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

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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}.