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So let's say that we have two bottles of orange juice: Orange juice A, and Orange juice B. Orange juice A is 1310ml, and Orange Juice B is 786ml. Now I know that their ratio of A:B is 1310:786. But how can I "simplify" it to the most smallest possible number?

Now I know I can go around this question by dividing them both with a number they can both accept. But in this case, the number is too big. I've subtracted 1310ml with 786ml, which returned 524ml. But my brain can't seem to get around the answer.

Any help will be appreciated. Thanks in advance!

Jeffrey10th
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  • Both numbers are clearly even. Have you divided throughout by $2$? – Landuros Apr 30 '18 at 07:24
  • Can you come up with any numbers that are factors of both $1310$ and $786$? At least you should see that they are both even numbers. – Matti P. Apr 30 '18 at 07:24
  • @Landuros You mean, to divide throughout by 2 until I get the answer? Well, that may work, but I'm trying to calculate them without using these tricks :( Thank you anyways – Jeffrey10th Apr 30 '18 at 07:27
  • @Jeffrey10th Well you might want to try finding the prime factorisation for both numbers and cancelling any common factors. – Landuros Apr 30 '18 at 07:37

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That's not a bad start at all. Any number that divides both $1310$ and $786$ must also divide $1310-786=524$. But there's no reason you have to stop there. Any number that divides both $786$ and $524$ must also divide $786-524=262$. Now can you finish from here?

saulspatz
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