Why Do Two Negatives Make a Positive? Explained for Students
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.
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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: Rules, Tricks, and Examples
1. What are the rules for multiplying negatives?
The rules for multiplying negatives are simple:
- If you multiply two numbers with the same sign (both negative or both positive), the answer is positive.
- If you multiply numbers with different signs, the answer is negative.
2. Why does multiplying 2 negative make a positive?
Multiplying two negative numbers gives a positive product because of the pattern in mathematics. If $-a \times -b = x$, the negatives cancel each other. This is based on the rules of arithmetic so the answer becomes positive during calculations.
3. What is negative 4 multiplied by negative 2?
When you multiply negative 4 by negative 2, you get a positive answer: $(-4) \times (-2) = 8$. The two negatives multiply to make a positive result, following the rule about same signs giving a positive.
4. What are the four rules of negative numbers?
The four rules of negative numbers are:
- Negative plus negative equals more negative
- Negative plus positive depends on which is larger
- Negative times positive is negative
- Negative times negative is positive
5. What happens when you multiply a positive and a negative number?
If you multiply a positive number by a negative number, the answer is always a negative number. For example, $5 \times (-3) = -15$. The product takes the sign of the negative number in the calculation.
6. Is zero affected when multiplied by a negative number?
Multiplying zero by any negative number always results in zero. The sign does not matter because zero times any value is always zero: $0 \times (-7) = 0$. Zero is neutral in multiplication.
7. How can you remember the rule for multiplying negatives?
To remember the multiplying negatives rule, recall:
- Same signs (both negative or both positive) make a positive
- Different signs (one negative, one positive) make a negative
8. What is the result if you multiply multiple negative numbers together?
When you multiply more than two negative numbers, count the negatives:
- Even number of negatives gives a positive answer
- Odd number of negatives gives a negative answer
9. Does the sign change if you multiply three negative numbers?
Multiplying three negative numbers results in a negative answer. For example, $(-2) \times (-3) \times (-4) = -24$. Since there are an odd number of negatives (three), the product remains negative after multiplication.
10. Can multiplying negatives be shown on a number line?
Yes, multiplying negatives can be shown on a number line. When you multiply by a negative number, it reverses direction. For example, $2 \times (-3)$ means move three units to the left, two times, ending at $-6$ on the number line.
