Problem 19 In Exercises $1-66,$ compute t... [FREE SOLUTION]

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Understanding Elementary Algebra with Geometry

Lewis Hirsch, Arthur Goodman

$Math Studyset 91影视 Explanations$ Math

6 Edition

Chapter 1: Problem 19

In Exercises $1-66,$ compute the value of each expression. $$12+(-16)$$

Short Answer

Expert verified

-4

Step by step solution

Understand the Problem

Identify the numbers and operations involved. In this expression, we have to add 12 and -16.

Add the Numbers

When adding a positive number and a negative number, subtract the smaller absolute value from the larger absolute value. Here, subtract the absolute value of 12 from the absolute value of 16: \[ 16 - 12 = 4 \text{.}\]

Determine the Sign

The result will have the sign of the number with the larger absolute value. Here, -16 has the larger absolute value, so the result is -4.

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Key Concepts

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

absolute value

When we talk about absolute value, we mean the distance of a number from zero on the number line. It's always a non-negative number. For example, the absolute value of both 5 and -5 is 5.

To find the absolute value of any number, simply look at how far that number is from zero without considering its sign.

In mathematical terms, it's represented as: $| x |$, where $| x |$ denotes the absolute value of $ x $.

So, in our example:

The absolute value of 12 is $| 12 | = 12$.
The absolute value of -16 is $| -16 | = 16$.

negative numbers

Negative numbers are the numbers that are less than zero, represented with a minus sign (-).

They are located to the left of zero on the number line. For example, -1, -2, -3, etc., are all negative numbers.

In the context of addition, when you add a negative number to a positive number, you are essentially subtracting.

For our example:

We add 12 (a positive number) and -16 (a negative number).
Since -16 is negative, we think about this problem as finding 16 - 12, which gives us 4.

sign determination

Determining the sign of the result is a crucial step when adding numbers with different signs.

The rule is: when you add a positive and a negative number, the result will take the sign of the number with the larger absolute value.

Let's break this down using our example of 12 + (-16):

The absolute value of 12 is 12.
The absolute value of -16 is 16.
Since 16 is greater than 12, we take the sign of -16, which is negative.
Thus, the result of 12 + (-16) is -4.

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91影视

In Exercises \(1-66,\) compute the value of each expression. $$12+(-16)$$

Short Answer

Step by step solution

Understand the Problem

Add the Numbers

Determine the Sign

Key Concepts

absolute value

negative numbers

sign determination

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