Explain why the reciprocal...

Question

Explain why the reciprocal of a nonzero number is not the same as the opposite of the number

Answer 1

Because if take x = 7 then opposite is -7

If take x = 1/2 then reciprocal is 2

Answer 2

When we think of the "opposite" of a number, we usually are referring to the negative of that number. So, the "opposite" of 5 is -5, because 5+(-5)=0, and zero is the most neutral number when dealing with addition, because any number + 0 = that number. Adding zero doesn't change anything about the original number. The reciprocal is the same thing as the opposite, but in the context of multiplication instead of addition. When using multiplication, zero is not the 'neutral' number because it turns everything into itself (0 times x = 0). But the number 1 keeps all numbers the same when multiplied (1 times x = x). Since adding zero is the 'identity' of addition, multiplying by one is the 'identity' of multiplication. So the "opposite" of a number when considering multiplication is another number that when multiplied gives the "identity" (1 for multiplication). With multiplication, this is 1/x, the reciprocal. So for any x, x+(-x)=0, with zero the additive identity, and for any x, x times (1/x) = 1, with one the multiplicative identity.

Answer 3

Opposite refers to sign, e.g. 4 is the opposit of -4.

Reciprocal refers to division, e.g. 3/5 is the reciprocal of 5/3