Problem 18 Find the sum of the given intege... [FREE SOLUTION]

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Prealgebra

David Arnold

$Math Studyset 91影视 Explanations$ Math

2020 Edition

Chapter 2: Problem 18

Find the sum of the given integers. $-1+(-7)$

Short Answer

Expert verified

The sum is -8.

Step by step solution

Identify the Integers

In this exercise, we are asked to find the sum of the integers -1 and -7. We will start by writing down both integers: -1 and -7.

Set Up the Addition

Since we're dealing with an addition task, we're summing the integers: -1 and -7. This can be expressed as: \[-1 + (-7)\]

Add the Integers

When adding integers, if the signs are the same, add their absolute values and give the result the common sign. Here, both integers are negative. Add the absolute values: \[ |{-1}| + |{-7}| = 1 + 7 = 8 \] Since both original numbers are negative, the result is also negative. Thus, \[-1 + (-7) = -8\]

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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 be a bit challenging at first but are crucial for grasping many math concepts. Simply put, a negative number is a number less than zero, found on the left side of the number line. When dealing with negative numbers:

Think of them as using a measure of worth below zero; like owing money.
Each negative number is a reflection of a positive one but in the opposite direction.
They have a "-" sign in front of them, such as -1, -7, etc.

You could consider negative numbers as taking away from something. When you see an equation involving several negative numbers like $-1 + (-7)$, it means combining two values that are both below zero. This results in a number that is even more negative.

Exploring Absolute Value

Absolute value is a measure of how far a number is from zero on the number line, regardless of direction. It tells us the size or magnitude of a number, but not the direction.

The absolute value of any number, whether positive or negative, is always positive.
For example, both $|-1|$ and $|1|$ equal 1. Essentially, you are looking at how far that number is away from zero.

When adding numbers, especially negative ones, understanding absolute values can simplify things. In this case, combining $-1$ and $-7$ requires recognizing that their absolute values $|-1| = 1$ and $|-7| = 7$ sum up to $1 + 7 = 8$. Knowing how absolute value works can help break down complex integer problems into smaller, more manageable pieces.

Calculating the Sum of Integers

The sum of integers involves combining numbers to get a total. Adding integers might seem straightforward, but it becomes a bit different with positive and negative numbers.

When integers share the same sign, you simply add their absolute values and keep the common sign.
When they have different signs, subtract the smaller absolute value from the larger and you take the sign from the bigger number.

Consider $-1 + (-7)$ as an example, both integers are negative. We add their absolute values, getting 8 from $1 + 7$ and then apply the negative sign. Thus, the sum of -1 and -7 results in -8. Keeping these rules in mind helps in consistently getting the correct sum.

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91影视

Find the sum of the given integers. \(-1+(-7)\)

Short Answer

Step by step solution

Identify the Integers

Set Up the Addition

Add the Integers

Key Concepts

Understanding Negative Numbers

Exploring Absolute Value

Calculating the Sum of Integers

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