Question

Solve: $8\frac{1}{2}-3\frac{5}{8}$

Answer 1

Step 1: Convert the mixed fraction into an improper fraction.

The given expression is $8\frac{1}{2}-3\frac{5}{8}$

Both the given fraction are mixed fractions. Therefore, we need to first convert them into improper fractions.

$$\begin{gathered} \Rightarrow 8\frac{1}{2}=\frac{\left(8\times 2\right)+1}{2}=\frac{17}{2} \\ \Rightarrow 3\frac{5}{8}=\frac{(8\times 3)+5}{8}=\frac{29}{8} \end{gathered}$$

Step 2: Solving the expression

$8\frac{1}{2}-3\frac{5}{8}$

$=$$\frac{17}{2}-\frac{29}{8}$

Since the denominators are different. These fractions are unlike fractions.

Now take the L.C.M of the denominator.

$$\begin{gathered} =\frac{17\times 4}{2\times 4}-\frac{29\times 1}{8\times 1} \\ =\frac{68-29}{8} \\ =\frac{39}{8} \end{gathered}$$

Step 3: Converting the improper fraction into a mixed fraction

$$\begin{gathered} =\frac{39}{8} \\ =8\overline{)39(}4 \\ \underline{-32} \\ \underline{7} \\ \therefore \frac{39}{8}=4\frac{7}{8} \end{gathered}$$

Therefore, $8\frac{1}{2}-3\frac{5}{8}$$=$$4\frac{7}{8}$.