Solve: Adding Mixed Numbers 4⅖ + 1³/₁₀ + 2¹/₂₀ + 2³/₅

$4\frac{2}{5}+1\frac{3}{10}+2\frac{1}{20}+2\frac{3}{5}=$

To solve this problem of adding mixed numbers, follow these well-defined steps:

• Step 1: Convert the mixed numbers to improper fractions.
• Step 2: Find the least common denominator (LCD).
• Step 3: Convert each fraction to have the LCD as the denominator.
• Step 4: Sum the fractions, and finally, convert back to a mixed number if necessary.

Let us apply these steps to the given numbers:

Step 1: Convert to improper fractions:
- $4\frac{2}{5} = \frac{22}{5}$
- $1\frac{3}{10} = \frac{13}{10}$
- $2\frac{1}{20} = \frac{41}{20}$
- $2\frac{3}{5} = \frac{13}{5}$

Step 2: Find the least common denominator: The denominators are 5, 10, and 20. The LCD of these is 20.

Step 3: Convert fractions to have this LCD:
- $\frac{22}{5} = \frac{88}{20}$
- $\frac{13}{10} = \frac{26}{20}$
- $\frac{41}{20} \text{ remains } \frac{41}{20}$
- $\frac{13}{5} = \frac{52}{20}$

Step 4: Add the fractions:
$\frac{88}{20} + \frac{26}{20} + \frac{41}{20} + \frac{52}{20} = \frac{207}{20}$

Convert $\frac{207}{20}$ into a mixed number:
$207 \div 20 = 10$ remainder $7$, so we have $10\frac{7}{20}$.

Therefore, the sum of the mixed numbers $4\frac{2}{5} + 1\frac{3}{10} + 2\frac{1}{20} + 2\frac{3}{5}$ is $10\frac{7}{20}$.