Adding and/or Subtracting Fractions - # 4
Posted: Thu Oct 15, 2026 3:40 am
\(\dfrac{14}{3} + \dfrac{5}{6} - \dfrac{3}{13}\)What is the solution?
\(3 \longrightarrow 3^{1}\)
\(6 \longrightarrow 3 * 2 \longrightarrow 3^{1} * 2^{1}\)
\(13 \longrightarrow 13^{1}\)
\(3^{1}\)The highest pairs of prime powers are:
\(2^{1}, 13^{1}\)The highest solo prime power/powers are:
\(LCM = 3^{1} * 2^{1} * 13^{1} \longrightarrow 3 * 2 * 13 = 78\)
\(A: 3(x) = 78 \longrightarrow x = 26\)
\(B: 6(x) = 78 \longrightarrow x = 13\)
\(C: 13(x) = 78 \longrightarrow x = 6\)
\(\dfrac{14}{3} * \dfrac{26}{26} + \dfrac{5}{6} * \dfrac{13}{13} - \dfrac{3}{13} * \dfrac{6}{6}\)
\(\dfrac{364}{78} + \dfrac{65}{78} - \dfrac{18}{78} = \dfrac{411}{78}\)
\(411 \longrightarrow 137 * 3 \longrightarrow 137^{1} * 3^{1}\)
\(78 \longrightarrow 26 * 3 \longrightarrow (13 * 2) * 3 \longrightarrow 13^{1} * 2^{1} * 3^{1}\)
\(3^{1}\)The lowest prime power common to both numbers is:
\(GCF = 3^{1} = 3^{1}\)
\(\dfrac{411 \div 3}{78 \div 3} = \dfrac{137}{26}\)