Problem 17 - Elementary and Intermediate Algebra

Question

Find the opposite, or additive inverse. $$ 39 $$

Step-by-Step Solution

Answer

The additive inverse of 39 is -39.

Step 1: Understand the definition of additive inverse

The additive inverse of a number is what you add to a number to get zero. For any number, the additive inverse is its negative.

Step 2: Apply the definition

Given the number 39, to find its additive inverse, simply change the sign of the number.

Step 3: Calculate the result

Change the sign of 39 to get -39.

Step 4: Verify the result

To check, add 39 and -39 and see if the result is zero: 39 + (-39) = 0 Since the result is zero, the additive inverse is correct.

Key Concepts

opposite numbers

Opposite numbers are pairs of numbers that are the same distance from zero on the number line but in opposite directions. If you have a positive number, its opposite is negative, and vice versa. For example, the opposite of 39 is -39. Opposite numbers are also known as additive inverses because they add up to zero. When you add a number to its opposite, they cancel out each other perfectly. Understanding opposite numbers is important in basic arithmetic and helps solve many mathematical problems. Keep in mind:

• Opposite of a positive number is always negative.
• Opposite of a negative number is always positive.

negative numbers

Negative numbers are those less than zero. They are found to the left of zero on the number line. Negative numbers have a minus sign (-) before them. In arithmetic, they represent a deficiency or lack of something. For instance, if you owe someone 10 dollars, you can say you have -10 dollars. When dealing with negative numbers, remember these points:

• When you add a negative number to a positive number, you are essentially subtracting.
• Two negative numbers add up to a bigger negative number.
• Subtracting a negative number is the same as adding a positive one.

Mastering negative numbers is essential because they come up frequently in everyday math, from calculating debts to understanding temperatures below zero.

basic arithmetic

Basic arithmetic includes the simple operations of addition, subtraction, multiplication, and division. These operations are the foundation of all math problems. Without a strong grasp of basic arithmetic, more advanced concepts can be difficult to tackle. Key components of basic arithmetic include:

• Addition: Combining two or more numbers to get a sum.
• Subtraction: Finding out how much remains when one number is taken away from another.
• Multiplication: Finding the total when one number is taken multiple times.
• Division: Splitting a number into equal parts.

Understanding these operations is crucial. With practice, they become second nature, making it easier to solve complex problems. For instance, knowing that the additive inverse of a number cancels out the original number helps simplify equations. Remember, consistent practice is key to mastering basic arithmetic.