Dividing Negative Numbers

Dividing negative numbers follows the same rules as dividing positive numbers. The sign of the result depends on the signs of the numbers being divided.

Table of Contents:

• Dividing Negative Numbers
• Formula
• Solved Examples
• FAQs

Dividing Negative Numbers

Dividing negative numbers can be a bit tricky, but it follows some simple rules. Here are the steps to divide two negative numbers:

Start by dividing the absolute values of the two negative numbers as you would with positive numbers.

If both numbers have the same sign, the result will be positive. For example, (-6) ÷ (-2) = 3

If the numbers have different signs, the result will be negative. For example, (-6) ÷ 2 = -3 or 6 ÷ (-2) = -3

In general, the rule for dividing negative numbers is “result of a negative number divided by a positive number is negative and result of a negative number divided by a negative number is positive.”

It’s important to remember that dividing by zero is undefined, regardless of whether the numbers are positive or negative.

Formula

The formula for dividing two negative numbers is the same as dividing two positive numbers. You simply divide the absolute values of the numbers and then determine the sign of the result based on the rules mentioned above.

The formula can be written as:

(-a) ÷ (-b) = a ÷ b

where a and b are both negative numbers.

If a and b have different signs, you can first take the absolute values of both numbers and then divide them as if they were positive. Then, you can apply the sign rule to determine the sign of the result.

The formula for dividing a negative number by a positive number can be written as:

(-a) ÷ b = -(a ÷ b)

where a is a negative number and b is a positive number.

Again, the same formula can be used for dividing a positive number by a negative number by simply switching the signs.

Solved Examples

Sure, here are some solved examples of dividing negative numbers:

Example 1: (-12) ÷ (-3)

Solution: We first divide the absolute values of the two negative numbers: 12 ÷ 3 = 4. Since both numbers are negative, the result is positive. Therefore, (-12) ÷ (-3) = 4.

Example 2: (-9) ÷ 3

Solution: We divide the absolute values of the two numbers: 9 ÷ 3 = 3. However, since one number is negative and the other is positive, the result is negative. Therefore, (-9) ÷ 3 = -3.

Example 3: 18 ÷ (-6)

Solution: We divide the absolute values of the two numbers: 18 ÷ 6 = 3. However, since one number is positive and the other is negative, the result is negative. Therefore, 18 ÷ (-6) = -3.

Example 4: (-36) ÷ (-6) ÷ (-2)

Solution: We first divide (-36) ÷ (-6) = 6. Then, we divide 6 ÷ (-2) = -3. The result of dividing first negative (-36) number by second negative number (-6) is positive and then this positive result is divided a negative number (-2) to get the final result. Therefore, (-36)  ÷ (-6)  ÷ (-2) = -3

Example 5: (-15) ÷ 0

Solution: Division by zero is undefined, so the answer is not defined or does not exist.

Dividing Negative Numbers FAQS

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