Solve the Mixed Number Equation: ? - 2¼ = 5½

We need to find the missing number in the equation $? - 2\frac{1}{4} = 5\frac{2}{4}$. This requires us to determine what number, when subtracted by $2\frac{1}{4}$, results in $5\frac{2}{4}$.

Step 1: Convert the mixed numbers into improper fractions.

• The denominator for both mixed numbers is 4.
• Convert $2\frac{1}{4}$ to an improper fraction:
  $2\frac{1}{4} = \frac{2 \times 4 + 1}{4} = \frac{9}{4}$.
• Convert $5\frac{2}{4}$ to an improper fraction:
  $5\frac{2}{4} = \frac{5 \times 4 + 2}{4} = \frac{22}{4}$.

Step 2: Solve for the unknown mixed number.

From the equation $? - \frac{9}{4} = \frac{22}{4}$, we rearrange to find $?$:
$? = \frac{22}{4} + \frac{9}{4}$.

Step 3: Add the improper fractions.

• Since they have a common denominator, add directly:
  $\frac{22}{4} + \frac{9}{4} = \frac{31}{4}$.

Step 4: Convert the result back to a mixed number.

• $\frac{31}{4}$ is converted to a mixed number:
  Divide 31 by 4: 31 ÷ 4 = 7 with a remainder of 3.
  So, $\frac{31}{4} = 7\frac{3}{4}$.

Therefore, the solution to the problem is $7\frac{3}{4}$.