Calculate Sum of Mixed Numbers

First, identify the whole number parts and the fractional parts of the given expression:

Expression: $3\frac{2}{3} + 6\frac{7}{12} + 4\frac{9}{36} + 5 + 7\frac{1}{12}$

• Whole Numbers: 3, 6, 4, 5, 7
• Fractions: $\frac{2}{3}$, $\frac{7}{12}$, $\frac{9}{36}$, $\frac{1}{12}$

Sum Whole Numbers and Fractions Separately

Sum of Whole Numbers:

$3 + 6 + 4 + 5 + 7 = 25$

Sum of Fractions:

Simplify $\frac{9}{36}$ to $\frac{1}{4}$.

Sum = $\frac{2}{3} + \frac{7}{12} + \frac{1}{4} + \frac{1}{12}$

Find the Least Common Multiple (LCM) of the denominators (3, 12, 4), which is 12.

Convert fractions to have a denominator of 12:

• $\frac{2}{3} = \frac{2 \times 4}{3 \times 4} = \frac{8}{12}$
• $\frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \frac{3}{12}$

Add the fractions: $\frac{8}{12} + \frac{7}{12} + \frac{3}{12} + \frac{1}{12} = \frac{8 + 7 + 3 + 1}{12} = \frac{19}{12}$

Combine Sums and Determine Fractional Part

Total Sum = Sum of Whole Numbers + Sum of Fractions

Total Sum = $25 + \frac{19}{12}$

Convert the improper fraction $\frac{19}{12}$ to a mixed number:

$\frac{19}{12} = 1\frac{7}{12}$

Total Sum = $25 + 1\frac{7}{12} = 26\frac{7}{12}$

Find Fraction to Add for Whole Number

The current sum is $26\frac{7}{12}$. To make this sum a whole number, we need to add a fraction that completes the current fractional part ($\frac{7}{12}$) to the next whole number (1).

Fraction needed = $1 - \frac{7}{12}$

Fraction needed = $\frac{12}{12} - \frac{7}{12} = \frac{5}{12}$

The smallest fraction that should be added is $\frac{5}{12}$.