randRange( 2, 3 ) randRange( 1, 14 ) randRange( 1, 14 ) randRange( NUM_1 + 1, 15 ) randRange( NUM_2 + 1, 15 ) getLCM( DEN_1, DEN_2 ) LCM / DEN_1 F1 === 1 ? "remains as" : "becomes" LCM / DEN_2 F2 === 1 ? "remains as" : "becomes" (function() { var f1 = NUM_1 / DEN_1; var f2 = NUM_2 / DEN_2; if ( f1 < f2 ) { return "<"; } else if ( f1 > f2 ) { return ">"; } else { return "="; } })()

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 BECOMES_1 \dfrac{NUM_1 * F1}{LCM}.

The second fraction BECOMES_2 \dfrac{NUM_2 * F2}{LCM}.

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

randRange( 1, 4 ) NUM_1 * FACTOR randRange( NUM_1 + 1, 5 ) DEN_1 * FACTOR
[ NUM_2, NUM_1 ] [ DEN_2, DEN_1 ] [ F2, F1 ] [ BECOMES_2, BECOMES_1 ]