Multiplying Negatives

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.

(Image will be uploaded soon)

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.)

(Image will be uploaded soon)

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. 

(Image will be uploaded soon)

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. 

(Image will be uploaded soon)

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.

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.