The lowest term of fraction 45/30 is 9/16 , but I do not understand? How is this problem broken down?

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In lowest terms, 45/30 = 3/2 (not 9/16) because

`45/30=(15*3)/(15*2)`

I don't understand either. 45/30ths is not a fraction but is equivalent to 1 and 15/30ths or 1 1/2. Isn't it?

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