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# Multiplying Negative Numbers

Multiplying negative numbers follows a simple rule: when you multiply two negative numbers, the result is positive. However, if you multiply a negative number by a positive number, the result is negative.

• Multiplying Negative Numbers
• Formula
• Solved Examples
• FAQs

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## Multiplying Negative Numbers

Multiplying negative numbers follows a simple rule: when you multiply two negative numbers, the result is positive. However, if you multiply a negative number by a positive number, the result is negative. Here are the steps to multiply two negative numbers:

Multiply the absolute values of the two negative numbers.

Determine the sign of the result based on the rule mentioned above.

In general, the rule for multiplying negative numbers is “a negative times a negative is positive, and a negative times a positive is negative.”

It’s important to remember that multiplying by zero results in zero, regardless of whether the numbers are positive or negative.

## Formula

The formula for multiplying two negative numbers can be written as:

(-a) x (-b) = ab

where a and b are both negative numbers.

If you are multiplying a negative number by a positive number, the formula can be written as:

(-a) x b = -(ab)

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

Similarly, if you are multiplying a positive number by a negative number, you can switch the order of the numbers and use the same formula as above:

a x (-b) = -(ab)

In both cases, you multiply the absolute values of the two numbers and then apply the sign rule to determine the sign of the result.

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## Solved Examples

Here are some solved examples of multiplying negative numbers:

Example 1: (-6) x (-4)

Solution: We multiply the absolute values of the two negative numbers: 6 x 4 = 24. Since both numbers are negative, the result is positive. Therefore, (-6) x (-4) = 24.

Example 2:(-5) x 3

Solution: We multiply the absolute values of the two numbers: 5 x 3 = 15. Since one number is negative and the other is positive, the result is negative. Therefore, (-5) x 3 = -15.

Example 3: 10 x (-2)

Solution: We multiply the absolute values of the two numbers: 10 x 2 = 20. Since one number is positive and the other is negative, the result is negative. Therefore, 10 x (-2) = -20.

Example 4: (-3) x (-2) x (-5)

Solution: We first multiply (-3) x (-2) = 6. Then, we multiply 6 x (-5) = -30. Since we are multiplying three negative numbers, the result is negative. Therefore, (-3) x (-2) x (-5) = -30.

Example 5: (-8) x 0

Solution: Multiplying by zero results in zero, regardless of whether the number is positive or negative. Therefore, (-8) x 0 = 0.

## Multiplying Negative Numbers FAQS

##### How do I multiply negative numbers?

To multiply negative numbers, multiply them as you would with positive numbers, and then apply the rule that a negative multiplied by a negative gives a positive result.

##### What happens when I multiply a positive number by a negative number?

When you multiply a positive number by a negative number, the result will be negative.

##### What happens when I multiply a negative number by a positive number?

When you multiply a negative number by a positive number, the result will be negative.

##### What happens when I multiply two negative numbers?

When you multiply two negative numbers, the result will be positive.

##### Can I multiply negative fractions?

Yes, you can multiply negative fractions. Multiply the numerators together and the denominators together, and then apply the rules of multiplying negative numbers to determine the sign of the result.

Gloria Mathew writes on math topics for K-12. A trained writer and communicator, she makes math accessible and understandable to students at all levels. Her ability to explain complex math concepts with easy to understand examples helps students master math. LinkedIn

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