Hi Andres,
You can think of the place value system and the values of the places to the right of the decimal. For example
3.1 is 3 and one tenth, that is 3 and ^{1}/_{10}
thus
3.1 = 3 + ^{1}/_{10} = ^{30}/_{10} + ^{1}/_{10} = ^{31}/_{10}
Likewise
3.134 = 3 + ^{1}/_{10} + ^{3}/_{100} + ^{4}/_{1000} = 3 + ^{100}/_{1000} + ^{30}/_{1000}+ ^{4}/_{1000} = ^{3000}/_{1000} + ^{134}/_{1000} = ^{3134}/_{1000}
At this point you might be able to simplify the fraction. In this case both the numerator and denominator are divisible by 2 so
3.134 = ^{3134}/_{1000} = ^{1567}/_{500}
For 18 + 12/9 I would first simplify ^{12}/_{9} since both the numerator and denominator are divisible by 3. Thus
^{12}/_{9} = ^{4}/_{3}
Hence
18 +  ^{12}/_{9} = 18 +  ^{4}/_{3}
But 18 = ^{54}/_{3} and hence
18 +  ^{12}/_{9} = 18 +  ^{4}/_{3} = ^{54}/_{3} +  ^{4}/_{3} = ^{54}/_{3}  ^{4}/_{3} = ^{50}/_{3}
Penny
