Adding and/or Subtracting Fractions with Different Denominators - # 3

[Jason]

What is the answer to the following problem?

\(\dfrac{1}{2} - \dfrac{2}{3} - \dfrac{3}{5}\)

\(2 \longrightarrow 2^{1}\)

\(3 \longrightarrow 3^{1}\)

\(5 \longrightarrow 5^{1}\)

The highest pairs of prime power/powers are:

none

The highest lone prime power/powers are:

\(2^{1}, 3^{1}, 5^{1} \)

\(LCM = 2^{1} * 3^{1} * 5^{1} = 30^{1} = 30\)


\(A: 2(x) = 30 \longrightarrow x = 15\)

\(B: 3(x) = 30 \longrightarrow x = 10\)

\(C: 5(x) = 30 \longrightarrow x = 6\)


\(\dfrac{1}{2} - \dfrac{2}{3} - \dfrac{3}{5} \longrightarrow \)

\(\dfrac{1}{2} * \dfrac{15}{15} - \dfrac{2}{3} * \dfrac{10}{10} - \dfrac{3}{5} * \dfrac{6}{6} \longrightarrow\)

\(\dfrac{15}{30} - \dfrac{20}{30} - \dfrac{18}{30} = -\dfrac{23}{30}\)


\(-23 \longrightarrow |-23| \longrightarrow 23 \longrightarrow 23^{1}\)

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

The lowest prime power/powers common to both numbers are:

none

\(GCF = 1\)

Since GCF = 1, answer cannot be reduced.