JEE Exam > JEE Videos > Sets and Functions > Promo: Why does a negative times a negative equal a positive?
Promo: Why does a negative times a negative equal a positive? Video Lecture | Sets and Functions - JEE
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FAQs on Promo: Why does a negative times a negative equal a positive? Video Lecture - Sets and Functions - JEE
| 1. Why does a negative times a negative equal a positive? |  |
Ans. The rule that states a negative times a negative equals a positive is a fundamental property of multiplication in mathematics. It is derived from the concept of the number line and the rules of algebra. When two negative numbers are multiplied, the result is positive because the negative sign indicates a direction opposite to the positive numbers. Multiplying two negative numbers implies reversing the direction twice, resulting in a positive value.
| 2. Is the rule of a negative times a negative equaling a positive always applicable? | |
Ans. Yes, the rule that a negative times a negative equals a positive is always applicable in mathematics. It is a fundamental property of multiplication that holds true for all real numbers. However, it is important to note that this rule applies specifically to multiplication and may not be applicable in other mathematical operations.
| 3. Can you provide an example to illustrate the rule of a negative times a negative equaling a positive? | |
Ans. Certainly! Let's consider the multiplication of -3 and -2. According to the rule, a negative times a negative equals a positive. Therefore, -3 multiplied by -2 is equal to +6. This example demonstrates how multiplying two negative numbers results in a positive product.
| 4. What happens when a negative number is multiplied by a positive number? | |
Ans. When a negative number is multiplied by a positive number, the result depends on the signs of the numbers involved. If the negative number is being multiplied by a positive number, the product will be negative. Conversely, if a positive number is multiplied by a negative number, the product will also be negative.
| 5. Is the rule of a negative times a negative equaling a positive applicable in all mathematical systems? | |
Ans. The rule of a negative times a negative equaling a positive is applicable in most mathematical systems, including the real numbers, integers, and rational numbers. However, it should be noted that in some specialized mathematical systems, such as complex numbers or matrices, the rule may not hold true. The concept of negative numbers and multiplication varies in different mathematical contexts.
Text Transcript from Video
why does a negative times a negative
equal a positive this rule is not just
made up there is a chain of reasoning a
mathematical argument that shows why the
rule has to be that negative times
negative equals positive here's how the
reasoning goes zero times anything
equals zero every number has exactly one
additive inverse this means that if M is
a positive number then minus M is its
additive inverse so that M plus minus M
equals zero likewise the additive
inverse of minus M is M we want negative
numbers to obey the distributive law
this says that the product of a and B
plus C equals a times B plus a times C
consider the expression the product of 2
+ 1 + -1 this equals 2 times 0 which is
0 but by the distributive law it equals
2 times 1 plus 2 times minus 1 so 2
times minus 1 does the job of additive
inverse of 2 times 1 and therefore 2
times minus 1 is the additive inverse of
2 times 1/2 times 1 equals 2 and the
additive inverse of 2 is minus 2 since a
number has exactly one additive inverse
2 times minus 1 equals -2 therefore we
have to accept that negative times
positive equals negative
now consider the expression the product
of -2 + 1 + minus 1 this equals minus 2
times 0 which is 0 using distributive
law we can write this expression as
minus 2 times 1 plus minus 2 times minus
1 so minus 2 times minus 1 does the job
of additive inverse of minus 2 times 1
and therefore minus 2 times minus 1 is
the additive inverse of minus 2 times 1
from the previous reasoning we know that
minus 2 times 1 equals minus 2 and minus
2 has exactly 1 additive inverse which
is 2 so minus 2 times minus 1 equals 2
so we have to accept the law that
negative times negative equals positive
equal a positive this rule is not just
made up there is a chain of reasoning a
mathematical argument that shows why the
rule has to be that negative times
negative equals positive here's how the
reasoning goes zero times anything
equals zero every number has exactly one
additive inverse this means that if M is
a positive number then minus M is its
additive inverse so that M plus minus M
equals zero likewise the additive
inverse of minus M is M we want negative
numbers to obey the distributive law
this says that the product of a and B
plus C equals a times B plus a times C
consider the expression the product of 2
+ 1 + -1 this equals 2 times 0 which is
0 but by the distributive law it equals
2 times 1 plus 2 times minus 1 so 2
times minus 1 does the job of additive
inverse of 2 times 1 and therefore 2
times minus 1 is the additive inverse of
2 times 1/2 times 1 equals 2 and the
additive inverse of 2 is minus 2 since a
number has exactly one additive inverse
2 times minus 1 equals -2 therefore we
have to accept that negative times
positive equals negative
now consider the expression the product
of -2 + 1 + minus 1 this equals minus 2
times 0 which is 0 using distributive
law we can write this expression as
minus 2 times 1 plus minus 2 times minus
1 so minus 2 times minus 1 does the job
of additive inverse of minus 2 times 1
and therefore minus 2 times minus 1 is
the additive inverse of minus 2 times 1
from the previous reasoning we know that
minus 2 times 1 equals minus 2 and minus
2 has exactly 1 additive inverse which
is 2 so minus 2 times minus 1 equals 2
so we have to accept the law that
negative times negative equals positive
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Dec 26, 2024 Last updated |
Video Description: Promo: Why does a negative times a negative equal a positive? for JEE 2024 is part of Sets and Functions preparation.
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