To add or subtract rational mixed numbers, follow these steps:

1. Convert the mixed numbers to improper fractions.
2. Find a common denominator for the fractions.
3. Add or subtract the fractions.
4. If necessary, simplify the resulting fraction or convert it back to a mixed number.

Let’s go through an example:

Example 1: Add 2 1/4 and 3 3/8.

Step 1: Convert the mixed numbers to improper fractions. 2 1/4 = (2 * 4 + 1) / 4 = 9/4 3 3/8 = (3 * 8 + 3) / 8 = 27/8

Step 2: Find a common denominator for the fractions. The denominators are already different, so we can use the product of the denominators, which is 4 * 8 = 32.

Step 3: Add the fractions. 9/4 + 27/8 = (9 * 8 + 27 * 4) / 32 = 72/32 + 108/32 = 180/32

Step 4: Simplify the resulting fraction. 180/32 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 4. 180/32 = (180 ÷ 4) / (32 ÷ 4) = 45/8

Step 5: Convert the improper fraction back to a mixed number (if desired). 45/8 = 5 5/8

Therefore, 2 1/4 + 3 3/8 = 5 5/8.

Example 2: Subtract 4 3/5 from 7 2/3.

Step 1: Convert the mixed numbers to improper fractions. 4 3/5 = (4 * 5 + 3) / 5 = 23/5 7 2/3 = (7 * 3 + 2) / 3 = 23/3

Step 2: Find a common denominator for the fractions. The denominators are already different, so we can use the product of the denominators, which is 5 * 3 = 15.

Step 3: Subtract the fractions. 23/3 - 23/5 = (23 * 5 - 23 * 3) / 15 = 115/15 - 69/15 = 46/15

Step 4: Simplify the resulting fraction. 46/15 cannot be simplified any further.

Step 5: Convert the improper fraction back to a mixed number (if desired). 46/15 = 3 1/15

Therefore, 7 2/3 - 4 3/5 = 3 1/15.