How do you find the reciprocal of 3?

2 Answers
Jun 12, 2018

The reciprocal of a number is another word for its multiplicative inverse, or the number which gives 1 when multiplied by the original number.

To find the reciprocal of any number, simply take 1 and divide it by that number. So, the reciprocal of #3# is:

#1 div 3 = color(red)(1/3)#

We can check that this is the multiplicative inverse of #color(limegreen)3# by multiplying those two numbers together and seeing if we get 1:

#color(limegreen)3 * color(red)(1/3) = cancel3 * 1/cancel3 = 1 #

Hope this helps!

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

As a side note for future problems, you may want to remember that the number #0# does not have a reciprocal. This is because there isn't any number you can multiply by zero to get #1#. Try it for yourself #-# you always get zero!

Jun 12, 2018

Answer:

The reciprocal of #3/1# is #1/3#

Explanation:

The reciprocal of a number is the same as its multiplicative inverse.

(The multiplying opposite)

It is the number 'turned upside down'.

The product of a number and its reciprocal is always #1#

#a/b xx b/a =1#

#5/2 xx 2/5 = 1#

So in this case, we can write #3# as: #3/1#

The reciprocal is #1/3#

#3/1 xx 1/3 = 1#

Note that #0# does not have a reciprocal because you cannot turn #0/1# upside down and then divide by #0#