Question

Question #edbb3

Answer 1

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

Explanation:

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.