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Chapter 1: Problem 1

In Exercises \(1-66,\) compute the value of each expression. $$+6+(-8)$$

Short Answer

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Step by step solution

01

Identify the numbers

Identify the numbers involved in the expression. In this case, the numbers are +6 and -8.
02

Understand the operation

The expression involves the addition of a positive number (+6) and a negative number (-8).
03

Apply the rules for adding integers

When adding a positive number and a negative number, subtract the smaller absolute value from the larger absolute value. Keep the sign of the number with the larger absolute value.
04

Calculate the result

Subtract 6 from 8: \(-8 + 6 = -2)\). Since 8 is the larger absolute value and it is negative, the result will be negative.

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Key Concepts

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

Integer Operations
Working with integers can be simple once you grasp a few fundamental rules. Integers are whole numbers that can be positive, negative, or zero. Understanding the basic operations like addition, subtraction, multiplication, and division with integers is key to solving many math problems. Let's focus on addition. When adding two positive integers, you just add them like regular numbers. The same goes for adding two negative integers, but remember the result will also be negative. Things get slightly trickier when adding a positive and a negative integer. The key is to look at their absolute values, which we'll explain next.
Absolute Value
The absolute value of a number is its distance from zero on the number line, regardless of direction. Think of it as the number without its sign. For example, the absolute value of +6 is 6, and the absolute value of -8 is 8. Absolute values are important when working with integer operations, especially when you're adding a positive and a negative number. By comparing their absolute values, you can easily determine the resultant sign and magnitude of the answer.
Addition Rules
Adding integers involves a few straightforward rules:
  • When adding two positive integers, just add them together as usual.
  • When adding two negative integers, add their absolute values and keep the result negative.
  • When adding a positive and a negative integer, subtract the smaller absolute value from the larger one. The result takes the sign of the number with the larger absolute value.
For example, in the expression +6 + (-8), you first compare the absolute values of 6 and 8. Since 8 is larger, you'll subtract 6 from 8, giving you 2. Because 8's absolute value is larger and it comes with a negative sign, the final result is -2. These rules will help simplify processes and make computations much easier.

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Most popular questions from this chapter

In Exercises \(73-84\), evaluate the given expression. $$9-(5 \cdot 4-2)$$

Compute the given expression. Round off your answer to two decimal places where necessary. $$15.7-35(0.6)-4.6$$

Evaluate the given expression. Remember to follow the order of operations. $$30 \div(5 \cdot 2)$$

In Exercises \(73-84\), evaluate the given expression. $$|7-10|-(7-10)$$

Evaluate the given expression. Remember to follow the order of operations. $$12-4 \cdot 3+6$$
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