Problem 69 - Fundamentals of Mathematics

Question

In the statement \(27 \div 3=9\), what name is given to the result \(9 ?\)

Step-by-Step Solution

Answer

The result, 9, is called the quotient.

Step 1: Understand the Division Process

The division statement given is \(27 \div 3 = 9\). In any division problem, there are three main components: the dividend, the divisor, and the quotient.

Step 2: Identify the Dividend and Divisor

Here, \(27\) is the number being divided, known as the dividend, and \(3\) is the number that divides the dividend, known as the divisor.

Step 3: Identify the Solution's Role

The result of the division operation, \(9\), is the quotient. In the expression \(27 \div 3 = 9\), \(9\) is the answer to the division and is specifically called the quotient.

Key Concepts

Quotient

In mathematics, the term "quotient" is used to represent the result of a division operation. When you divide one number by another, the quotient is the number you get as the answer. Think of it as the number of times the divisor fits into the dividend. For example, in the equation \(27 \div 3 = 9\), the number \(9\) is the quotient. It shows how many times \(3\) goes into \(27\) exactly, which is nine times.Whenever you're solving a division problem:

• The quotient tells you the final answer.
• Pay close attention to the role it plays in concluding the arithmetic operation.
• Ensure that it accurately reflects the division performed.

Remember that the quotient can be a whole number or a fraction, depending on whether the dividend is completely divisible by the divisor.

Dividend

The dividend is the number you want to divide up in the division process. It's the initial amount you start with before carrying out the division. For example, in the expression \(27 \div 3 = 9\), \(27\) is the dividend.Some important aspects to remember about the dividend:

• It can be any real number, positive, negative, or even zero.
• The size of the dividend relative to the divisor will affect the size of the quotient.
• In a word problem, it represents the total quantity you're dealing with.

Understanding the role of the dividend is crucial as it helps set up the basis for the division operation to get to your quotient.

Divisor

In the division equation, the divisor is the number that divides the dividend. It determines how the dividend is distributed or split. In simple terms, it is the number you are dividing by. Considering \(27 \div 3 = 9\), the number \(3\) is the divisor.A few key facts about the divisor:

• The divisor can never be zero, as division by zero is undefined in mathematics.
• The magnitude of the divisor affects how large or small the quotient will be. A large divisor results in a smaller quotient.
• Just like the dividend, the divisor can also be positive or negative, influencing the sign of the quotient.

When solving division problems, keeping track of the divisor is important to ensure accurate results and interpretations.