Adding and/or Subtracting Fractions with Different Denominators - # 2

[Jason]

What's the answer?

\(\dfrac{10}{30} + \dfrac{5}{19}\)

\(30 \longrightarrow 6 * 5 \longrightarrow (3 * 2) * 5 \longrightarrow 3^{1} * 2^{1} * 5^{1}\)

\(19 \longrightarrow 19^{1} \longrightarrow 19^{1} \)

The highest pairs of prime power/powers are:

none

The highest solo prime power/powers are:

\(3^{1}, 2^{1}, 19^{1}\)

\(LCM = 3^{1} * 2^{1} * 19^{1} = 570\)

\(A: 30(x) = 570 \longrightarrow x = 19 \)

\(B: 19(x) = 570 \longrightarrow x = 30\)


\(\dfrac{10}{30} + \dfrac{5}{19} \longrightarrow \dfrac{10}{30} * \dfrac{19}{19} + \dfrac{5}{19} * \dfrac{30}{30} = \)
\(\dfrac{190}{570} + \dfrac{150}{570} = \dfrac{340}{570}\)

Can this be reduced?

\(340 \longrightarrow 34 * 10 \longrightarrow (17 * 2) * (5 * 2) \longrightarrow 17^{1} * 2^{1} * 5^{1} * 2^{1} \longrightarrow 17^{1} * 5^{1} * 2^{2} \)

\(570 \longrightarrow 57 * 10 \longrightarrow (19 * 3) * (5 * 2) \longrightarrow 19^{1} * 3^{1} * 5^{1} * 2^{1} \)

The lowest prime powers, common to all numbers, are:

\(2^{1}, 5^{1}\)

\(GCF = 2^{1} * 5^{1} = 10^{1} = 10\)

\(\dfrac{340 \div 10}{570 \div 10} = \dfrac{34}{57}\)