Idenify pairs of Additive and Multiplictive Inverses.
WHAT in the world are additive and multiplicative inverses???
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if A is a number, its additive inverse is B such that A + B = 0
A's multiplicative inverse is B such that A * B = 1
All real numbers have exactly one additive inverse.
All real numbers except 0 have exactly one multiplicative inverse.
Don't worry, I'll explain it to you! Additive and multiplicative inverses are mathematical concepts related to operations like addition and multiplication.
1. Additive Inverse: For any number 'a', its additive inverse is the number '-a'. When you add a number and its additive inverse, you get the identity element for addition, which is zero (0). In simpler terms, if you have a number and you add its negative, the result will always be zero.
Example: The additive inverse of 5 is -5, because 5 + (-5) = 0.
2. Multiplicative Inverse: For any number 'a', except for zero, its multiplicative inverse is the number '1/a'. When you multiply a number and its multiplicative inverse, you get the identity element for multiplication, which is one (1). In simpler terms, if you have a number and you multiply it by its reciprocal, the result will always be one.
Example: The multiplicative inverse of 3/4 is 4/3, because (3/4) * (4/3) = 1.
Now, let's identify pairs of additive and multiplicative inverses.
Additive Inverses:
-2 and 2
5 and -5
-7 and 7
Multiplicative Inverses:
1/2 and 2
3 and 1/3
-4/5 and -5/4
These pairs consist of numbers that, when added or multiplied together, will result in the identity element (0 for addition and 1 for multiplication).