1. The problem involves understanding and working with mixed numbers and fractions: $1 \frac{7}{8}$, $\frac{3}{4}$, $\frac{3}{8}$, and $1 \frac{7}{8}$.\n\n2. First, convert the mixed numbers to improper fractions for easier calculation. For $1 \frac{7}{8}$, multiply the whole number 1 by the denominator 8 and add the numerator 7: $$1 \times 8 + 7 = 8 + 7 = 15.$$ So, $1 \frac{7}{8} = \frac{15}{8}$.\n\n3. Now, the fractions are $\frac{15}{8}$, $\frac{3}{4}$, $\frac{3}{8}$, and $\frac{15}{8}$.\n\n4. To compare or perform operations, find a common denominator. The denominators are 8 and 4. The least common denominator (LCD) is 8.\n\n5. Convert $\frac{3}{4}$ to eighths: multiply numerator and denominator by 2 to get $\frac{6}{8}$.\n\n6. Now all fractions are $\frac{15}{8}$, $\frac{6}{8}$, $\frac{3}{8}$, and $\frac{15}{8}$.\n\n7. You can now add, subtract, or compare these fractions easily since they share the same denominator. For example, adding $\frac{15}{8} + \frac{6}{8} = \frac{21}{8} = 2 \frac{5}{8}$.\n\nThis process helps in simplifying and working with mixed numbers and fractions by converting to improper fractions and finding a common denominator.