Multiplying and Dividing Negative Numbers

Q: What happens when you multiply two negative numbers?

Multiplying two negative numbers gives a positive result. There are two negative signs, which is an even number, so the answer is positive. For example, negative 2 multiplied by negative 5 gives positive 10. The same applies when you divide two negative numbers.

Q: Do you multiply and divide negative numbers using the same rule?

Yes. Multiplication and division follow the same sign rule. For both operations, the number of negative signs decides the sign of the answer. An odd number of negative signs gives a negative result, while an even number of negative signs gives a positive result.

Q: How do you multiply and divide three numbers with negative signs?

Work from left to right, two numbers at a time, unless there are brackets. Apply the sign rule to each operation as you go. At the end, count all the negative signs to check whether the final answer should be positive or negative.

Q: Does the order matter when multiplying and dividing?

Work from left to right when a calculation mixes multiplication and division, unless there are brackets. If there are brackets, work out what is inside them first. Following this order keeps each running result correct, so your signs and values stay accurate.

Key concept

Multiplying and dividing negative numbers follows sign rules. An odd number of negatives gives a negative answer, while an even number gives a positive answer, like (−12) ÷ (−3) = +4.

Multiplying and Dividing Negative Numbers - introduction visual

Video Lesson

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$Multiplying and Dividing Negative Numbers poster$

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Flashcards

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Multiplication and division of negative numbers, showing odd negative signs give a negative result and even negative signs give a positive result.

Steps for multiplication and division with rules for odd and even negative signs determining result positivity.

Combining multiplication and division with examples showing the rules for odd and even numbers of negative signs, calculating from left to right.

Sign Rules for Multiplication and Division

An odd number of negative signs gives a negative answer, for example $5 \times (- 3) = - 15$ .
An even number of negative signs gives a positive answer, for example $(- 12) \div (- 3) = + 4$ .

Practice Questions

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Q1Easy

Simplify: 7 × (−2).

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Interactive Activity

Master multiplying and dividing negative numbers

(-28)

(-3)

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Students Also Ask

The questions students bump into most on this topic

What happens when you multiply two negative numbers?

Multiplying two negative numbers gives a positive result. There are two negative signs, which is an even number, so the answer is positive. For example, negative 2 multiplied by negative 5 gives positive 10. The same applies when you divide two negative numbers.

Do you multiply and divide negative numbers using the same rule?

Yes. Multiplication and division follow the same sign rule. For both operations, the number of negative signs decides the sign of the answer. An odd number of negative signs gives a negative result, while an even number of negative signs gives a positive result.

How do you multiply and divide three numbers with negative signs?

Work from left to right, two numbers at a time, unless there are brackets. Apply the sign rule to each operation as you go. At the end, count all the negative signs to check whether the final answer should be positive or negative.

Does the order matter when multiplying and dividing?

Work from left to right when a calculation mixes multiplication and division, unless there are brackets. If there are brackets, work out what is inside them first. Following this order keeps each running result correct, so your signs and values stay accurate.

How do you check whether the answer is positive or negative?

Count all the negative signs in the calculation. If the total is an odd number, the final answer is negative. If the total is an even number, the final answer is positive. This quick count confirms the sign of your result.

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