randFromArray(smallDenominators) randFromArray(smallDenominators) randRange(1, DEN_1 - 1) randRange(1, DEN_2 - 1) getLCM(DEN_1, DEN_2) LCM / DEN_1 LCM / DEN_2 DEN_1 * F1 DEN_2 * F1 (function() { var f1 = NUM_1 / DEN_1; var f2 = NUM_2 / DEN_2; if (f1 === f2) { return "="; } else { return f1 < f2 ? "<" : ">"; } })()

Compare.

`\dfrac{NUM_1}{DEN_1}` ____ `\dfrac{NUM_2}{DEN_2}`

`SOLUTION`

- `<`
- `>`
- `=`

Let's change the fractions to have a common denominator of `LCM`:

`\qquad\begin{eqnarray} \blue{\dfrac{NUM_1}{DEN_1}} \times \dfrac{F1}{F1} &=& \blue{\dfrac{N1}{LCM}} \\ \\ \green{\dfrac{NUM_2}{DEN_2}} \times \dfrac{F2}{F2} &=& \green{\dfrac{N2}{LCM}} \end{eqnarray}`

Now that our fractions have the same denominator, we compare their numerators:

`\qquad \blue{N1} SOLUTION \green{N2}`

`\qquad \blue{\dfrac{N1}{LCM}} SOLUTION \green{\dfrac{N2}{LCM}}`

`\qquad \blue{\dfrac{NUM_1}{DEN_1}} SOLUTION \green{\dfrac{NUM_2}{DEN_2}}`