Basic College Mathematics (10th Edition)

(a) $\displaystyle 8\frac{3}{8}$ (b) $\displaystyle 3\frac{21}{40}$
We add or subtract the fractions using both methods: (a) Method 1: $\displaystyle 4\frac{5}{8}+3\frac{3}{4}$ $=\displaystyle 4\frac{5}{8}+3\frac{6}{8}$ $=\displaystyle 7\frac{11}{8}$ $=\displaystyle 8\frac{3}{8}$ Method 2: $\displaystyle 4\frac{5}{8}+3\frac{3}{4}$ $\displaystyle =\frac{37}{8}+\frac{15}{4}$ $\displaystyle =\frac{37}{8}+\frac{30}{8}$ $\displaystyle =\frac{67}{8}$ $\displaystyle =8\frac{3}{8}$ We confirm that we obtained the same answer with both methods. (b) Method 1: $\displaystyle 12\frac{2}{5}-8\frac{7}{8}$ $=\displaystyle 12\frac{16}{40}-8\frac{35}{40}$ $=\displaystyle 11\frac{56}{40}-8\frac{35}{40}$ $=\displaystyle 3\frac{21}{40}$ Method 2: $\displaystyle 12\frac{2}{5}-8\frac{7}{8}$ $=\displaystyle \frac{62}{5}-\frac{71}{8}$ $=\displaystyle \frac{496}{40}-\frac{355}{40}$ $=\displaystyle \frac{141}{40}$ $=\displaystyle 3\frac{21}{40}$ We confirm that we obtained the same answer with both methods. Both methods have their advantages and disadvantages. In this case, it seems that working with whole numbers is a bit simpler because the numbers are smaller.