Problem 18 - Algebra 1

Question

Find the quotient. $$-24 \div 4$$

Step-by-Step Solution

Answer

-6

Step 1: Recognize the signs

Note the signs of the numbers involved in the division. The number -24 is negative and 4 is positive. When you divide a negative by a positive, the answer is a negative number.

Step 2: Perform the division ignoring signs

Ignore the signs for a moment and just divide 24 by 4 to get a result of 6.

Step 3: Apply the sign

After performing the division, apply the negative sign to the result, we get -6. Therefore, -24 divided by 4 results in -6.

Key Concepts

Understanding Negative Numbers

Negative numbers are numbers that are less than zero. They are typically represented with a minus sign (-) in front of them. Negative numbers are used to express a lack or opposite of something. For instance, if you owe $24, you could represent it as -24 dollars. Negative numbers are crucial in various mathematical calculations, as they allow for the representation of debt, temperature below zero degrees, or other scenarios where a value is less than nothing.

When working with negative numbers, particularly in division, it’s important to understand how their signs affect the results. Remember that negative numbers, like -24, are the opposite of their positive counterparts.

Division Rules with Negative Numbers

Dividing numbers follows specific rules, especially when negative numbers are involved. These rules help determine the sign of the quotient.

• Positive divided by Positive: The result is positive. For example, 24 divided by 4 is 6.
• Negative divided by Positive: The result is negative. For example, -24 divided by 4 is -6.
• Positive divided by Negative: The result is negative. For example, 24 divided by -4 is -6.
• Negative divided by Negative: The result is positive. For example, -24 divided by -4 is 6.

These division rules tell us that when you divide a negative number by a positive number, the result (or quotient) will always be a negative number. It’s important to keep the signs in mind when performing division to get the correct answer.

Understanding the Quotient

The quotient is the result of a division problem, such as when you divide -24 by 4. When you perform the division here, you end up with a quotient of -6.

To find a quotient, divide the dividend (the number you want to divide) by the divisor (the number you are dividing by). Here, the dividend is -24, and the divisor is 4. First, ignore the negative sign and calculate 24 divided by 4, which is 6.

Then, reapply the sign based on the division rules covered earlier: since a negative divided by a positive results in a negative quotient, our final answer is -6. This demonstrates how important it is to not only perform the numerical division correctly but also to consider the signs of the numbers involved to get the accurate quotient.