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Chapter 2: Problem 43

Find the opposite. $$-12$$

Short Answer

Expert verified
The opposite of -12 is 12.

Step by step solution

01

Identify the given number

The number given in the exercise is \(-12\)
02

Understand what is meant by 'opposite'

The opposite of a number is the same distance from zero on the number line but in the opposite direction. For any number \( x \) , the opposite is \(-x \).
03

Find the opposite of -12

Apply the definition of the opposite for the number \(-12\) . The opposite is \( -(-12) = 12\) .

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Key Concepts

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

negative numbers
Understanding negative numbers is essential for solving many math problems, including finding opposites. Negative numbers are numbers less than zero, typically denoted with a minus sign (-) in front. For instance, -12 is a negative number. When visualizing, think of negative numbers as a financial debt or temperature below freezing. These numbers lie to the left of zero on a number line. Working with negative numbers often involves understanding how they relate to their positive counterparts, as well as how they behave in various arithmetic operations, like addition, subtraction, multiplication, and division.
number line
A number line is a visual way to represent numbers, both positive and negative. It's a horizontal line with numbers placed at equal intervals. Zero sits in the middle, acting as a separation point between positive and negative numbers. To find the opposite of a number using a number line, locate the number and then move the same distance from zero in the opposite direction. For example, to find the opposite of -12, you locate -12 on the number line and move 12 units to the right, landing on +12. This visualization helps understand the concept of opposites easily.
absolute value
The absolute value of a number is its distance from zero on the number line, regardless of direction. Denoted by two vertical bars around the number (|x|), it is always positive or zero. For example, the absolute value of -12 is written as |-12|, which equals 12. This concept is crucial when finding opposites because the opposite of a number is simply its absolute value, but in the opposing direction. So, if you start with -12, its opposite is 12, because both numbers are 12 units away from zero, but on opposite sides of the number line.

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Most popular questions from this chapter

Simplify using the order of operations. $$-7+(1-5)^{2} \div 4$$

For Exercises \(9-16,\) rewrite the subtraction problem as an equivalent addition problem. Then simplify. \( \)12-(-8)=$$

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