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Chapter 1: Problem 44

Find each quotient. \(\frac{-4.6}{2.3}\)

Short Answer

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Step by step solution

01

Identify the numbers

Identify the numbers that need to be divided. Here, we have \( -4.6 \) as the numerator and \( 2.3 \) as the denominator.
02

Understand the sign rules for division

When dividing two numbers with different signs, the quotient will be negative. Therefore, the result of \( \frac{-4.6}{2.3} \) will be negative.
03

Perform the division

Divide the absolute values of the numbers: \( \frac{4.6}{2.3} = 2 \). Since the original problem had a negative sign, the quotient becomes \( -2 \).

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Key Concepts

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

Sign rules in division
When dividing numbers, understanding the sign rules is essential. A positive number divided by another positive number will always result in a positive quotient. Similarly, a negative number divided by another negative number will also give a positive quotient, as the two negative signs cancel out each other.

However, when you divide a negative number by a positive number, or vice versa, the quotient will always be negative. The differing signs mean the result inherits the negative sign.

In our exercise, we divided \( -4.6 \) by \( 2.3 \). Since one number is negative and the other is positive, the quotient \( -2 \) is negative.
Numerator and denominator
In any division problem, it鈥檚 essential first to identify the numerator and the denominator. The numerator is the top number in a fraction, representing the part of the whole we鈥檙e considering. The denominator is the bottom number, representing the total or whole.

For the given problem, \( \frac{-4.6}{2.3} \), \( -4.6 \) is the numerator, and \( 2.3 \) is the denominator. This structure helps to easily identify what we鈥檙e dividing.

Remember, the numerator (top number) signifies what is being divided, while the denominator (bottom number) shows into how many parts it is being divided.
Absolute values
To perform division correctly, using the absolute values of the numbers can simplify the process. An absolute value of a number is its distance from zero on a number line, regardless of direction. So, for any number \( n \), the absolute value is always positive.

For example, the absolute value of both \( -4.6 \) and \( 4.6 \) is \( 4.6 \). In our given problem, using the absolute values, we initially calculate the division without considering the sign: \( \frac{4.6}{2.3} = 2 \).

Once the division of absolute values is done, we apply the sign rule. Since one of our original numbers is negative, the result \( 2 \) adopts a negative sign, leading to the final answer \( -2 \).

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Most popular questions from this chapter

Solve each problem. The lowest temperature ever recorded in Illinois was \(-36^{\circ} \mathrm{F}\) on January \(5,1999 .\) The lowest temperature ever recorded in Utah was on February \(1,1985,\) and was \(33^{\circ} \mathrm{F}\) lower than Illinois's record low. What is the record low temperature for Utah? (Data from National Climatic Data Center.)

Write a numerical expression for each phrase, and simplify the expression. The sum of -7 and -13 , increased by 14

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Write a numerical expression for each phrase, and simplify the expression. The product of \(-\frac{2}{3}\) and \(-\frac{1}{5},\) divided by \(\frac{1}{7}\)
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