Question

What is the simplified form of the opposite of the opposite of 12 ? A. \(-(-12)\) B. 12 C. \(\frac{1}{12}\) D. \(-\frac{1}{12}\)

Short answer

12

Step-by-step solution

Identify the Opposites

The problem asks for the simplified form of the opposite of the opposite of 12. Start by identifying the first opposite of 12.

Determine the First Opposite

The opposite of 12 is -12.

Determine the Second Opposite

Now, find the opposite of -12. The opposite of -12 is 12.

Simplify the Expression

Since the opposite of -12 is 12, the simplified form of the opposite of the opposite of 12 is 12.

Conclusion

Therefore, 12 is the simplified form of the opposite of the opposite of 12.

Key concepts

opposite numbers

When we talk about opposite numbers, we're referring to numbers that are the same distance from zero on a number line, but in opposite directions. For example, the opposite of 5 is -5 because they are both 5 units from zero, just on different sides. The same goes for larger numbers like 12. The opposite of 12 is -12. This concept is crucial for many math problems, especially those that involve simplifying expressions and integer operations.

integer operations

Integer operations are basic math operations involving whole numbers. These operations include addition, subtraction, multiplication, and division. Understanding how to work with integers, both positive and negative, is essential for solving many types of math problems. For example, when we perform the operation of finding the opposite of a number, we're essentially 'flipping' it across zero. So the opposite of 12 is -12, and the opposite of -12 is back to 12. Remembering these rules helps in simplifying expressions and solving equations efficiently.

simplification

Simplification in math means making an expression easier to understand or work with. This can involve reducing fractions, combining like terms, or, as in our problem, finding opposites. To simplify the expression 'the opposite of the opposite of 12,' we identify each opposite step-by-step. The opposite of 12 is -12, and the opposite of -12 is 12. Hence, the expression simplifies to 12. Simplification helps to make math problems more straightforward and less confusing.