1. Let's state the problem clearly: You want to understand how to work with a first number that is a fraction and a second number that is a whole number. 2. Suppose the first number is a fraction $\frac{a}{b}$ and the second number is a whole number $c$. 3. If the operation is addition, then: $$\frac{a}{b} + c = \frac{a}{b} + \frac{cb}{b} = \frac{a + cb}{b}$$ We convert the whole number to a fraction with the same denominator to add. 4. For subtraction: $$\frac{a}{b} - c = \frac{a}{b} - \frac{cb}{b} = \frac{a - cb}{b}$$ 5. For multiplication: $$\frac{a}{b} \times c = \frac{a}{b} \times \frac{c}{1} = \frac{ac}{b}$$ 6. For division: $$\frac{a}{b} \div c = \frac{a}{b} \times \frac{1}{c} = \frac{a}{bc}$$ Each case turns the whole number into a fraction ($\frac{c}{1}$) for consistent operation with the fraction. This method works for any fraction combined with any whole number.