Express your answer as a mixed number simplified to lowest terms.
expr(["+", W1 + fraction( N1, D1 ), W2 + fraction( N2, D2 )]) = {?}
Separate the whole numbers from the fractional parts:
= \color{red}{W1} + \color{red}{fraction( N1, D1 )} SIGN \color{blue}{abs( W2 )} SIGN \color{blue}{fraction( N2, D2 )}
Bring the whole numbers together and the fractions together:
= \color{red}{W1} SIGN \color{blue}{abs( W2 )} + \color{red}{fraction( N1, D1 )} SIGN \color{blue}{fraction( N2, D2 )}
AddSubtract the whole numbers:
=W1 + W2 + \color{red}{fraction( SIMP_N1, SIMP_D1 )} SIGN \color{blue}{fraction( SIMP_N2, SIMP_D2 )}
Simplify each fraction:
= \color{red}{W1} SIGN \color{blue}{abs( W2 )} + \color{red}{fraction( SIMP_N1, SIMP_D1 )} SIGN \color{blue}{fraction( SIMP_N2, SIMP_D2 )}
Find a common denominator for the fractions:
= expr(["+", W1 + W2, fraction( SIMP_N1 * LCM / SIMP_D1, LCM ),fraction( PM * SIMP_N2 * LCM / SIMP_D2, LCM )])
AddSubtract the fractions:
= expr(["+", W1 + W2, fraction( SIMP_N1 * LCM / SIMP_D1 + PM * SIMP_N2 * LCM / SIMP_D2, LCM )])
Combine the whole and fractional parts into a mixed number:
= W1 + W2 + fraction( SIMP_N1 * LCM / SIMP_D1 + PM * SIMP_N2 * LCM / SIMP_D2, LCM )
Simplify to lowest terms:
= W1 + W2 + fractionReduce( SIMP_N1 * LCM / SIMP_D1 + PM * SIMP_N2 * LCM / SIMP_D2, LCM )