Sunil purchased \(12\dfrac{1}{2}\) litres of juice on Monday and \(14\dfrac{3}{4}\) litres on Tuesday. How many litres did he purchase together in two days?
\(27\dfrac{1}{4}\,\text{litres}\)
Goal: Add the amounts bought on Monday and Tuesday.
Step 1: Convert mixed numbers to improper fractions.
\(12\dfrac{1}{2} = 12 + \tfrac{1}{2} = \tfrac{24}{2} + \tfrac{1}{2} = \tfrac{25}{2}\)
\(14\dfrac{3}{4} = 14 + \tfrac{3}{4} = \tfrac{56}{4} + \tfrac{3}{4} = \tfrac{59}{4}\)
Step 2: Make denominators the same.
LCM of 2 and 4 is 4, so \(\tfrac{25}{2} = \tfrac{50}{4}\).
Step 3: Add the fractions.
\(\tfrac{50}{4} + \tfrac{59}{4} = \tfrac{109}{4}\,\text{litres}\)
Step 4: Convert the improper fraction to a mixed number.
\(\tfrac{109}{4} = 27\text{ remainder }1 = 27\dfrac{1}{4}\,\text{litres}\)
Quick decimal check (optional):
\(12.5 + 14.75 = 27.25 = 27\dfrac{1}{4}\,\text{litres}\)