| Topic Included: | Formulas, Definitions & Exmaples. |
| Main Topic: | Quantitative Aptitude. |
| Quantitative Aptitude Sub-topic: | Simplification Aptitude Notes & Questions. |
| Questions for practice: | 10 Questions & Answers with Solutions. |
In the mixed fraction, there is a whole number and a fraction number, and for adding and subtracting the mixed fractions, add and subtract the whole numbers and fraction numbers separately and add them together. Let's understans through examples.
Example(1): \(4 \frac{5}{9} + 3 \frac{5}{6} = \ ?\)
Solution: $$ 4 \frac{5}{9} + 3 \frac{5}{6} $$ $$ = (4 + 3) + \left(\frac{5}{9} + \frac{5}{6}\right) $$ $$ = 7 + \left(\frac{10 + 15}{18}\right) $$ $$ = 7 + \frac{25}{18} $$ $$ = \frac{151}{18} = 8 \frac{7}{18} $$
Example(2): \(3 \frac{4}{5} - 2 \frac{4}{7} = \ ?\)
Solution: $$ 3 \frac{4}{5} - 2 \frac{4}{7} $$ $$ = (3 - 2) + \left(\frac{4}{5} + \frac{4}{7}\right) $$ $$ = 1 + \left(\frac{28 - 20}{35}\right) $$ $$ = 1 + \frac{8}{35} $$ $$ = \frac{43}{35} = 1 \frac{8}{35} $$
Example(3): \(6 \frac{2}{3} + 4 \frac{3}{5} - 2 \frac{4}{5} = \ ?\)
Solution: $$ 6 \frac{2}{3} + 4 \frac{3}{5} - 2 \frac{4}{5} $$ $$ = (6 + 4 - 2) + \left(\frac{2}{3} + \frac{3}{5} - \frac{4}{5}\right) $$ $$ = 8 + \left(\frac{10 + 9 - 12}{15}\right) $$ $$ = 8 + \frac{7}{15} $$ $$ = \frac{127}{15} = 8 \frac{7}{15} $$
Example(4): \(4 \frac{3}{2} - 3 \frac{4}{5} - 1 \frac{2}{3} = \ ?\)
Solution: $$ 4 \frac{3}{2} - 3 \frac{4}{5} - 1 \frac{2}{3} $$ $$ = (4 - 3 - 1) + \left(\frac{3}{2} - \frac{4}{5} - \frac{2}{3}\right) $$ $$ = 0 + \left(\frac{45 - 24 - 20}{30}\right) $$ $$ = \frac{1}{30} $$
Example(5): \(3 \frac{3}{4} - 2 \frac{3}{5} - 4 \frac{2}{10} + 6 \frac{6}{5} = \ ?\)
Solution: $$ 3 \frac{3}{4} - 2 \frac{3}{5} - 4 \frac{2}{10} + 6 \frac{6}{5} $$ $$ (3 - 2 - 4 + 6) + \left(\frac{3}{4} - \frac{3}{5} - \frac{2}{10} + \frac{6}{5}\right) $$ $$ = 3 + \left(\frac{15 - 12 - 4 + 24}{20}\right) $$ $$ = 3 + \frac{23}{20} $$ $$ = \frac{83}{20} = 4 \frac{3}{20} $$
Example(6): \(5 \frac{1}{2} + 4 \frac{2}{3} + 6 \frac{1}{6} - 2 \frac{1}{6} = \ ?\)
Solution: $$ 5 \frac{1}{2} + 4 \frac{2}{3} + 6 \frac{1}{6} - 2 \frac{1}{6} $$ $$ (5 + 4 + 6 -2) + \left(\frac{1}{2} + \frac{2}{3} + \frac{1}{6} - \frac{1}{6}\right) $$ $$ = 13 + \left(\frac{3 + 4 + 1 - 1}{6}\right) $$ $$ = 13 + \frac{7}{6} $$ $$ = \frac{85}{6} = 14 \frac{1}{6} $$