Answer
(a)
$\displaystyle 8\frac{3}{8}$
(b)
$\displaystyle 3\frac{21}{40}$
Work Step by Step
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.
