The next topic we’re going to tackle is one I’ve been trying to work with because it affects so many different math skills: creating equivalent fractions.We sometimes need a fraction to be cut into more or fewer pieces to make it simpler to work with. To do this, we need to change the numbers in the fraction without changing the value of the number.
Let’s take 
for example. Right now, it’s a whole that’s been broken into three pieces,but I may want it broken into fifteen pieces. The first thing I’m going to ask myself is, “What do I have to multiply 3 by to get 15?”, or, “3 x what equals 15?” I know that 3 X 5 equals 15, so I set up the following to change my thirds into fifteenths.
x 
You’ll note that I have created the fraction from my 5. Basically, this is because I don’t want to change the value of my fraction, just the numbers in it. The only number you can multiply something by and not change its value is 1, and is equivalent to 1.
We can now multiply straight across the numerators and the denominators.
x = 
That’s great, but what if I have something like 
and I want to simplify it? We can use a similar process, but instead of figuring out what number we have to multiply by, we have to find the greatest common factor. The greatest common factor for 21 and 24 is 3, so we’re going to have to divide both the numerator and the denominator by 3, again trying to change the numbers without changing the value of the fraction. (Even though the notation looks similar to dividing fractions, which we covered later this week, remember that we’re just trying to simplify the fraction, not divide one by the other.)
= 
simplifies to
We’ll be using this skill over the next couple of days as we look at adding and subtracting simple fractions.
[...] Fractions: Creating equivalent fractions [...]
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[...] our case, we have fifths and tenths. Well, we know the five is a factor of ten, so we can change that one fifth into tenths. Five goes into ten twice, so we’re going to create an equivalent fraction of two tenths. We [...]
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[...] the numerator is larger than the denominator. To change a mixed number into an improper fraction, change the whole number into a fraction that has a common denominator with the fraction, and then add the two [...]
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