How do you write three equivalent fractions for 3/5 ?

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Feb 8, 2018


Multiply top and bottom by the same number to get a new fraction which is equivalent to the original fraction.


ie #3/5 * 2/2 = 6/10# which is the same as #3/5#

We can repeat this for any real number, eg 5 and 10,

#3/5 * 5/5 = 15/25#

#3/5 * 10/10 = 30/50#

But why can we do this? If you look at all the multiplying factors you will see that each one is a number divided by itself:

#2/2, 5/5, 10/10 to (cancel(2)1)/(cancel(2)1), (cancel(5)1)/(cancel(5)1),(cancel(10)1)/(cancel(10)1)# the multiplier always cancels to #1#

And #1xx#(anything) = (the same thing)

So three equivalent fractions are #6/10, 15/25, 30/50#

It should be noted that there are in fact an infinite number of equivalent fractions which can be found like this.

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