Find, correct to two decimal, the mean of 1$\frac{1}{2}$, 2$\frac{2}{3}$, 3$\frac{3}{4}$, 4$\frac{4}{5}$, and 5$\frac{5}{6}$.

Analyze the question: We need the mean of five mixed numbers, given to 2 decimal places.

Concept: Mean = (sum of values) ÷ (number of values).

Solution:

Separate the whole numbers and the fractions.

Whole numbers: 1 + 2 + 3 + 4 + 5 = 15

Fractions: 1/2 + 2/3 + 3/4 + 4/5 + 5/6

The LCM of 2, 3, 4, 5, 6 is 60:

• 1/2 = 30/60
• 2/3 = 40/60
• 3/4 = 45/60
• 4/5 = 48/60
• 5/6 = 50/60

Sum of fractions = (30 + 40 + 45 + 48 + 50)/60 = 213/60 = 3.55

Total sum = 15 + 3.55 = 18.55

Mean = 18.55 ÷ 5 = 3.71

Answer: The mean is 3.71, which is option A.

Tip: With mixed numbers, add the whole parts and the fractional parts separately. This keeps the working simple and reduces errors. Always divide by the number of items, which is 5 here.