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Chapter 1: Problem 45

Find each quotient. $$ \frac{-8.8}{2.2} $$

Short Answer

Expert verified
-4

Step by step solution

01

- Identify the numbers

Identify the numerator and the denominator of the fraction. Here, the numerator is -8.8 and the denominator is 2.2.
02

- Divide the numbers

Perform the division: \(\frac{-8.8}{2.2}\). To do this, divide -8.8 by 2.2.
03

- Calculate the result

Calculate the quotient of \(\frac{-8.8}{2.2}\). \(-8.8 \, \div \, 2.2 = -4\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Numerator
In a fraction, the numerator is the top number. It tells you how many parts of the whole you have. For instance, in the fraction \(\frac{-8.8}{2.2}\), \(-8.8\) is the numerator. It represents the part of the number we are focusing on and want to divide.

Here's a simple way to think about it: if you have 8.8 slices of pizza and you owe someone, that puts you in a negative state, just like negative numbers.

Recognizing the numerator in a problem is the first step in solving any fraction or decimal division.
Denominator
The denominator is the bottom number in a fraction. It shows the total number of equal parts the whole is divided into. In \(\frac{-8.8}{2.2}\), the denominator is 2.2. This means we want to see how many times 2.2 fits into -8.8.

Think of the denominator as the 'divider' in any division operation. It helps us understand the scale or size of each part in comparison to the whole. Realizing the denominator is crucial because it tells us 'what' we're dividing by.
Quotient
When you perform division, the result you get is called the quotient. In our problem, after dividing \(-8.8 \div 2.2\), the quotient is -4. This means -8.8 is four times bigger (in negative) than 2.2.

The quotient not only gives you the answer but also indicates the relationship between the numerator and denominator. It's essential to verify your division to ensure the quotient is accurate.

In summary, the quotient is the outcome of the division, representing how much one number fits into another.
Division
Division is a mathematical operation that determines how many times one number is contained within another. It's like distributing something into equal parts. In the problem \(\frac{-8.8}{2.2}\), dividing -8.8 by 2.2 gives us -4.

To divide decimals, align the numbers properly and perform the division as you would with whole numbers. If the divisor, like 2.2, has decimals, you can multiply both the divisor and the dividend by 10 until they become whole numbers. This often makes the division simpler.

Understanding division helps in many real-life scenarios, such as splitting bills, sharing food, or calculating rates.

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Most popular questions from this chapter

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