Nazima gave \(2\dfrac{3}{4}\) litres out of the \(5\dfrac{1}{2}\) litres of juice she purchased to her friends. How many litres are left with her?
\(2\dfrac{3}{4}\,\text{litres}\)
Goal: Find how much juice is left.
She bought \(5\dfrac{1}{2}\) L and gave \(2\dfrac{3}{4}\) L.
Step 1: Convert mixed numbers to improper fractions.
\(5\dfrac{1}{2} = \dfrac{(5\times 2)+1}{2} = \dfrac{11}{2}\)
\(2\dfrac{3}{4} = \dfrac{(2\times 4)+3}{4} = \dfrac{11}{4}\)
Step 2: Make the denominators the same.
\(\dfrac{11}{2} = \dfrac{22}{4}\) (multiply top and bottom by 2)
Step 3: Subtract the fractions.
\(\dfrac{22}{4} - \dfrac{11}{4} = \dfrac{11}{4}\)
Step 4: Convert back to a mixed number.
\(\dfrac{11}{4} = 2\dfrac{3}{4}\)
Therefore, juice left = \(2\dfrac{3}{4}\,\text{litres}\).
Quick check (optional):
\(5\dfrac{1}{2} = 5.5\), \(2\dfrac{3}{4} = 2.75\)
\(5.5 - 2.75 = 2.75 = 2\dfrac{3}{4}\,\text{L}\)