Final answer:
To add the mixed numbers 2 1/5 and 1 3/4, first convert them to improper fractions 11/5 and 7/4, find a common denominator (20), add them to get 79/20, and finally convert this to the mixed number 3 19/20.
Step-by-step explanation:
The question asks to add two mixed numbers, 2 1/5 and 1 3/4, and express the sum as a fraction. To add mixed numbers, first convert them into improper fractions. For 2 1/5, multiply the whole number by the denominator (2 * 5 = 10) and add the numerator (10 + 1 = 11) to get the improper fraction 11/5. For 1 3/4, multiply the whole number by the denominator (1 * 4 = 4) and add the numerator (4 + 3 = 7) to get the improper fraction 7/4.
Next, find a common denominator to add the fractions. The least common denominator (LCD) for 5 and 4 is 20. Convert both fractions to have the LCD as the new denominator. The first fraction becomes (11/5) * (4/4) = 44/20 and the second fraction becomes (7/4) * (5/5) = 35/20. Add the numerators to get the sum as 44/20 + 35/20 = 79/20, which is an improper fraction.