Problem 52 Find each difference. SEE EXAMPL... [FREE SOLUTION]

91影视

Beginning Algebra: A Guided Approach

Rosemary Karr, Marilyn Massey, R. David Gustafson

$Math Studyset 91影视 Explanations$ Math

10 Edition

Chapter 1: Problem 52

Find each difference. SEE EXAMPLE $5 .$ (OBJECTIVE 3 ) $-8-(-4)$

Short Answer

Expert verified

The difference is -4.

Step by step solution

Analyze the Problem

We are asked to find the difference between -8 and -4, which is written as $-8-(-4)$. The minus sign in front of the 4 indicates that we are subtracting a negative number.

Change Subtraction to Addition

When subtracting a negative number, we can convert the operation to addition. Hence, $-8-(-4)$ becomes $-8+4$. This is because subtracting a negative number is equivalent to adding a positive number.

Add Numbers

Now, simply add the numbers: $-8+4=-4$.

Validate the Result

A quick way to validate if the result is sensible, the absolute value of -8 is larger than the absolute value of 4, hence the resulting difference should be negative. With the result of -4, this condition checks out.

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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 seem tricky at first, but they're just numbers less than zero. You often see them when dealing with debts, temperatures below freezing, or even in certain scoring systems. Whenever dealing with negative numbers, imagine you're below ground level.
Rather than climbing upwards, you're moving downwards. For example,

$-8$ means 8 units below zero.
$-4$ signifies 4 units below zero.

These numbers behave differently than positive ones, particularly when you're adding or subtracting. In our example, the exercise asks us to subtract $-4$ from $-8$. When you subtract a negative, it's like flipping the direction 鈥� which we'll explore next.

Exploring Absolute Value

The absolute value of a number is its distance from zero on the number line, always expressed as a positive value. It doesn't care about direction; it only measures the size.
For instance,

The absolute value of $-8$ is written as $|-8|$ and is 8.
Similarly, the absolute value of $-4$ is $|-4|$, which equals 4.

Using absolute values can help gauge which number has a greater size, independent of their negative or positive status. In solving problems, comparing absolute values helps to understand why subtracting or adding yields a specific result. Here, since 8 is larger than 4, the result of an operation starting at $-8$ tends towards being negative.

Addition of Integers Unveiled

Adding integers involves combining their values, considering their signs. A helpful tip is that subtracting a negative is like adding a positive. This is because two minus signs interact, forming a plus.
In the problem:

We convert $-8 - (-4)$ into $-8 + 4$.

This transformation is key since adding 4 moves us up on the number line from $-8$, resulting in $-4$. Another way to think about addition with integers is using a number line, where negative adds movement to the left and positive to the right. For our calculation here, starting at $-8$ and adding 4 brings you closer to zero, landing at $-4$. Understanding these shifts between negative operations simplifies many arithmetic tasks.

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91影视

Find each difference. SEE EXAMPLE \(5 .\) (OBJECTIVE 3 ) \(-8-(-4)\)

Short Answer

Step by step solution

Analyze the Problem

Change Subtraction to Addition

Add Numbers

Validate the Result

Key Concepts

Understanding Negative Numbers

Exploring Absolute Value

Addition of Integers Unveiled

One App. One Place for Learning.

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