Problem 50 - Introductory and Intermediate Algebra for College Students 4th

Question

In Exercises \(47-76\), perform the indicated division or state that the expression is undefined. $$\frac{-60}{6}$$

Step-by-Step Solution

Answer

The solution to \(\frac{-60}{6}\) is -10.

Step 1: Identify Numbers

First, identify the numbers to be divided. Here, -60 is the dividend, which is the number to be divided, and 6 is the divisor - the number we are dividing by.

Step 2: Perform Division

Now perform the division by dividing the dividend by the divisor. Divide -60 by 6.

Step 3: Write down Result

After performing the division, write down the result. The result of the division is the quotient which in this case is -10.

Key Concepts

Division

In mathematics, division is one of the basic operations involving numbers. It is essentially the process of determining how many times a number—the divisor—can be subtracted from another number—the dividend.
For example, if there are 60 apples and you want to distribute them equally into groups of 6, division will help you find out how many apples will be in each group.

• You start with 60, the total number of apples. This is our dividend.
• The number 6, which represents the amount each group will contain, is our divisor.

By dividing, you are figuring out how many groups you can make. This process is simple but forms the backbone for many complex mathematical concepts.

Divisor

The divisor is the number by which you divide the dividend. It plays a crucial role in the division process.
To understand the divisor better, imagine that you have a long strip and you are cutting it into equal smaller strips.

• In the division expression \(\frac{-60}{6}\), 6 is the divisor.
• It tells us into how many equal parts we are breaking up the number -60.

A practical way of thinking about the divisor is that it acts like a measure or a guide, telling us the quantity per group when splitting something up into smaller parts.

Dividend

In any division process, the dividend is the number you want to divide up. It is the starting amount that you have.
For example, with \(\frac{-60}{6}\), -60 is our dividend. It represents the quantity that you are about to split using division.

• The dividend can be a whole number, a fraction, or even a negative number, like in our example.
• It is what you are breaking into parts or groups determined by the divisor.

This is the number that, when divided by the divisor, gives us the result or quotient.

Quotient

The quotient is the result of dividing one number by another. In a division equation, it represents how many times the divisor fits into the dividend.
Continuing with our example, when you divide -60 by 6, the quotient is -10.

• This means that when you break -60 into groups of 6, you will get exactly -10 groups.
• The quotient can be a positive number, a negative number, or even a fraction, depending on what the dividend and divisor are.

The quotient represents the final piece of information in division, providing the answer to how many times the divisor is contained within the dividend.