Simplifying Fractions

[One Speaker]

Narrator: Simplify the fraction to lowest terms so we are going to take this fraction right here [30/48] and we are going to put it in its simplest form. And we’re going to do that using prime factorization so we are going to find the prime factors of both 30 and 48 and see what we can cancel. So for 30 if we look at that it’s an even number so we know that it’s divisible by 2 and 2 times 15 equals 30. So two factors of 30 would be 2 and 15. 2 is prime because it is only divisible evenly by itself and 1 but 15 is not so we can take that one further and we know that 3 times 5 equals 15. So 3 and 5 are factors of 15 and both 3 and 5 are prime cuz they’re only divisible evenly by themselves and 1. So the prime factors of 30 are 2 times 3 times 5.

Now we can find the prime factors of 48. We know that 48 is even so one of the factors of 48 would be 2 and 2 times 24 is 48. Now 2 is prime but 24 is not so we can break this down by its factors. And again it's even so I know that 2 is a factor. So 2 times 12 equals 24. Ok and again 2 is prime so we can move onto 12 and find the factors of 12. And it's still even so we can pull out a 2 again. 2 times 6 is 12 so we know that 2 and 6 are factors of 12. Now we can break 6 down into its factors and once again we can pull out a 2 so 2 times 3 is 6. So 2 and 3 are factors of 6 and both 2 and 3 are prime so we can write the prime factors of 48 as 2 times 2 times 2 times 2 times 3.

Now let’s scroll this up to give us a  bit more room and we can rewrite our faction so let’s rewrite 30 over 48 and we found the prime factors of 30 were 2 times 3 times 5 and the prime factors of 48 were 2 times 2 times 2 times 2 times 3. Let’s extend our line out there. So now anywhere that we have the same number on top and bottom we can cross them out because remember that 2 over 2 is the same as 1 so it’s essentially as we’re multiplying everything else by and so here we have a 3 and 3 that we can cancel out and we are left with 5 over 2 times 2 times 2. And 2 times 2 is 4 times 2 is 8. So 30 over 48 written in simplest form is 5 over 8 or ⅝.

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