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Chapter 0: Problem 88

Find each quotient where possible. $$ \frac{-45}{-9} $$

Short Answer

Expert verified
5

Step by step solution

01

Identify the Numerator and Denominator

The given expression is \( \frac{-45}{-9} \). Here, -45 is the numerator and -9 is the denominator.
02

Simplify the Signs

Both the numerator and denominator are negative. When dividing two negative numbers, the result is a positive number. Thus, \( \frac{-45}{-9} \) simplifies to \( \frac{45}{9} \).
03

Divide the Numbers

Now, divide 45 by 9. Perform the division: \( 45 \, 梅 \, 9 = 5 \).
04

State the Quotient

The quotient of \( \frac{-45}{-9} \) is 5.

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Key Concepts

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

Numerator and Denominator
When working with fractions, it's crucial to understand the terms numerator and denominator.
The **numerator** is the number above the fraction bar.
The **denominator** is the number below the fraction bar.
For example, in the expression \( \frac{-45}{-9} \):
* -45 is the numerator.
* -9 is the denominator.
Recognizing the numerator and denominator allows you to perform various operations, like division, with ease.
Simplifying Signs
To simplify signs in a division problem, follow these rules:
* **Positive 梅 Positive** results in a positive quotient
* **Negative 梅 Negative** also results in a positive quotient
* **Positive 梅 Negative** results in a negative quotient
* **Negative 梅 Positive** also results in a negative quotient
In our example, \( \frac{-45}{-9} \), both the numerator and denominator are negative.
When we divide two negative numbers, the negative signs cancel out.
This makes the fraction positive: \( \frac{45}{9} \).
Quotient
The **quotient** is the result you get when you divide the numerator by the denominator.
To find the quotient of \( \frac{45}{9} \), you perform the division: \( 45 eq 9 = 5 \).
So, the quotient of \( \frac{-45}{-9} \) is 5.
Remember:
* The quotient is always the outcome of the division.
* The division must be performed correctly to arrive at the correct quotient.
In our example:
* Numerator: 45
* Denominator: 9
45 divided by 9 equals 5.

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Most popular questions from this chapter

Solve each problem. The amount, in billions of dollars, that Americans spent on their pets from 2003 to 2016 can be approximated by substituting a given year for \(x\) in the following expression. $$2.493 x-4962$$ (Data from American Pet Products Manufacturers Association.) Find the amount spent in each year. Round answers to the nearest tenth. (a) 2003 (b) 2010 (c) 2016 (d) How did the amount Americans spent on their pets change from 2003 to \(2016 ?\)

Write each fraction as a decimal. For repeating decimals, write the answer by first using bar notation and then rounding to the nearest thousandth. See Example 11. $$ \frac{8}{9} $$

Find each square root. If it is not a real number, say so. $$ \sqrt{-36} $$

Simplify each expression. $$ -14\left(-\frac{2}{7}\right) \div(2 \cdot 6-10) $$

If \(a\) is a positive number, is \(-\sqrt{-a}\) positive, negative, or not a real number?
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