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Chapter 3: Problem 448

In the following exercises, divide. $$ -120 \div(-6) $$

Short Answer

Expert verified
The result of \(-120 \div -6\) is 20.

Step by step solution

01

Identify the numbers

Recognize the two numbers involved in the division problem: - The dividend is \(-120\). - The divisor is \(-6\).
02

Simplify the signs

When dividing two negative numbers, the negatives cancel out, resulting in a positive number. Therefore, we can simplify the division of \(-120\) by \(-6\) as the division of positive numbers, \(120 \div 6\).
03

Perform the division

Divide 120 by 6: \[ 120 \div 6 = 20 \]

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Key Concepts

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

Division
When you think about division, it helps to picture it as splitting something into equal parts. For instance, if you divide 10 apples among 5 friends, each friend gets 2 apples. Mathematically, this looks like \(10 \div 5 = 2\).

The number you are dividing is called the dividend, and the number you are dividing by is called the divisor. The answer you get is called the quotient.

In our exercise, we are dividing \(-120\) by \(-6\). Here, \(-120\) is the dividend, and \(-6\) is the divisor. So, we are looking for the quotient of these two numbers.
Negative Numbers
Negative numbers are numbers less than zero. They are usually written with a minus sign in front of them, such as \(-5\) or \(-120\). They represent values below zero, like temperatures below freezing or levels underground.

When you work with negative numbers in operations such as division, it's important to understand how signs interact. Negative numbers add a layer of complexity to math problems. But don't worry, with practice, it will become second nature!
Simplifying Signs
One crucial step in dividing negative numbers involves simplifying the signs.

Here鈥檚 a key rule to remember:
  • If you divide a negative number by another negative number, the negatives cancel out, making the result positive. This is because a negative divided by a negative equals a positive, much like how a positive divided by a positive remains positive.


Using this rule, dividing \(-120\) by \(-6\) simplifies to dividing their absolute values, \(120 \div 6\), giving us 20.
Pre-Algebra
Pre-algebra is the foundation of all future math studies. It includes the basics of arithmetic, such as addition, subtraction, multiplication, and division, applied to both positive and negative numbers.

Understanding pre-algebra concepts ensures that you have a solid base for tackling more advanced topics in algebra and beyond. By mastering the division of negative numbers, you prepare yourself for more complex operations and equations that you will encounter in future math courses.

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