \(-6\).

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Most popular questions from this chapter

Graph the given set on a number line. \(\\{a | a \text { is a natural number less than } 12 \text { and not divisible by } 3\\}\)

In Exercises \(1-72\), compute the value of each expression. $$-561-412-(-678)$$

Consider the following statements. If the statement is true, explain why. If the statement is false, explain why and/or give an example illustrating why. (a) Every rational number is an integer. (b) Every integer is a rational number. (c) \(-15\) is greater than \(-10\) (d) The absolute value of \(-15\) is greater than the absolute value of \(-10 .\) (e) A rational number must be positive. (f) An integer must be positive. (g) Every real number is a rational number. (h) Every rational number is a real number.

In Exercises \(73-84\), evaluate the given expression. $$7-3 \cdot 5-1$$

We know that multiplication means repeated addition. That is, 4 times 3 means add 3 four times. In view of this and the rule for adding negative integers, what should 4 times \(-3\) be equal to?
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