Solve the Mixed Number Equation: 5¾ + ? = 7½

To solve for the missing value, we employ the following plan:

• Convert both mixed numbers into improper fractions.
• Perform subtraction of the improper fractions.
• Convert the resulting fraction back into a mixed number, if necessary.

Let's walk through these steps:

Step 1: Convert the mixed numbers.
Convert $5\frac{3}{4}$ into an improper fraction:
$\frac{4 \times 5 + 3}{4} = \frac{20 + 3}{4} = \frac{23}{4}$.
Convert $7\frac{1}{2}$ into an improper fraction:
$\frac{2 \times 7 + 1}{2} = \frac{14 + 1}{2} = \frac{15}{2}$.
Since $\frac{15}{2} = \frac{30}{4}$ (after finding a common denominator), we will use $\frac{30}{4}$ for subtraction.

Step 2: Subtract the improper fractions.
Now, calculate $\frac{30}{4} - \frac{23}{4} = \frac{30 - 23}{4} = \frac{7}{4}$.

Step 3: Convert back to a mixed number.
$\frac{7}{4} = 1\frac{3}{4}$ (since 7 divided by 4 is 1 with a remainder of 3).

After solving, we find that the missing number in the equation is $1\frac{3}{4}$.