Nasir travelled \(3\tfrac{1}{2}\) km in a bus and then walked \(1\tfrac{1}{8}\) km to reach a town. How much did he travel to reach the town?
\(4\tfrac{5}{8}\,\text{km}\)
Idea: Total distance = distance by bus + distance walked.
Step 1: Convert mixed numbers to improper fractions.
\(3\tfrac{1}{2} = \dfrac{(3\times 2)+1}{2} = \dfrac{7}{2}\,\text{km}\)
\(1\tfrac{1}{8} = \dfrac{(1\times 8)+1}{8} = \dfrac{9}{8}\,\text{km}\)
Step 2: Make the denominators the same. (LCM of 2 and 8 is 8)
\(\dfrac{7}{2} = \dfrac{7\times 4}{2\times 4} = \dfrac{28}{8}\,\text{km}\)
Step 3: Add the fractions.
\(\dfrac{28}{8} + \dfrac{9}{8} = \dfrac{37}{8}\,\text{km}\)
Step 4: Convert \(\dfrac{37}{8}\) to a mixed number.
\(37 \div 8 = 4\) remainder \(5\) \(\Rightarrow\) \(\dfrac{37}{8} = 4\tfrac{5}{8}\)
Answer: Nasir travelled \(4\tfrac{5}{8}\,\text{km}\) in total.
(Quick check with decimals: \(3.5 + 1.125 = 4.625 = 4\tfrac{5}{8}\) km.)