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Multiplying Negatives

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Last updated date: 19th Jul 2024
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Multiplying Negatives - Introduction

Numbers less than zero are referred to as negative numbers. Numbers above zero are positive numbers. There are rules for adding, subtracting, multiplying, or dividing positive and negative numbers. 


Students can download the Multiplying Negatives - Signs, Examples, Rules, Solved Examples, and FAQs PDF from the Vedantu website. Anyone can download the Multiplying Negatives - Signs, Examples, Rules, Solved Examples, and FAQs PDF for free from the website. Multiplying Negatives is a very important topic of maths from which many questions get asked in exams. A proper understanding of the topic is necessary for students to score good marks in their exams. This topic is important for competitive exams like IIT and NEET. Thus, students should make proper efforts while studying the topic. The expert faculty of Vedantu who have had a lot of experience teaching students have prepared the Multiplying Negatives - Signs, Examples, Rules, Solved Examples and FAQs PDF. 


Students can use the Multiplying Negatives - Signs, Examples, Rules, Solved Examples and FAQs PDF for many purposes. They can use it for revisions before their exams or for learning the topic. 


Thus, students can gain a lot of benefits by downloading the Multiplying Negatives - Signs, Examples, Rules, Solved Examples and FAQs PDF.


Some of the topics which have been explained in the Multiplying Negatives - Signs, Examples, Rules, Solved Examples and FAQs PDF are as follows:

  • Signs

  • Rules for Multiplying Negatives

  • Division of Negative Numbers

  • What Happens When We Multiply Negatives with Matrices?


Signs

We know that "+" is a positive sign, "−" is a negative sign. When a sign is not denoted before a number, it usually means it's positive.


Example: 8 is actually +8

Note: To avoid confusion of signs, we can put () around the numbers. For example, 5 × −8 can be written as 5 × (−8)


Rules for Multiplying Negatives

We may have positive and negative integer values when working with integers in multiplication. There are rules for multiplying integers and dividing integers which are very similar to the rule for addition and subtraction.

  • If the signs are different, the answer is negative.

  • If the signs are the same, the answer is positive.

Refer to the description below for a better understanding.


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Plus Times Plus is Plus

Example: 2 × 5 = 10 

(We already discussed that when a number doesn't have a sign, it usually means it's positive.)


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Minus Multiply Minus is Plus

Example: (-10) × (-5) = 50

Negative multiplied by Negative is a positive number, which means that the product of two negative integers is always positive. 


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Plus Times Minus is Minus

Example: 5 x (-5) = - 25

Multiplication of Negative numbers with a positive number will always result in a Negative number. 


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Minus Times Plus is Minus

Note: These rules work in the same way as rules for dividing integers; you just have to replace "times" with "divided by". 


Division of Negative Numbers

The division of negative numbers works in the same way as that of positive numbers except that the results are sometimes negative. It depends on the two numbers involved in this division whether the answer is negative. The answer would also be negative if only one of the numbers is negative. The outcome would be positive, if both numbers are negative.


Expression 

Quotient

Example

Positive ÷ Positive

Positive

25 ÷ 5 = + 5

Negative ÷ Negative

Positive

- 25 ÷ - 5 = +5

Negative ÷ Positive

Negative

-25 ÷ 5 = -5

Positive ÷ Negative

Negative 

25 ÷ -5 = - 5


What happens when we Multiply Negatives with Matrices?

An integer matrix is a matrix, all of which are integer entries. The negative of a matrix is obtained by multiplying it by -1. 

So, if A is a given matrix

Then, − A = − 1 A


Solved Examples

1. What is −6 × 3?

Ans: 6 x 3 is 18. But here we have one negative and one positive number. Hence, the sign of the answer will be minus. 

Therefore, the answer is −18.


2. What is −80 ÷ 8?

Ans: 80 ÷ 8 is 10. Again, we have a positive and negative number. Hence, the sign will be negative in the final answer. 

Therefore, the answer is −10.


3. What is −50 x −5?

Ans: 50 x 5 is 250. This time, we have 2 negative numbers. Hence, the sign will be positive in the answer. Therefore, the answer is 250.


Conclusion

Only remember 2 things when you multiply negative numbers. 

  • Two negative numbers give a positive result at all times. 

  • Your answer would also be negative if you have only one negative value. Only remember these two rules and the rest is easy to calculate.


Why should Students join Vedantu?

Students can attend online classes for their school exam or competitive exams like NEET or JEE. They can attend the classes from the comforts of their homes. They just need to have a working internet connection and a device like a laptop, tablet or smartphone. They also have the option of downloading the classes in order to watch them later for revision. Students can get access to these classes at very affordable rates which makes them attainable for many students. 


The website has a vast question bank with questions based on the pattern of the exams they are preparing for. Apart from this, students can get access to other resources such as revision notes, NCERT solutions, solutions to other books,sample papers, PYQs and online tests. 

Thus, joining Vedantu will be very beneficial for students.

FAQs on Multiplying Negatives

1. Is the Multiplying Negatives - Signs, Examples, Rules, Solved Examples and FAQs article available in pdf form?

Yes, the Multiplying Negatives - Signs, Examples, Rules, Solved Examples and FAQs article is available in pdf form. Students can download the Multiplying Negatives - Signs, Examples, Rules,, Solved Examples and FAQs PDF from the Vedantu website very simply. It is very useful for students to keep the Multiplying Negatives - Signs, Examples, Rules, Solved Examples and FAQs article in PDF form as they can access it even when they don’t have any internet connection. 


Thus, the Multiplying Negatives - Signs, Examples, Rules, Solved Examples and FAQs will, be very advantageous for students in their studies.

2. How to download Multiplying Negatives - Signs, Examples, Rules, Solved Examples and FAQs pdf?

Students can download the Multiplying Negatives - Signs, Examples, Rules, Solved Examples and FAQs PDF in a very easy manner. The steps to download the PDF are as follows:

  1. Search for “Multiplying Negatives - Signs, Examples, Rules, Solved Examples and FAQs” on the search bar

  2. Click on the download PDF button

  3. Sign up using your email or mobile

  4. If you are already a registered user, log in using your password

  5. A confirmation message will be sent on your device with the Multiplying Negatives - Signs, Examples, Rules, Solved Examples and FAQs PDF file

  6. The PDF will be downloaded on your device separately too.

3. How to study Multiplying Negatives - Signs, Examples, Rules, Solved Examples and FAQs topic?

It is very important for students to study the topic from the NCERT before solving any other book. Once they have mastered the NCERT, they can start solving other books in order to become better at the topic. They can make use of the Multiplying Negatives - Signs, Examples, Rules, Solved Examples, and FAQs PDF for revising the topic. 


They should also solve sample papers on the topic in order to become familiar with the variety of questions that can be asked in exams.

4. How do you multiply negative numbers?

Negative multiplied by Negative is a positive number and multiplication of Negative numbers with a positive number will always result in a Negative number. 

Examples: 

  • -3 x -6 = +18

  • -6 x 5 = - 30

5. Why does negative multiplied by negative give a positive value?

When you multiply a negative by a negative you get a positive because the two negative signs are canceled out. So, a negative multiplied by a negative is always a positive.

6. What is the sign of the product of a negative and a positive number?

An answer is a negative number when you multiply a negative number and a positive number. Regardless of the order in which the positive and negative numbers are multiplied, the answer is always a negative one.