Is #0.6# is the multiplicative inverse of #6 2/3.# Why? or why not?

2 Answers
May 12, 2018

#0.6# is not the multiplicative inverse of #6 2/3#

Explanation:

The multiplicative inverse of a number is the same as the reciprocal. (Turn it upside down).

Background:
The reciprocal of #a/b# is #b/a# (if #a and b# are not #0#)

The reciprocal of #2/3# is #3/2#

The product of a number and its multiplicative inverse is always #1#.

#a/b xx b/a = 1" and "2/3 xx 3/2 = 1#

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#0.6 = 6/10 = 3/5" and "6 2/3 = 20/3#

The reciprocal of #3/5 " is " 5/3# which is not #20/3#

#3/5 xx20/3 = 4#

#0.6# is not the multiplicative inverse of #6 2/3#

May 12, 2018

#3/20#

Explanation:

#"the product of a number and it's inverse "=1#

#6 2/3=20/3larrcolor(blue)"improper fraction"#

#"the inverse of "20/3=1/(20/3)=3/20#

#"note that "cancel(20)^1/cancel(3)^1xxcancel(3)^1/cancel(20)^2=1#

#0.6=6/10=3/5!=3/20#