Solve Mixed Number Addition: 2¼ Plus Negative Fraction -12/24

$(+2\frac{1}{4})+(-\frac{12}{24})=$

To solve this problem, we'll follow these steps:

• Step 1: Convert the mixed number to an improper fraction.
• Step 2: Simplify the negative fraction, if necessary.
• Step 3: Find the least common denominator (LCD) to add both fractions.
• Step 4: Perform the addition of the two fractions.
• Step 5: Simplify the result or convert back to a mixed number.

Now, let's work through each step:

Step 1: The mixed number $2\frac{1}{4}$ is converted to the improper fraction $\frac{9}{4}$ because $2 \times 4 + 1 = 9$.

Step 2: The fraction $-\frac{12}{24}$ simplifies to $-\frac{1}{2}$ because $\frac{12}{24} = \frac{1}{2}$.

Step 3: The least common denominator for $\frac{9}{4}$ and $-\frac{1}{2}$ is 4. We rewrite $-\frac{1}{2}$ with this denominator: $-\frac{1}{2} \equiv -\frac{2}{4}$.

Step 4: Add the fractions: $\frac{9}{4} + \left(-\frac{2}{4}\right) = \frac{9 - 2}{4} = \frac{7}{4}$.

Step 5: Convert $\frac{7}{4}$ back to a mixed number: $1\frac{3}{4}$.

Therefore, the solution to the problem is $1\frac{3}{4}$.