Solving the Fraction Equation

The problem asks us to find the value represented by the question mark (?) in the given equation:

$? + \frac{18}{24} + 3\frac{3}{4} = 23\frac{13}{24}$

To solve for ?, we first need to simplify the equation by working with a common denominator.

Step 1: Convert Mixed Numbers and Fractions

Convert the mixed number $3\frac{3}{4}$ into an improper fraction:

$3\frac{3}{4} = \frac{(3 \times 4) + 3}{4} = \frac{12 + 3}{4} = \frac{15}{4}$

The equation now is:

$? + \frac{18}{24} + \frac{15}{4} = 23\frac{13}{24}$

Convert the mixed number $23\frac{13}{24}$ into an improper fraction:

$23\frac{13}{24} = \frac{(23 \times 24) + 13}{24} = \frac{552 + 13}{24} = \frac{565}{24}$

The equation becomes:

$? + \frac{18}{24} + \frac{15}{4} = \frac{565}{24}$

Step 2: Find a Common Denominator

The denominators are 24, 24, and 4. The least common denominator is 24.

Convert $\frac{15}{4}$ to an equivalent fraction with a denominator of 24:

$\frac{15}{4} = \frac{15 \times 6}{4 \times 6} = \frac{90}{24}$

Substitute this back into the equation:

$? + \frac{18}{24} + \frac{90}{24} = \frac{565}{24}$

Step 3: Combine Known Fractions

Add the known fractions on the left side:

$\frac{18}{24} + \frac{90}{24} = \frac{18 + 90}{24} = \frac{108}{24}$

The equation is now:

$? + \frac{108}{24} = \frac{565}{24}$

Step 4: Isolate the Unknown (?)

To find ?, subtract $\frac{108}{24}$ from both sides of the equation:

$? = \frac{565}{24} - \frac{108}{24}$

Perform the subtraction:

$? = \frac{565 - 108}{24} = \frac{457}{24}$

Step 5: Convert to Mixed Number

Convert the improper fraction $\frac{457}{24}$ back to a mixed number:

Divide 457 by 24:

$457 \div 24 = 19 \text{ with a remainder of } 1$

So, $\frac{457}{24} = 19\frac{1}{24}$.

Therefore, the number that replaces the question mark (?) is $19\frac{1}{24}$.