What Happens When You Multiply Negative Numbers with Rules and Examples
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.
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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.
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.
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FAQs on Multiplying Negatives Explained with Sign Rules
1. What happens when you multiply two negative numbers?
When you multiply two negative numbers, the result is positive. This follows the standard rule of multiplying integers.
- Negative × Negative = Positive
- Example: (−4) × (−3) = 12
- The signs cancel each other out, leaving a positive product.
2. What is the rule for multiplying negative numbers?
The rule for multiplying negative numbers depends on the signs of the numbers involved. The sign rules are:
- Positive × Positive = Positive
- Negative × Negative = Positive
- Positive × Negative = Negative
- Negative × Positive = Negative
3. Why is a negative times a negative a positive?
A negative times a negative equals a positive because it preserves consistency in the rules of arithmetic. For example:
- We know 3 × (−2) = −6.
- To keep patterns consistent, (−3) × (−2) must equal 6.
- 0 = (−3) × 0 = (−3) × [2 + (−2)]
- = (−3 × 2) + (−3 × −2)
4. How do you multiply a positive and a negative number?
To multiply a positive and a negative number, multiply the numbers normally and make the answer negative. Steps:
- Ignore the signs and multiply the numbers.
- Apply the sign rule: one negative means the product is negative.
- 5 × (−4) = 20
- Final answer = −20
5. Can you give an example of multiplying negative numbers?
Yes, an example of multiplying negative numbers is (−7) × (−5) = 35. Solution steps:
- Multiply 7 × 5 = 35.
- Since both numbers are negative, the result is positive.
6. What happens when you multiply three negative numbers?
When you multiply three negative numbers, the result is negative because there is an odd number of negatives. Rule:
- An even number of negative factors gives a positive result.
- An odd number of negative factors gives a negative result.
- (−2) × (−3) × (−4)
- (−2 × −3) = 6
- 6 × (−4) = −24
7. How do you multiply negative fractions?
To multiply negative fractions, multiply the numerators together and the denominators together, then apply the sign rule. Steps:
- Multiply the numerators.
- Multiply the denominators.
- Determine the sign using integer sign rules.
- (−2/3) × (−4/5)
- Numerators: −2 × −4 = 8
- Denominators: 3 × 5 = 15
- Result = 8/15
8. What is the difference between multiplying and adding negative numbers?
The difference is that multiplying negatives follows sign rules, while adding negatives depends on direction on the number line. Key differences:
- Multiplying: Use sign rules (e.g., − × − = +).
- Adding: Combine values and keep track of direction.
- (−3) + (−2) = −5
- (−3) × (−2) = 6
9. What are common mistakes when multiplying negative numbers?
A common mistake when multiplying negative numbers is forgetting the sign rule. Typical errors include:
- Thinking (−4) × (−6) = −24 instead of 24.
- Ignoring one negative sign.
- Confusing multiplication rules with addition rules.
10. How do you know if the product of integers will be positive or negative?
You can determine the sign of the product by counting the number of negative factors. Rule:
- Even number of negatives → Positive product
- Odd number of negatives → Negative product
- (−1) × (−2) × (−3) × (−4)
- There are 4 negatives (even).
- Product = 24 (positive).
