Problem 25 - Prealgebra

Question

Subtract \(-3\) from the quotient of 27 and 9.

Step-by-Step Solution

Answer

The result of subtracting -3 from the quotient is 6.

Step 1: Calculate the Quotient

The first step is to find the quotient when 27 is divided by 9. The quotient can be calculated using the formula: \( \text{Quotient} = \frac{\text{Dividend}}{\text{Divisor}} \). Here, the dividend is 27 and the divisor is 9, hence \( \text{Quotient} = \frac{27}{9} = 3 \).

Step 2: Subtract -3 from the Quotient

Now that we have the quotient as 3, the next step is to subtract -3 from this quotient. Subtraction of a negative number is equivalent to adding the absolute value of that number. Therefore, \( 3 - (-3) = 3 + 3 = 6 \).

Key Concepts

Understanding the Quotient

In mathematics, a quotient is the result you get when you divide one number by another. When we say 'divide,' we mean how many times a number (called the divisor) can fit into another number (called the dividend).
For example, consider the operation 27 divided by 9. Here, 27 is the dividend, and 9 is the divisor.

• If you divide 27 by 9, you get 3, meaning 9 fits into 27 exactly 3 times.
• Thus, 3 is the quotient of this division.

This process is essential in understanding divided quantities or splitting items into equal parts. When calculating quotients, once you've divided the two numbers, you can easily interpret the result as how many complete groups you can form with the divisor from the dividend.

Working with Negative Numbers

Negative numbers can be a bit tricky, but understanding them is important in math. A negative number is less than zero and is indicated by a minus sign (-) before the number.
When you're dealing with negative numbers in operations, remember these key tips:

• Adding a negative number is like subtracting its absolute value.
• Subtracting a negative number is like adding the absolute value of that number.
• This is because negative numbers essentially represent direction or subtraction itself.

So when you see something like subtracting -3 from a number, think of it as the opposite of subtraction, which is addition. It's like taking away a deficit, thus increasing the total.

Principles of Subtraction

Subtraction in mathematics is the operation of removing objects from a collection. To subtract means to take away a certain amount from another.
In simple terms, subtraction is finding the difference between two numbers.

• It is a critical operation in arithmetic, as it allows for measuring change and calculating things like remaining amounts or differences.
• When you subtract a larger number from a smaller number, you get a negative result, and when you subtract a negative number, it's similar to adding its positive counterpart.

For example, in subtracting -3 from the quotient 3, instead of a decrease, you actually increase the value, resulting in 6. Understanding this helps in managing values efficiently in both everyday and mathematical contexts.