Problem 431 - Prealgebra

Question

Translate and simplify. The quotient of 45 and 15

Step-by-Step Solution

Answer

The quotient is 3.

Step 1: Understand the Problem

The problem asks for the quotient of 45 and 15. Quotient means the result of division.

Step 2: Set Up the Division

Write the division operation: \[ \frac{45}{15} \]

Step 3: Perform the Division

Divide 45 by 15:\[ 45 \, \div \, 15 = 3 \]

Step 4: Simplify

The result of the division \( \frac{45}{15} \) simplifies to 3.

Key Concepts

Quotient

In mathematics, the term 'quotient' is used to describe the result of a division operation. When you divide one number by another, the outcome is called the quotient. For example, in the exercise you provided, the quotient of 45 and 15 is the result we get after performing the division of these two numbers.
In the given problem, the quotient is obtained as follows:

• The dividend (the number to be divided) is 45
• The divisor (the number by which we divide) is 15

When you perform the division \[ \frac{45}{15} \], the resulting quotient is 3.
This result means that 45 can be evenly divided by 15 exactly 3 times.

Simplification

Simplification in division is the process of reducing the expression to its simplest form. It involves performing the division operation and presenting the result in its lowest terms.
In our exercise:

• We start with the quotient \[\frac{45}{15}\]
• We then divide 45 by 15 to get 3
• The quotient 3 is already in its simplest form

Simplifying the division ensures our answer is as clear and concise as possible.
Always remember, simplification makes it easier to understand and work with the result. In some cases, you might need to simplify further, but here, since 3 is already a whole number, no further simplification is required.

Division Operation

The division operation is one of the basic arithmetic operations. It involves splitting a number into equal parts and determining how many times one number fits into another. Here's how it works:

• The number you want to divide is called the dividend
• The number you divide by is called the divisor
• The result of the division is the quotient

For example, in the problem provided, we divide 45 (the dividend) by 15 (the divisor). We set it up as follows: \[ \frac{45}{15} \].
Performing the division gives us the quotient, which is 3.
Division can be visualized in many contexts, such as spreading out items evenly or measuring segments. The key takeaway is that the division operation helps us determine how many times one number is contained within another.