Problem 43 - Beginning and Intermediate Algebra

Question

Find each quotient. \(\frac{-8.8}{2.2}\)

Step-by-Step Solution

Answer

-4

Step 1: Understand the Problem

You need to find the quotient of \(-8.8\) divided by \(2.2\). Simply put, determine how many times \(2.2\) goes into \(-8.8\).

Step 2: Perform the Division

Divide the numerator \(-8.8\) by the denominator \(2.2\). Calculate \(-8.8 \div 2.2\).

Step 3: Simplify the Division

Perform the division to get \-4\, because \(-8.8 \div 2.2 = -4\).

Key Concepts

quotient

In mathematics, the term quotient is the result you get after dividing one number by another. When you look at the exercise \(\frac{-8.8}{2.2}\), you are essentially asked to find out the quotient of -8.8 divided by 2.2.
The process involves determining how many times 2.2 can 'fit' into -8.8. In our example, the quotient is -4 because when you divide -8.8 by 2.2 evenly, you get -4.

negative division

Negative division might seem tricky at first, but it's simply a division involving a negative number. When one of the numbers involved in a division is negative, the quotient will also be negative.
In our exercise, -8.8 is negative, while 2.2 is positive. So the quotient we calculated -4 is negative.
To make it simpler, remember:

• Negative ÷ Positive = Negative
• Positive ÷ Negative = Negative
• Negative ÷ Negative = Positive

These rules can help you quickly determine the sign of your quotient.

division steps

Understanding the steps in division helps make the process clearer. Let's break down the steps we followed to solve \(\frac{-8.8}{2.2}\):

• Step 1: Understand the Problem - We need to find how many times 2.2 goes into -8.8.
• Step 2: Perform the Division - Divide -8.8 by 2.2. You can think of –8.8 ÷ 2.2 as a simpler form of the problem.
• Step 3: Simplify the Division - We calculate that -8.8 divided by 2.2 equals -4.

By following these steps, you not only solve the problem but also understand how to approach similar problems in the future. Breaking down the process can help make division, even with negative numbers, much easier to handle.