Problem 44
Question
Find each quotient. \(\frac{-4.6}{2.3}\)
Step-by-Step Solution
Verified Answer
-2
1Step 1: 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.
2Step 2: 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.
3Step 3: 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 \( -2 \).
Key Concepts
Sign rules in divisionNumerator and denominatorAbsolute values
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.
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’s 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’re 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’re 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.
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’re 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 \( -2 \).
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 \( -2 \).