Rewrite the fractions with the common denominator \(\displaystyle LCM(3,5) = 15\), and add numerators:

\(\displaystyle \frac{3}{5} + \frac{1}{3} = \frac{3\times 3}{5\times 3} + \frac{1\times 5}{3\times 5} =\frac{9}{15} + \frac{ 5}{15} = \frac{ 14}{15}\)

The least common denominator of the three fractions is \(\displaystyle LCM (2,4,5) = 20\), so write each fraction in terms of this denominator:

\(\displaystyle \frac{1}{2} - \frac{1}{5} + \frac{1}{4} = \frac{10}{20} - \frac{4} {20} + \frac{5}{20}\)

By order of operations, subtract, then add:

\(\displaystyle \frac{10}{20} - \frac{4} {20} + \frac{5}{20} = \frac{10-4}{20} + \frac{5}{20} = \frac{6}{20} + \frac{5}{20} = \frac{11}{20}\),

which is the correct result.

Rewrite each fraction with the least common denominator, which is \(\displaystyle LCM (2,5) = 10\):

\(\displaystyle 6 \frac{3}{5} + 7 \frac{1}{2} + 4 \frac{3}{5} = 6 \frac{6}{10} + 7 \frac{5}{10} + 4 \frac{6}{10}\)

We can add vertically, adding the fractions and the whole numbers:

   \(\displaystyle 6 \frac{6}{10}\)

\(\displaystyle + 7 \frac{5}{10}\)

\(\displaystyle +\underline{ 4 \frac{6}{10}}\)

 \(\displaystyle 17 \frac{17}{10} = 17 + 1 \frac{7}{10} = 18 \frac{7}{10}\)

Rewrite using the least common denominator, which is \(\displaystyle LCM (5,10,20) = 20\); then add numerators:

\(\displaystyle \frac{2}{5} + \frac{7}{10} + \frac{17}{20}\)

\(\displaystyle = \frac{2\times 4}{5\times 4} + \frac{7\times 2}{10\times 2} + \frac{17}{20}\)

\(\displaystyle = \frac{8}{20} + \frac{14}{20} + \frac{17}{20}\)

\(\displaystyle = \frac{8+14+17}{20} = \frac{39}{20} = 1 \frac{19}{20}\)

Rewrite each as an improper fraction, then as a fraction in terms of the least common denominator, which is \(\displaystyle LCM (2,3) = 6\):

\(\displaystyle 5 \frac{1}{2} =\frac{11}{2} = \frac{33}{6}\)

\(\displaystyle 4 \frac{1}{3} = \frac{13}{3} = \frac{26}{6}\)

\(\displaystyle 3 \frac{2}{3} = \frac{11}{3}= \frac{22}{6}\)

Rewrite the expression, evaluate it, and rewrite the result as a mixed number:

\(\displaystyle 5 \frac{1}{2}- 4 \frac{1}{3} +3 \frac{2}{3}= \frac{33}{6} - \frac{26}{6} + \frac{22}{6} = \frac{33- 26+22}{6} = \frac{7+22}{6} = \frac{29}{6} = 4 \frac{5}{6}\)

Since the denominators of the two fractions are the same, we can simply add the numerators:

\(\displaystyle \frac{2}{10}+\frac{5}{10}=\frac{7}{10}\)

Since the denominators of the two fractions are the same, we can simply add the numerators:

\(\displaystyle \frac{6}{20}+\frac{7}{20}=\frac{13}{20}\)

Since the denominators of the two fractions are the same, we can simply add the numerators:

\(\displaystyle \frac{6}{50}+\frac{11}{50}=\frac{17}{50}\)

Find the least common denominator between \(\displaystyle 9\) and \(\displaystyle 4\). In this case, it is \(\displaystyle 36\).

\(\displaystyle \frac{2}{9}=\frac{8}{36}\)

\(\displaystyle \frac{3}{4}=\frac{27}{36}\)

\(\displaystyle \frac{8}{36}+\frac{27}{36}=\frac{35}{36}\)

Add the numerators and keep the denominator:

\(\displaystyle \frac{5}{20}+\frac{4}{20}=\frac{9}{20}\)

Answer: \(\displaystyle \frac{9}{20}\)