Problem 42 - Elementary Algebra

Question

Find the quotient of -54 and -3 .

Step-by-Step Solution

Answer

The quotient of -54 and -3 is 18.

Step 1: Understand the Problem

The problem asks us to find the quotient of two numbers: -54 and -3. The quotient refers to the result of a division operation.

Step 2: Set Up the Division

We need to divide -54 by -3. This can be written as \[-54 \div -3\] or as a fraction \[\frac{-54}{-3}\].

Step 3: Consider the Signs

When dividing two numbers with the same sign, the result is positive. Since both -54 and -3 are negative, the quotient will be positive.

Step 4: Perform the Division

Now divide the absolute values of the numbers, ignoring the signs: \[\frac{54}{3} = 18\]. Since the quotient is positive, the final answer is 18.

Key Concepts

Quotient

In mathematics, the term "quotient" refers to the result you get when you divide one number by another. It is an essential concept in understanding division. For example, dividing a total amount of 54 candies among 3 children would give each child a share of 18 candies. Here, 18 is the quotient. Similarly, the quotient of -54 and -3 is also 18. Remember, a division can be written in different forms such as \[-54 \div -3\] or as a fraction \[-54/-3\]. Both expressions represent the same division operation.
In many real-world problems, the quotient is vital to determine results over shared quantities or rates. Understanding how to find it is crucial for solving division exercises.

Negative Numbers

Negative numbers are numbers less than zero, and they are usually written with a minus sign. They represent values below zero, like temperatures in the winter. Negative numbers play an important role in arithmetic operations, including division.
When dividing negative numbers, you must pay close attention to the signs, as negative numbers can change the outcome of your operation significantly. For instance, dividing -54 by -3 involves understanding these numbers' signs, which leads to the next key concept: managing division with signs.

Division with Signs

Dividing numbers with signs can be tricky, but it's quite straightforward once you understand the rules. When dividing two numbers:

• If both numbers have the same sign, the quotient is positive.
• If the numbers have different signs, the quotient is negative.

For instance, when you divide -54 by -3, both numbers are negative, so their signs match. This means the quotient is positive, resulting in a final quotient of 18.
It's essential to manage division with signs correctly to ensure your calculations are accurate. Practicing different combinations of sign divisions can help you become more comfortable with this aspect of division.