# publicKhan/khan-exercises

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randRange( 1, 9 )        randRange( N1 + 1, 13 )        getGCD( N1, D1 )        N1 / GCD1        D1 / GCD1        randRange( 1, 9 )        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

1                2                getGCD( N1, D1 )                N1 / GCD1                D1 / GCD1                1                4                getGCD( N2, D2 )                N2 / GCD2                D2 / GCD2                getLCM( SIMP_D1, SIMP_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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