# Question #edbb3

Apr 21, 2017

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

#### Explanation:

ie $\frac{3}{5} \cdot \frac{2}{2} = \frac{6}{10}$ which is the same as $\frac{3}{5}$

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

$\frac{3}{5} \cdot \frac{5}{5} = \frac{15}{25}$

$\frac{3}{5} \cdot \frac{10}{10} = \frac{30}{50}$

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:

$\frac{2}{2} , \frac{5}{5} , \frac{10}{10} \to \frac{\cancel{2} 1}{\cancel{2} 1} , \frac{\cancel{5} 1}{\cancel{5} 1} , \frac{\cancel{10} 1}{\cancel{10} 1}$ the multiplier always cancels to $1$

And $1 \times$(anything) = (the same thing)

So three equivalent fractions are $\frac{6}{10} , \frac{15}{25} , \frac{30}{50}$

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