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Chapter 2: Problem 101

Perform the indicated operation. [ 1.2] $$ -12.9 \div(-3) $$

Short Answer

Expert verified
4.3

Step by step solution

01

- Identify the operation

The operation here is division. You need to divide -12.9 by -3.
02

- Understand the signs

When you divide two negative numbers, the result will be positive. This is because a negative divided by a negative gives a positive result.
03

- Perform the division

Now, perform the division of the absolute values: \[\begin{equation} \frac{12.9}{3} = 4.3.\text{Since both the numbers were negative, the result is positive.}\text{Thus, } -12.9 \frac{-3}=4.3 \end{equation}\]

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Key Concepts

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

Division
Division is one of the four basic operations in arithmetic. It is often introduced as the process of finding out how many times one number is contained within another. For example, in our original exercise, we are asked to divide -12.9 by -3. This can be represented as \(-12.9 \div (-3)\) or \(\frac{-12.9}{-3}\). When dividing, always identify which number is the dividend (the number being divided) and which is the divisor (the number you are dividing by). In our case, -12.9 is the dividend, and -3 is the divisor.
Negative Numbers
Negative numbers are numbers that are less than zero. They are commonly found in many real-world situations, such as in temperature, where -5 degrees is colder than 0 degrees. When working with negative numbers in mathematical operations like division, it's important to understand how the negative signs affect the outcome. In our example problem, both -12.9 and -3 are negative numbers. Understanding the rules for operations involving negative numbers helps in correctly solving problems.
Absolute Value
The absolute value of a number is its distance from zero on the number line, regardless of direction. It is always a positive number. For instance, the absolute value of both -3 and 3 is 3, because both are 3 units away from zero. To solve our division problem, \(-12.9 \div (-3)\), it is helpful to think about the absolute values of -12.9 and -3. First, divide the absolute values: \(\frac{12.9}{3} = 4.3\). Understanding absolute value simplifies the computation since you can temporarily ignore the signs of the numbers, making it easier to perform the division.
Positive Result
A key rule to remember when dividing numbers is that a negative divided by a negative yields a positive result. This is based on the principle that the product of two negative numbers is positive. In simpler terms, \( - \div - \) equals +. So, when we divide \(-12.9 \div (-3)\), we know the result should be positive. Using the absolute values from earlier, \(\frac{12.9}{3} = 4.3\), we get a positive result. Therefore, \(-12.9 \div (-3) = 4.3\).

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