# Write a fraction equivalent to 45

So if we multiply the numerator times 7 and the denominator times 7, we'll get because 3 times 7 is over Since the numerator and the denominator are coprime numbers prime to each othertheir greatest common factor is 1, so this fraction is in its simplest form it cannot be reduced anymore.

And instead of eating one piece, this time I actually ate 2 of the 4 pieces. So if we multiply the denominator by 3, we also have to multiply the numerator by 3. OK, good.

### Equivalent fractions for 3/4

All we did is multiply the number by 1 and we know that any number times 1 is still that number. So we ate 4 out of 8 pieces. And instead of eating one piece, this time I actually ate 2 of the 4 pieces. We ate half of the pie. Well, we still ended up eating the same amount of the pie. Nothing too complicated there. We multiply the denominator by 2. Let's say we divided that pie into 8 pieces. Sorry for that. So that's why we're saying those two fractions are equivalent. They're two fractions that although they use different numbers, they actually represent the same thing. Let's do some more examples of equivalent fractions and hopefully it'll hit the point home.

Let me show you an example. Well, by the same principle, as long as we multiply the numerator and the denominator by the same numbers, we'll get an equivalent fraction.

Operations with fractions often involve bringing them to the same denominator and sometimes both the numerators and the denominators are large numbers. We ate half of the pie.

### Equivalent fractions for 1/4

So that's why we're saying those two fractions are equivalent. Well, what if instead of dividing the pie into two pieces, let me just draw that same pie again. Doing calculations with such large numbers could be difficult. Prime Factorization: One way to calculate the greatest common factor is to find all the prime factors of the two numbers and build their prime decomposition in exponential form, and then to multiply all the common prime factors by their lowest exponents, see below. And I wanted to write that with the denominator-- let's say I wanted to write that with the denominator And now, instead of eating 2 we ate 4 of those 8 pieces. The reduced fraction has now a numerator that is equal to 6 and a denominator that is equal to 8. They're two fractions that although they use different numbers, they actually represent the same thing. This fraction is called an irreducible fraction. Another way, if we actually had-- let's do another one. Let's say I did that. We did the same thing here. Times 3.

And just going to our original example, all that's saying is, if I had a pie with 12 pieces and I ate 5 of them. Let me make sure I get the right color here.

## What is equivalent to 4/5 in decimal

Well, to go from 12 to 36, what do we have to multiply by? Let's say I did that. So if we multiply the numerator times 7 and the denominator times 7, we'll get because 3 times 7 is over So we ate 4 out of 8 pieces. And that makes sense because well, if I double the number of pieces in the pie, then I have to eat twice as many pieces to eat the same amount of pie. So that's why we're saying those two fractions are equivalent. By simplifying, reducing a fraction to lower terms, both the numerator and denominator of the fraction are reduced to smaller values, much easier to work with, reducing the resulting computational effort. The reduced fraction has now a numerator that is equal to 6 and a denominator that is equal to 8. This fraction is called an irreducible fraction. Let me erase this. And if you look at this, what we're doing here isn't magic. We multiply the denominator by 2. Nothing too complicated there. And I wanted to write that with the denominator-- let's say I wanted to write that with the denominator Oh boy, this thing is messing up.

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