## Elementary Algebra

$\frac{2}{3}$ - $\frac{3}{4}$ + $\frac{1}{6}$ $\gt$ $\frac{1}{5}$ + $\frac{3}{4}$ - $\frac{7}{10}$ Firstly, we need to find the least common multiple (LCM) of 3, 4, 5, 6, and 10 through each number's prime factors. $3 = 3$ $4 = 2^{2}$ $5 = 5$ $6 = 2 \times 3$ $10 = 2 \times 5$ $LCM = 2^{2} \times 3 \times 5 = 60$ Now that we know the LCM, we can multiply the fractions by 1 such that all the denominators will be equal to 60 but the value of the each fraction does not change. $(\frac{2}{3}$ $\times$ $\frac{20}{20}$) - ($\frac{3}{4}$ $\times$ $\frac{15}{15}$) + ($\frac{1}{6}$ $\times$ $\frac{10}{10}$) $\gt$ $(\frac{1}{5}$ $\times$ $\frac{12}{12}$) + ($\frac{3}{4}$ $\times$ $\frac{15}{15}$) - ($\frac{7}{10}$ $\times$ $\frac{6}{6}$) $\frac{40}{60}$ - $\frac{45}{60}$ + $\frac{10}{60}$ $\gt$ $\frac{12}{60}$ + $\frac{45}{60}$ - $\frac{42}{60}$ $\frac{5}{60}$ $\gt$ $\frac{15}{60}$ Because the denominators are both 60, we can look the numerators and see that 5 is not bigger than 15, so the inequality is false.