Put the next fractions in an increasingly order: 1/2, 3/4, 2/3, 5/6

To solve the problem, we will have to find the maximum common denominator (mcd). We decompose the denominator of every fraction obtaining, 2=2; 3=3; 4=2²; 6=2x3. Now, we take the common factors with the bigger exponent as every factor that is different. Multiplying them we obtain: mcd=2²x3=12, that is the common denominator.

We change each fraction multipliying and dividing by the mcd, as: 1/2=(12x1) / (12x2)=6/12; 2/4=(12x3) / (12x4)=9/12; 2/3=(12x2) / (12x3)=8/12; 5/6=(12x5) / (12x6)=10/12.

Having every fraction with the same denominator, we just have to compare the numerador and place them from the smallest to the biggest: 6/12 ; 8/12 ; 9/12 ; 10/12.

And, finally, reversing the change: 1/2 ; 2/3 ; 3/4 ; 5/6.