Question

Add the following algebraic expression:

\[\frac{3}{2}a - \frac{5}{4}b + \frac{2}{5}c, \frac{2}{3}a - \frac{7}{2}b + \frac{7}{2}c, \frac{5}{3}a + \frac{5}{2}b - \frac{5}{4}c\]

Answer 1

To add, we proceed as follows:

\[\left( \frac{3}{2}a - \frac{5}{4}b + \frac{2}{5}c \right) + \left( \frac{2}{3}a - \frac{7}{2}b + \frac{7}{2}c \right) + \left( \frac{5}{3}a + \frac{5}{2}b - \frac{5}{4}c \right)\]

\[ = \frac{3}{2}a - \frac{5}{4}b + \frac{2}{5}c + \frac{2}{3}a - \frac{7}{2}b + \frac{7}{2}c + \frac{5}{3}a + \frac{5}{2}b - \frac{5}{4}c\]

\[ = \frac{3}{2}a + \frac{2}{3}a + \frac{5}{3}a - \frac{5}{4}b - \frac{7}{2}b + \frac{5}{2}b + \frac{2}{5}c + \frac{7}{2}c - \frac{5}{4}c (\text { Collecting like terms })\]

\[ = \frac{23}{6}a - \frac{9}{4}b + \frac{53}{20}c (\text { Combining like terms })\]