Final answer:
To add 2 1/4 and (-1 2/5), we first convert to improper fractions, find a common denominator, and then add. This results in 17/20.
Step-by-step explanation:
The student asked how to add the numbers 2 1/4 and (-1 2/5). To solve this, first, we convert the mixed numbers into improper fractions. For 2 1/4, we multiply the whole number 2 by the denominator 4, add the numerator 1, and place the result over the denominator to get 9/4. For -1 2/5, we again multiply the whole number 1 by the denominator 5, add the numerator 2, and place the result over the denominator with a negative sign to get -7/5.
Next, we find a common denominator for the two fractions. The smallest one that 4 and 5 share is 20. To convert 9/4 to a denominator of 20, we multiply both the numerator and denominator by 5 to get 45/20. To convert -7/5 to a denominator of 20, we multiply both the numerator and denominator by 4 to get -28/20.
Now we can add the fractions: 45/20 + (-28/20) = (45 - 28)/20 = 17/20. The answer is an improper fraction and does not require conversion back to a mixed number, as the numerator is less than the denominator. Therefore, the answer to 2 1/4 + (-1 2/5) is 17/20.