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 (function() { var f1 = NUM_1 / DEN_1; var f2 = NUM_2 / DEN_2; if (f1 === f2) { return "="; } else { return f1 < f2 ? "<" : ">"; } })()

Fill in the blank.

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

`SOLUTION`

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

It is easier to compare these two fractions when they have the same denominator.

Their smallest common denominator is the LCM of `DEN_1` and `DEN_2`.

`\lcm(DEN_1, DEN_2) = LCM`

The first fraction remains `\dfrac{NUM_1}{LCM}`.

The first fraction becomes `\dfrac{NUM_1 * F1}{LCM}`.

The second fraction remains `\dfrac{NUM_2}{LCM}`.

The second fraction becomes `\dfrac{NUM_2 * F2}{LCM}`.

We see that `\dfrac{NUM_1 * F1}{LCM} SOLUTION \dfrac{NUM_2 * F2}{LCM}`.