Add: \( \frac{\mathrm{11} }{\mathrm{14}} + \frac{\mathrm{2} }{\mathrm{7}}+ \frac{\mathrm{13} }{\mathrm{28}} \)

Step 1: Find the Least Common Denominator (LCD). There are two ways we can do this:
Method 1: Find the first common multiple. List out all multiples of each denominator and find the first common one.
Multiples of 14 : 14, 28, …
Multiples of 7 : 7, 14, 21, 28, …
Multiples of 28 : 28, …
Therefore, the LCD is 28.
Method 2: Prime Factors. List all prime factors of each denominator and find the union of these primes.
Prime factors of 14 : 2, 7
Prime factors of 7 : 7
Prime factors of 28 : 2, 2, 7
LCD = 28
Step 2: Make the denominators the same as the LCD.
\(\frac{\mathrm{11 \times 2} }{\mathrm{14 \times 2}} + \frac{\mathrm{2 \times 4} }{\mathrm{7 \times 4}} + \frac{\mathrm{13} }{\mathrm{28}} \)
Step 3: Simplify. The denominators are now the same.
\(\frac{\mathrm{22} }{\mathrm{28}} + \frac{\mathrm{8} }{\mathrm{28}} + \frac{\mathrm{13} }{\mathrm{28}}\)
Step 4: Join the denominators.
\(\frac{\mathrm{22+8+13} }{\mathrm{28}}\)
Step 5: Simplify.
\( \frac{\mathrm{43} }{\mathrm{28}}\)
Step 6: Convert to a mixed number.
\(1\frac{\mathrm{15} }{\mathrm{28}}\)
To convert to a mixed fraction, we divide the numerator by the denominator. The quotient is the whole number. Any remainder stays in the numerator.