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Chapter 1: Problem 36

Change the sign. (Find the opposite.) $$ 10 $$

Short Answer

Expert verified
-10

Step by step solution

01

Identify the number

The given number is 10.
02

Find the opposite sign

Changing the sign of a positive number means making it negative. Therefore, the opposite of 10 is -10.

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Key Concepts

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

opposite numbers
In mathematics, opposite numbers are two numbers that are the same distance away from zero, but on opposite sides of the number line.
For example, the opposite of 10 is -10 because they are both 10 units away from zero, one on the positive side and one on the negative side.
When you find the opposite of a number, you essentially change its sign:
  • If the number is positive, its opposite is negative.
  • If the number is negative, its opposite is positive.
The concept of opposite numbers is crucial in understanding integer operations. Learning about opposites helps grasp addition, subtraction, and solving equations that involve integers.
negative integers
Negative integers are numbers less than zero. They are written with a minus sign (-) in front of them.
For example, -1, -2, -3, and so on.
These numbers are found on the left side of a number line, starting from zero.
  • They represent values less than zero.
  • They are often used to signify debt, temperature below zero, or anything that decreases below a certain point.
In the context of the given exercise, when we change the sign of 10, we turn it into a negative integer: -10.
It's important to understand negative numbers to perform integer operations and solve various mathematical problems.
sign change
The sign change in mathematics is the process of changing a number from positive to negative, or from negative to positive.
This is also referred to as finding the 'opposite' of a number. When we change the sign of a number:
  • A positive number, like 10, becomes negative, turning into -10.
  • A negative number, like -5, becomes positive, turning into 5.
This process is essential in solving equations and understanding the behavior of integers.
For the exercise, the sign change of the number 10 is straightforward. By changing the sign of 10, you find its opposite, which is -10. This knowledge is fundamental for mastering more complex math topics, including algebra and beyond.

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Most popular questions from this chapter

Given that \(0.3 \overline{3}=\frac{1}{3}\) and \(0.6 \overline{6}=\frac{2}{3},\) express each of the following as a ratio of two integers. $$0.1 \overline{1}$$

Simplify. $$ 8 x-(6 x+7) $$

Use a commutative law to write an expression equivalent to \(a b+5\).

SYNTHESIS Write the sentence \(-|x| \neq-x\) in words. Explain why \(-|x|\) and \(-x\) are not equivalent.

List in order from least to greatest. $$\frac{4}{5}, \frac{4}{3}, \frac{4}{8}, \frac{4}{6}, \frac{4}{9}, \frac{4}{2},-\frac{4}{3}$$
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