# Adding and Subtracting Mixed Fractions:

#### Overview:

 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: $$5 \frac{1}{2} + 4 \frac{2}{3} + 6 \frac{1}{6} - 2 \frac{1}{6}$$ $$(5 + 4 + 6 -2) + \left(\frac{1}{2} + \frac{2}{3} + \frac{1}{6} - \frac{1}{6}\right)$$ $$= 13 + \left(\frac{3 + 4 + 1 - 1}{6}\right)$$ $$= 13 + \frac{7}{6}$$ $$= \frac{85}{6} = 14 \frac{1}{6}$$