# Khan/khan-exercises

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 Subtracting fractions
randRange( 5, 12 ) randRange( N1 + 1, 13 ) getGCD( N1, D1 ) N1 / GCD1 D1 / GCD1 randRange( 1, N1 - 1 ) randRange( N2 + 1, 13 ) getGCD( N2, D2 ) N2 / GCD2 D2 / GCD2 getLCM( SIMP_D1, SIMP_D2 )

fraction( N1, D1 ) - fraction( N2, D2 ) = {?}

N1 / D1 - N2 / D2

Simplify each fraction.

fraction( SIMP_N1, SIMP_D1 ) - fraction( SIMP_N2, SIMP_D2 )

Find a common denominator by finding the least common multiple of SIMP_D1 and SIMP_D2.

\lcm(SIMP_D1, SIMP_D2) = LCM

Change each fraction to an equivalent fraction with a denominator of LCM.

fraction( SIMP_N1, SIMP_D1 ) - fraction( SIMP_N2, SIMP_D2 )

=fraction( SIMP_N1, SIMP_D1 ) \cdot fraction( LCM / SIMP_D1, LCM / SIMP_D1 ) - fraction( SIMP_N2, SIMP_D2 ) \cdot fraction( LCM / SIMP_D2, LCM / SIMP_D2 )

=fraction( SIMP_N1 * LCM / SIMP_D1, LCM ) - fraction( SIMP_N2 * LCM / SIMP_D2, LCM )

=fraction( SIMP_N1 * LCM / SIMP_D1 - SIMP_N2 * LCM / SIMP_D2, LCM )

Simplify.

=fractionReduce( SIMP_N1 * LCM / SIMP_D1 - SIMP_N2 * LCM / SIMP_D2, LCM )

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