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Chapter 3: Problem 5

Perform the subtractions. $$ -8-12 $$

Short Answer

Expert verified
Answer: $$ -20 $$

Step by step solution

01

Rewrite the subtraction as addition

When we have a subtraction of two negative numbers, we can rewrite the subtraction as the addition of one negative number and the positive value of the other number. In this case, the equation becomes: $$ -8 + ( -12) $$
02

Add the absolute values

Next, we need to add the absolute values of the two integers, which are 8 and 12. The sum of the absolute values is: $$ 8 + 12 = 20 $$
03

Assign the negative sign

Since both numbers in the original equation are negative, the final result will also be negative. We assign the negative sign to the summed absolute values: $$ -20 $$ The result of the subtraction $$ -8 - 12 $$ is $$ -20 $$.

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Key Concepts

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

Negative Numbers
Negative numbers can be a bit tricky, but they're really just numbers that are less than zero. We typically see them represented with a minus sign, like \(-3\) or \(-8\). These numbers are used to describe values below a defined point. For example, if you owe someone money, your balance might be a negative amount.

  • They are crucial in many real-world situations, like temperatures below freezing or elevations below sea level.
  • In mathematics, negative numbers help us express values that otherwise wouldn't be possible with just positive numbers.
Understanding how they interact with each other through operations like addition and subtraction is key to mastering algebra.
Absolute Value
Absolute value is a measure of a number's distance from zero on the number line, regardless of direction. It is always a positive number or zero.

To find the absolute value of any number, we look at the number without its sign:
  • The absolute value of \(-8\) is \(8\) because it is 8 units away from 0.
  • Similarly, the absolute value of \(12\) is \(12\), as it is also 12 units from 0.
It's an essential concept, especially when dealing with integers, because it provides a way to talk about size without worrying about direction. So whenever you see absolute values in math problems, focus on how far that number is from zero.
Integer Addition
Integer addition is simply the process of combining two whole numbers, which can include both positive and negative integers. In the context of subtracting \(-8 - 12\), subtraction can be rewritten as the addition of one number and the negative of the other, making the expression easier to handle as \(-8 + (-12)\).

When adding integers:
  • Combine the numbers like you would with positive numbers.
  • If both integers have the same sign (like \(-8\) and \(-12\)), add their absolute values and keep the common sign.
For instance, adding the absolute values, \(8 + 12\), gives \(20\), and since the original integers were negative, the result of the addition \(-8 + (-12)\) will also be \(-20\).

Understanding these steps makes operations with integers straightforward and provides clarity for more complex mathematical concepts.

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Most popular questions from this chapter

Find the value of each of the following expressions. $$ \frac{-3(4-2)+(-3)(-6)}{-4} $$

Find the value of each of the following expressions. $$ -2[-5(-10+11)-2(5-7)] $$

Convert the numbers used in the following problems to scientific notation. The average mass of a newborn American female is about 3360 grams.

Convert the numbers used in the following problems to scientific notation. The principal protein of muscle is myosin. Myosin has a mass of 0.00000000000000000103 gram.

For the following problems, convert the numbers from scientific notation to standard decimal form. A ribosome of \(\mathbf{E}\). coli has a mass of about \(4.7 \times 10^{-19}\) grams.
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