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Chapter 3: Problem 51

Rewrite the problem in a simpler form. $$ 18-(-12) $$

Short Answer

Expert verified
Question: Rewrite the given expression in a simpler form and find its value: \(18-(-12)\) Answer: 30

Step by step solution

01

Understand the given expression

The given expression is \(18-(-12)\). Notice that we have subtraction and a negative number. We need to rewrite this expression in a simpler form.
02

Apply the rule for subtracting negative numbers

When we subtract a negative number, it is the same as adding its absolute value. We can rewrite the given expression as: \(18 + 12\).
03

Perform the addition

Now, simply add the numbers \(18\) and \(12\). \(18+12=30\).
04

Write the final answer

The expression \(18-(-12)\) has been rewritten in a simpler form and the result is \(30\).

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Key Concepts

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

Elementary Algebra
Elementary algebra is the branch of mathematics that deals with the properties and manipulations of numbers, especially the solving of equations. It serves as a stepping stone to advanced mathematical concepts and operations.

In elementary algebra, you'll encounter expressions and equations that require you to combine different numbers and variables. Subtraction is one of the basic operations you'll often perform. When subtracting numbers, especially if they include negative numbers, it's crucial to understand the rules thoroughly to simplify expressions correctly.
Negative Numbers
Negative numbers are numbers with a value less than zero. They are represented with a minus (-) sign before them. Understanding negative numbers is essential in various mathematical contexts, including real-world situations like bank overdrafts or temperatures below freezing.

When you're dealing with negative numbers, it's important to know how to properly add and subtract them. A common misconception is that subtracting a negative number results in a lower value, while in fact, it increases the overall value, as seen in the exercise where subtracting a negative number is equivalent to adding its positive counterpart.
Addition of Integers
Integers include all whole numbers, both positive and negative, as well as zero. Adding integers is a fundamental concept in math, and it's governed by specific rules.

For example, when you add two positive numbers, the sum is always positive. When you add two negative numbers, the result is also negative. Things get a bit more interesting when you mix positive and negative numbers in addition. The general rule is to subtract the smaller absolute value from the larger absolute value and keep the sign of the number with the larger absolute value. However, subtracting a negative number, as shown in the exercise, simplifies to addition instead.
Absolute Value
The absolute value of a number is its distance from zero on the number line, regardless of the direction. Symbolically, it's represented with vertical bars around the number: for example, the absolute value of -5 is denoted as \(|-5|\) and equals 5.

The concept of absolute value is particularly useful when subtracting negative numbers, as demonstrated in the given exercise. By converting the subtraction of a negative number to the addition of its absolute value, we avoid confusion and simplify the calculation. This is because the absolute value represents a magnitude without considering direction, making it a critical component in solving algebraic expressions.

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Most popular questions from this chapter

For the following problems, convert the numbers from scientific notation to standard decimal form. One year is about \(3 \times 10^{7}\) seconds.

Find the value of each of the following expressions. $$ 3(4-6) $$

Perform the following operations. $$ \left(6 \times 10^{14}\right)\left(6 \times 10^{-10}\right) $$

Find the value of each of the following expressions. $$ -9(0-2)+4(8-9)+0(-3) $$

Convert the numbers used in the following problems to scientific notation. Mount Kilimanjaro is the highest mountain in Africa. It is 5890 meters high.
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